TSTP Solution File: ITP249^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP249^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 03:25:46 EDT 2023
% Result : Timeout 299.97s 300.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.52/2.54 % Problem : ITP249^1 : TPTP v8.1.2. Released v8.1.0.
% 2.52/2.55 % Command : do_cvc5 %s %d
% 2.55/2.76 % Computer : n013.cluster.edu
% 2.55/2.76 % Model : x86_64 x86_64
% 2.55/2.76 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.55/2.76 % Memory : 8042.1875MB
% 2.55/2.76 % OS : Linux 3.10.0-693.el7.x86_64
% 2.55/2.76 % CPULimit : 300
% 2.55/2.76 % WCLimit : 300
% 2.55/2.76 % DateTime : Sun Aug 27 15:07:04 EDT 2023
% 2.55/2.76 % CPUTime :
% 5.12/5.31 %----Proving TH0
% 5.12/5.32 %------------------------------------------------------------------------------
% 5.12/5.32 % File : ITP249^1 : TPTP v8.1.2. Released v8.1.0.
% 5.12/5.32 % Domain : Interactive Theorem Proving
% 5.12/5.32 % Problem : Sledgehammer problem VEBT_Bounds 00615_028958
% 5.12/5.32 % Version : [Des22] axioms.
% 5.12/5.32 % English :
% 5.12/5.32
% 5.12/5.32 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.12/5.32 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.12/5.32 % Source : [Des22]
% 5.12/5.32 % Names : 0071_VEBT_Bounds_00615_028958 [Des22]
% 5.12/5.32
% 5.12/5.32 % Status : Theorem
% 5.12/5.32 % Rating : 1.00 v8.1.0
% 5.12/5.32 % Syntax : Number of formulae : 11243 (6005 unt; 999 typ; 0 def)
% 5.12/5.32 % Number of atoms : 27151 (12372 equ; 0 cnn)
% 5.12/5.32 % Maximal formula atoms : 71 ( 2 avg)
% 5.12/5.32 % Number of connectives : 114082 (2654 ~; 480 |;1888 &;99500 @)
% 5.12/5.32 % ( 0 <=>;9560 =>; 0 <=; 0 <~>)
% 5.12/5.32 % Maximal formula depth : 39 ( 6 avg)
% 5.12/5.32 % Number of types : 97 ( 96 usr)
% 5.12/5.32 % Number of type conns : 4097 (4097 >; 0 *; 0 +; 0 <<)
% 5.12/5.32 % Number of symbols : 906 ( 903 usr; 55 con; 0-8 aty)
% 5.12/5.32 % Number of variables : 25443 (2243 ^;22395 !; 805 ?;25443 :)
% 5.12/5.32 % SPC : TH0_THM_EQU_NAR
% 5.12/5.32
% 5.12/5.32 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.12/5.32 % from the van Emde Boas Trees session in the Archive of Formal
% 5.12/5.32 % proofs -
% 5.12/5.32 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.12/5.32 % 2022-02-18 02:28:42.978
% 5.12/5.32 %------------------------------------------------------------------------------
% 5.12/5.32 % Could-be-implicit typings (96)
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 5.12/5.32 produc5542196010084753463at_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 5.12/5.32 produc5491161045314408544at_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 5.12/5.32 produc1193250871479095198on_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 5.12/5.32 produc8306885398267862888on_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.12/5.32 produc6121120109295599847at_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J_J,type,
% 5.12/5.32 produc3368934014287244435at_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.12/5.32 produc4471711990508489141at_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 5.12/5.32 produc7036089656553540234on_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 5.12/5.32 produc2233624965454879586on_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J_J,type,
% 5.12/5.32 set_fi4554929511873752355omplex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.12/5.32 list_P7413028617227757229T_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 5.12/5.32 produc3447558737645232053on_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.12/5.32 produc4953844613479565601on_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 5.12/5.32 produc2963631642982155120at_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.12/5.32 produc7248412053542808358at_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
% 5.12/5.32 set_fi7789364187291644575l_real: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 5.12/5.32 filter6041513312241820739omplex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.12/5.32 list_P7037539587688870467BT_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.12/5.32 list_P4547456442757143711BT_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.12/5.32 list_P5647936690300460905T_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.12/5.32 list_P7524865323317820941T_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 produc8243902056947475879T_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 5.12/5.32 set_Pr5085853215250843933omplex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.12/5.32 produc8923325533196201883nteger: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.12/5.32 list_P3126845725202233233VEBT_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.12/5.32 list_P7495141550334521929T_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 5.12/5.32 filter2146258269922977983l_real: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
% 5.12/5.32 list_P8526636022914148096eger_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.12/5.32 option4927543243414619207at_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.12/5.32 filter1242075044329608583at_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 5.12/5.32 set_Pr6218003697084177305l_real: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_J,type,
% 5.12/5.32 list_P3744719386663036955um_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 5.12/5.32 list_P1726324292696863441at_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.12/5.32 list_P6011104703257516679at_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
% 5.12/5.32 list_P3521021558325789923at_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.12/5.32 list_P5707943133018811711nt_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.12/5.32 produc9072475918466114483BT_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 produc8025551001238799321T_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.12/5.32 set_Pr958786334691620121nt_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.12/5.32 produc4411394909380815293omplex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 5.12/5.32 list_P7333126701944960589_nat_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_J,type,
% 5.12/5.32 list_P5087981734274514673_int_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.12/5.32 list_P3795440434834930179_o_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 5.12/5.32 set_list_VEBT_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.12/5.32 produc334124729049499915VEBT_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.12/5.32 produc6271795597528267376eger_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.12/5.32 produc2422161461964618553l_real: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.12/5.32 product_prod_num_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.12/5.32 product_prod_nat_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 product_prod_nat_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 5.12/5.32 product_prod_nat_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.12/5.32 product_prod_int_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.12/5.32 list_P4002435161011370285od_o_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__List__Olist_It__Complex__Ocomplex_J_J,type,
% 5.12/5.32 set_list_complex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Complex__Ocomplex_J_J,type,
% 5.12/5.32 set_set_complex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 list_VEBT_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 5.12/5.32 set_list_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__List__Olist_It__Int__Oint_J_J,type,
% 5.12/5.32 set_list_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 5.12/5.32 product_prod_nat_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.32 list_set_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.12/5.32 list_Code_integer: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 set_VEBT_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.32 set_set_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 5.12/5.32 set_set_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 5.12/5.32 set_Code_integer: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 5.12/5.32 set_Product_unit: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.12/5.32 list_complex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__List__Olist_I_Eo_J_J,type,
% 5.12/5.32 set_list_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.32 set_complex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Filter__Ofilter_It__Real__Oreal_J,type,
% 5.12/5.32 filter_real: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 5.12/5.32 set_set_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
% 5.12/5.32 option_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Option__Ooption_It__Nat__Onat_J,type,
% 5.12/5.32 option_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
% 5.12/5.32 filter_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 5.12/5.32 set_char: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Real__Oreal_J,type,
% 5.12/5.32 list_real: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.32 set_real: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Num__Onum_J,type,
% 5.12/5.32 list_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 5.12/5.32 list_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
% 5.12/5.32 list_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 vEBT_VEBT: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
% 5.12/5.32 set_rat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
% 5.12/5.32 set_num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 set_nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.32 set_int: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Code____Numeral__Ointeger,type,
% 5.12/5.32 code_integer: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Extended____Nat__Oenat,type,
% 5.12/5.32 extended_enat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__List__Olist_I_Eo_J,type,
% 5.12/5.32 list_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Complex__Ocomplex,type,
% 5.12/5.32 complex: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 5.12/5.32 set_o: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__String__Ochar,type,
% 5.12/5.32 char: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Real__Oreal,type,
% 5.12/5.32 real: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Rat__Orat,type,
% 5.12/5.32 rat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Num__Onum,type,
% 5.12/5.32 num: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Nat__Onat,type,
% 5.12/5.32 nat: $tType ).
% 5.12/5.32
% 5.12/5.32 thf(ty_n_t__Int__Oint,type,
% 5.12/5.32 int: $tType ).
% 5.12/5.32
% 5.12/5.32 % Explicit typings (903)
% 5.12/5.32 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 5.12/5.32 archim2889992004027027881ng_rat: rat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
% 5.12/5.32 archim7802044766580827645g_real: real > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 5.12/5.32 archim3151403230148437115or_rat: rat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
% 5.12/5.32 archim6058952711729229775r_real: real > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Archimedean__Field_Ofrac_001t__Real__Oreal,type,
% 5.12/5.32 archim2898591450579166408c_real: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 5.12/5.32 archim7778729529865785530nd_rat: rat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
% 5.12/5.32 archim8280529875227126926d_real: real > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Binomial_Obinomial,type,
% 5.12/5.32 binomial: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 5.12/5.32 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Oand__not__num,type,
% 5.12/5.32 bit_and_not_num: num > num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 5.12/5.32 bit_concat_bit: nat > int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 5.12/5.32 bit_or_not_num_neg: num > num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 5.12/5.32 bit_ri7919022796975470100ot_int: int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 5.12/5.32 bit_ri631733984087533419it_int: nat > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 5.12/5.32 bit_se725231765392027082nd_int: int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 5.12/5.32 bit_se727722235901077358nd_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
% 5.12/5.32 bit_se8568078237143864401it_int: nat > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
% 5.12/5.32 bit_se8570568707652914677it_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
% 5.12/5.32 bit_se2159334234014336723it_int: nat > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
% 5.12/5.32 bit_se2161824704523386999it_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 bit_se2119862282449309892nteger: nat > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Int__Oint,type,
% 5.12/5.32 bit_se2000444600071755411sk_int: nat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
% 5.12/5.32 bit_se2002935070580805687sk_nat: nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
% 5.12/5.32 bit_se1409905431419307370or_int: int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
% 5.12/5.32 bit_se1412395901928357646or_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
% 5.12/5.32 bit_se545348938243370406it_int: nat > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
% 5.12/5.32 bit_se547839408752420682it_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 bit_se2793503036327961859nteger: nat > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
% 5.12/5.32 bit_se7879613467334960850it_int: nat > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
% 5.12/5.32 bit_se7882103937844011126it_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 bit_se1745604003318907178nteger: nat > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
% 5.12/5.32 bit_se2923211474154528505it_int: nat > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
% 5.12/5.32 bit_se2925701944663578781it_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 bit_se8260200283734997820nteger: nat > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Int__Oint,type,
% 5.12/5.32 bit_se4203085406695923979it_int: nat > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Nat__Onat,type,
% 5.12/5.32 bit_se4205575877204974255it_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Int__Oint,type,
% 5.12/5.32 bit_se6526347334894502574or_int: int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Nat__Onat,type,
% 5.12/5.32 bit_se6528837805403552850or_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
% 5.12/5.32 bit_se1146084159140164899it_int: int > nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Nat__Onat,type,
% 5.12/5.32 bit_se1148574629649215175it_nat: nat > nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Otake__bit__num,type,
% 5.12/5.32 bit_take_bit_num: nat > num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations_Oand__num,type,
% 5.12/5.32 bit_un1837492267222099188nd_num: num > num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations_Oxor__num,type,
% 5.12/5.32 bit_un6178654185764691216or_num: num > num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oand__num,type,
% 5.12/5.32 bit_un7362597486090784418nd_num: num > num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oxor__num,type,
% 5.12/5.32 bit_un2480387367778600638or_num: num > num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Numeral_Obit__cut__integer,type,
% 5.12/5.32 code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Numeral_Odivmod__abs,type,
% 5.12/5.32 code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Numeral_Odivmod__integer,type,
% 5.12/5.32 code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
% 5.12/5.32 code_int_of_integer: code_integer > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
% 5.12/5.32 code_integer_of_int: int > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Numeral_Ointeger__of__num,type,
% 5.12/5.32 code_integer_of_num: num > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Numeral_Onat__of__integer,type,
% 5.12/5.32 code_nat_of_integer: code_integer > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Numeral_Onum__of__integer,type,
% 5.12/5.32 code_num_of_integer: code_integer > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Target__Int_Onegative,type,
% 5.12/5.32 code_Target_negative: num > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Code__Target__Int_Opositive,type,
% 5.12/5.32 code_Target_positive: num > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 5.12/5.32 comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 5.12/5.32 comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Real__Oreal,type,
% 5.12/5.32 comple4887499456419720421f_real: set_real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 comple7806235888213564991et_nat: set_set_nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Int__Oint,type,
% 5.12/5.32 complete_Sup_Sup_int: set_int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Real__Oreal,type,
% 5.12/5.32 comple1385675409528146559p_real: set_real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 comple7399068483239264473et_nat: set_set_nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complex_OArg,type,
% 5.12/5.32 arg: complex > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complex_Ocis,type,
% 5.12/5.32 cis: real > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complex_Ocnj,type,
% 5.12/5.32 cnj: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complex_Ocomplex_OComplex,type,
% 5.12/5.32 complex2: real > real > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complex_Ocomplex_OIm,type,
% 5.12/5.32 im: complex > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complex_Ocomplex_ORe,type,
% 5.12/5.32 re: complex > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complex_Ocsqrt,type,
% 5.12/5.32 csqrt: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Complex_Oimaginary__unit,type,
% 5.12/5.32 imaginary_unit: complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Deriv_Odifferentiable_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Deriv_Ohas__derivative_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Deriv_Ohas__field__derivative_001t__Real__Oreal,type,
% 5.12/5.32 has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Oadjust__div,type,
% 5.12/5.32 adjust_div: product_prod_int_int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Oadjust__mod,type,
% 5.12/5.32 adjust_mod: int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Odivmod__nat,type,
% 5.12/5.32 divmod_nat: nat > nat > product_prod_nat_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Oeucl__rel__int,type,
% 5.12/5.32 eucl_rel_int: int > int > product_prod_int_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 5.12/5.32 unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 5.12/5.32 unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 5.12/5.32 unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 5.12/5.32 unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 5.12/5.32 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 5.12/5.32 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 comm_s8582702949713902594nteger: code_integer > nat > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Complex__Ocomplex,type,
% 5.12/5.32 comm_s2602460028002588243omplex: complex > nat > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Int__Oint,type,
% 5.12/5.32 comm_s4660882817536571857er_int: int > nat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
% 5.12/5.32 comm_s4663373288045622133er_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
% 5.12/5.32 comm_s4028243227959126397er_rat: rat > nat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Real__Oreal,type,
% 5.12/5.32 comm_s7457072308508201937r_real: real > nat > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 semiri3624122377584611663nteger: nat > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 5.12/5.32 semiri5044797733671781792omplex: nat > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
% 5.12/5.32 semiri1406184849735516958ct_int: nat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 5.12/5.32 semiri1408675320244567234ct_nat: nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
% 5.12/5.32 semiri773545260158071498ct_rat: nat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 5.12/5.32 semiri2265585572941072030t_real: nat > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 5.12/5.32 invers8013647133539491842omplex: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 5.12/5.32 inverse_inverse_rat: rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 5.12/5.32 inverse_inverse_real: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 5.12/5.32 at_bot_real: filter_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 5.12/5.32 at_top_nat: filter_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 5.12/5.32 at_top_real: filter_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 5.12/5.32 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.12/5.32 eventu5826381225784669381omplex: ( produc4411394909380815293omplex > $o ) > filter6041513312241820739omplex > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.12/5.32 eventu3244425730907250241l_real: ( produc2422161461964618553l_real > $o ) > filter2146258269922977983l_real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 5.12/5.32 eventually_real: ( real > $o ) > filter_real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.12/5.32 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.12/5.32 princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.12/5.32 princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 5.12/5.32 finite_card_o: set_o > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 5.12/5.32 finite_card_complex: set_complex > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 5.12/5.32 finite_card_nat: set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 5.12/5.32 finite410649719033368117t_unit: set_Product_unit > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 finite_card_set_nat: set_set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 5.12/5.32 finite_card_char: set_char > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
% 5.12/5.32 finite_finite_o: set_o > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 5.12/5.32 finite3207457112153483333omplex: set_complex > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 5.12/5.32 finite_finite_int: set_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
% 5.12/5.32 finite_finite_list_o: set_list_o > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.12/5.32 finite8712137658972009173omplex: set_list_complex > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
% 5.12/5.32 finite3922522038869484883st_int: set_list_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
% 5.12/5.32 finite8100373058378681591st_nat: set_list_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 5.12/5.32 finite_finite_nat: set_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
% 5.12/5.32 finite_finite_num: set_num > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.12/5.32 finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 5.12/5.32 finite_finite_rat: set_rat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 5.12/5.32 finite_finite_real: set_real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.32 finite6551019134538273531omplex: set_set_complex > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.32 finite6197958912794628473et_int: set_set_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 finite1152437895449049373et_nat: set_set_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Finite__Set_Ofinite_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.12/5.32 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.12/5.32 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 5.12/5.32 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 5.12/5.32 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 comp_int_real_real: ( int > real ) > ( real > int ) > real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.12/5.32 comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 5.12/5.32 inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 inj_on_real_real: ( real > real ) > set_real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.12/5.32 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.12/5.32 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 5.12/5.32 gcd_Gcd_int: set_int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 5.12/5.32 gcd_Gcd_nat: set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_GCD_Obezw,type,
% 5.12/5.32 bezw: nat > nat > product_prod_int_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_GCD_Obezw__rel,type,
% 5.12/5.32 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 5.12/5.32 gcd_gcd_int: int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 5.12/5.32 gcd_gcd_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_GCD_Ogcd__nat__rel,type,
% 5.12/5.32 gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 abs_abs_Code_integer: code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 5.12/5.32 abs_abs_complex: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 5.12/5.32 abs_abs_int: int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 5.12/5.32 abs_abs_rat: rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 5.12/5.32 abs_abs_real: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
% 5.12/5.32 minus_minus_complex: complex > complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 5.12/5.32 minus_minus_int: int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 5.12/5.32 minus_minus_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 5.12/5.32 minus_minus_rat: rat > rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 5.12/5.32 minus_minus_real: real > real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.32 minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.32 minus_minus_set_int: set_int > set_int > set_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.32 minus_minus_set_real: set_real > set_real > set_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.32 minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 one_one_Code_integer: code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex,type,
% 5.12/5.32 one_one_complex: complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oone__class_Oone_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 one_on7984719198319812577d_enat: extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 5.12/5.32 one_one_int: int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 5.12/5.32 one_one_nat: nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
% 5.12/5.32 one_one_rat: rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 5.12/5.32 one_one_real: real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex,type,
% 5.12/5.32 plus_plus_complex: complex > complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oplus__class_Oplus_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 5.12/5.32 plus_plus_int: int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 5.12/5.32 plus_plus_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 5.12/5.32 plus_plus_num: num > num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oplus__class_Oplus_001t__Rat__Orat,type,
% 5.12/5.32 plus_plus_rat: rat > rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 5.12/5.32 plus_plus_real: real > real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Osgn__class_Osgn_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 sgn_sgn_Code_integer: code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Osgn__class_Osgn_001t__Complex__Ocomplex,type,
% 5.12/5.32 sgn_sgn_complex: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Osgn__class_Osgn_001t__Int__Oint,type,
% 5.12/5.32 sgn_sgn_int: int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Osgn__class_Osgn_001t__Rat__Orat,type,
% 5.12/5.32 sgn_sgn_rat: rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Osgn__class_Osgn_001t__Real__Oreal,type,
% 5.12/5.32 sgn_sgn_real: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex,type,
% 5.12/5.32 times_times_complex: complex > complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Otimes__class_Otimes_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 5.12/5.32 times_times_int: int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 5.12/5.32 times_times_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
% 5.12/5.32 times_times_num: num > num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
% 5.12/5.32 times_times_rat: rat > rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 5.12/5.32 times_times_real: real > real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 5.12/5.32 uminus1680532995456772888plex_o: ( complex > $o ) > complex > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Int__Oint_M_Eo_J,type,
% 5.12/5.32 uminus_uminus_int_o: ( int > $o ) > int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Nat__Onat_M_Eo_J,type,
% 5.12/5.32 uminus_uminus_nat_o: ( nat > $o ) > nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 5.12/5.32 uminus7117520113953359693_int_o: ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Real__Oreal_M_Eo_J,type,
% 5.12/5.32 uminus_uminus_real_o: ( real > $o ) > real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 5.12/5.32 uminus6401447641752708672_nat_o: ( set_nat > $o ) > set_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 uminus1351360451143612070nteger: code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex,type,
% 5.12/5.32 uminus1482373934393186551omplex: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 5.12/5.32 uminus_uminus_int: int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Rat__Orat,type,
% 5.12/5.32 uminus_uminus_rat: rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 5.12/5.32 uminus_uminus_real: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.32 uminus8566677241136511917omplex: set_complex > set_complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.32 uminus1532241313380277803et_int: set_int > set_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 uminus5710092332889474511et_nat: set_nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.12/5.32 uminus6221592323253981072nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.32 uminus612125837232591019t_real: set_real > set_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.32 uminus613421341184616069et_nat: set_set_nat > set_set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 zero_z3403309356797280102nteger: code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex,type,
% 5.12/5.32 zero_zero_complex: complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ozero__class_Ozero_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 zero_z5237406670263579293d_enat: extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 5.12/5.32 zero_zero_int: int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 5.12/5.32 zero_zero_nat: nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ozero__class_Ozero_001t__Rat__Orat,type,
% 5.12/5.32 zero_zero_rat: rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 5.12/5.32 zero_zero_real: real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001_Eo_001t__Nat__Onat,type,
% 5.12/5.32 groups8507830703676809646_o_nat: ( $o > nat ) > set_o > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 5.12/5.32 groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 5.12/5.32 groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Rat__Orat,type,
% 5.12/5.32 groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 5.12/5.32 groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Int__Oint,type,
% 5.12/5.32 groups4538972089207619220nt_int: ( int > int ) > set_int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Nat__Onat,type,
% 5.12/5.32 groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Rat__Orat,type,
% 5.12/5.32 groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Real__Oreal,type,
% 5.12/5.32 groups8778361861064173332t_real: ( int > real ) > set_int > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Int__Oint,type,
% 5.12/5.32 groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.12/5.32 groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.12/5.32 groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Int__Oint,type,
% 5.12/5.32 groups1932886352136224148al_int: ( real > int ) > set_real > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.12/5.32 groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Rat__Orat,type,
% 5.12/5.32 groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 groups8097168146408367636l_real: ( real > real ) > set_real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups8255218700646806128omplex: ( set_nat > complex ) > set_set_nat > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.12/5.32 groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Real__Oreal,type,
% 5.12/5.32 groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__VEBT____Definitions__OVEBT_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups1794756597179926696omplex: ( vEBT_VEBT > complex ) > set_VEBT_VEBT > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.12/5.32 groups769130701875090982BT_int: ( vEBT_VEBT > int ) > set_VEBT_VEBT > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.12/5.32 groups771621172384141258BT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__VEBT____Definitions__OVEBT_001t__Rat__Orat,type,
% 5.12/5.32 groups136491112297645522BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.12/5.32 groups2240296850493347238T_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups3708469109370488835omplex: ( complex > complex ) > set_complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 5.12/5.32 groups858564598930262913ex_int: ( complex > int ) > set_complex > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 5.12/5.32 groups861055069439313189ex_nat: ( complex > nat ) > set_complex > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Complex__Ocomplex_001t__Rat__Orat,type,
% 5.12/5.32 groups225925009352817453ex_rat: ( complex > rat ) > set_complex > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 5.12/5.32 groups766887009212190081x_real: ( complex > real ) > set_complex > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups7440179247065528705omplex: ( int > complex ) > set_int > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Int__Oint,type,
% 5.12/5.32 groups1705073143266064639nt_int: ( int > int ) > set_int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Nat__Onat,type,
% 5.12/5.32 groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Rat__Orat,type,
% 5.12/5.32 groups1072433553688619179nt_rat: ( int > rat ) > set_int > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Real__Oreal,type,
% 5.12/5.32 groups2316167850115554303t_real: ( int > real ) > set_int > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Int__Oint,type,
% 5.12/5.32 groups705719431365010083at_int: ( nat > int ) > set_nat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.12/5.32 groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.12/5.32 groups129246275422532515t_real: ( nat > real ) > set_nat > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 5.12/5.32 groups713298508707869441omplex: ( real > complex ) > set_real > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Real__Oreal_001t__Int__Oint,type,
% 5.12/5.32 groups4694064378042380927al_int: ( real > int ) > set_real > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.12/5.32 groups4696554848551431203al_nat: ( real > nat ) > set_real > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Real__Oreal_001t__Rat__Orat,type,
% 5.12/5.32 groups4061424788464935467al_rat: ( real > rat ) > set_real > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.32 groups1681761925125756287l_real: ( real > real ) > set_real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__VEBT____Definitions__OVEBT_001t__Rat__Orat,type,
% 5.12/5.32 groups5726676334696518183BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.12/5.32 groups2703838992350267259T_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Groups__List_Ocomm__semiring__0__class_Ohorner__sum_001_Eo_001t__Int__Oint,type,
% 5.12/5.32 groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_HOL_OThe_001t__Int__Oint,type,
% 5.12/5.32 the_int: ( int > $o ) > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_HOL_OThe_001t__Real__Oreal,type,
% 5.12/5.32 the_real: ( real > $o ) > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.12/5.32 if_int_int: $o > ( int > int ) > ( int > int ) > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 if_Code_integer: $o > code_integer > code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Complex__Ocomplex,type,
% 5.12/5.32 if_complex: $o > complex > complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Int__Oint,type,
% 5.12/5.32 if_int: $o > int > int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
% 5.12/5.32 if_list_int: $o > list_int > list_int > list_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Nat__Onat,type,
% 5.12/5.32 if_nat: $o > nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Num__Onum,type,
% 5.12/5.32 if_num: $o > num > num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.12/5.32 if_option_nat: $o > option_nat > option_nat > option_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.12/5.32 if_option_num: $o > option_num > option_num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.12/5.32 if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.12/5.32 if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.12/5.32 if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Rat__Orat,type,
% 5.12/5.32 if_rat: $o > rat > rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Real__Oreal,type,
% 5.12/5.32 if_real: $o > real > real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 if_set_nat: $o > set_nat > set_nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_OAbs__Integ,type,
% 5.12/5.32 abs_Integ: product_prod_nat_nat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_ORep__Integ,type,
% 5.12/5.32 rep_Integ: int > product_prod_nat_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Oint__ge__less__than,type,
% 5.12/5.32 int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Oint__ge__less__than2,type,
% 5.12/5.32 int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Onat,type,
% 5.12/5.32 nat2: int > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 5.12/5.32 ring_1_Ints_real: set_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 ring_18347121197199848620nteger: int > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 5.12/5.32 ring_17405671764205052669omplex: int > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.12/5.32 ring_1_of_int_int: int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.12/5.32 ring_1_of_int_rat: int > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.12/5.32 ring_1_of_int_real: int > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.12/5.32 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 5.12/5.32 sup_sup_nat: nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 5.12/5.32 sup_sup_set_set_o: set_set_o > set_set_o > set_set_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.32 sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 5.12/5.32 lattic8263393255366662781ax_int: set_int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.12/5.32 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.12/5.32 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.12/5.32 append_int: list_int > list_int > list_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.12/5.32 append_nat: list_nat > list_nat > list_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 5.12/5.32 distinct_int: list_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.12/5.32 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.12/5.32 cons_int: int > list_int > list_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.12/5.32 cons_nat: nat > list_nat > list_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.12/5.32 nil_int: list_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.12/5.32 nil_nat: list_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.12/5.32 set_o2: list_o > set_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.12/5.32 set_complex2: list_complex > set_complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.12/5.32 set_int2: list_int > set_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.12/5.32 set_nat2: list_nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.12/5.32 set_real2: list_real > set_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 set_set_nat2: list_set_nat > set_set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.12/5.32 list_update_o: list_o > nat > $o > list_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 5.12/5.32 list_update_complex: list_complex > nat > complex > list_complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.12/5.32 list_update_int: list_int > nat > int > list_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.12/5.32 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.12/5.32 list_update_real: list_real > nat > real > list_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001_Eo,type,
% 5.12/5.32 nth_o: list_o > nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.12/5.32 nth_complex: list_complex > nat > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.12/5.32 nth_int: list_int > nat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.12/5.32 nth_nat: list_nat > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.12/5.32 nth_num: list_num > nat > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.12/5.32 nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 5.12/5.32 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 5.12/5.32 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.12/5.32 nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.12/5.32 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.12/5.32 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.12/5.32 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.12/5.32 nth_real: list_real > nat > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 nth_set_nat: list_set_nat > nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.12/5.32 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.12/5.32 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.12/5.32 produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Int__Oint_001_Eo,type,
% 5.12/5.32 product_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 5.12/5.32 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 produc662631939642741121T_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.12/5.32 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Int__Oint,type,
% 5.12/5.32 product_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.32 product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Num__Onum,type,
% 5.12/5.32 product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.12/5.32 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.12/5.32 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.12/5.32 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.12/5.32 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.12/5.32 replicate_o: nat > $o > list_o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.12/5.32 replicate_complex: nat > complex > list_complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.12/5.32 replicate_int: nat > int > list_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.12/5.32 replicate_nat: nat > nat > list_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.12/5.32 replicate_real: nat > real > list_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 replicate_set_nat: nat > set_nat > list_set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oupto,type,
% 5.12/5.32 upto: int > int > list_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oupto__aux,type,
% 5.12/5.32 upto_aux: int > int > list_int > list_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_List_Oupto__rel,type,
% 5.12/5.32 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_OSuc,type,
% 5.12/5.32 suc: nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.12/5.32 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.12/5.32 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.12/5.32 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Onat_Opred,type,
% 5.12/5.32 pred: nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 semiri4939895301339042750nteger: nat > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.12/5.32 semiri8010041392384452111omplex: nat > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.12/5.32 semiri1314217659103216013at_int: nat > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.12/5.32 semiri1316708129612266289at_nat: nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.12/5.32 semiri681578069525770553at_rat: nat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.12/5.32 semiri5074537144036343181t_real: nat > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.12/5.32 size_size_list_o: list_o > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.12/5.32 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.12/5.32 size_s3451745648224563538omplex: list_complex > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.12/5.32 size_size_list_int: list_int > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.12/5.32 size_size_list_nat: list_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.12/5.32 size_size_list_num: list_num > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.12/5.32 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.12/5.32 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.12/5.32 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_J,type,
% 5.12/5.32 size_s4246224855604898693_int_o: list_P5087981734274514673_int_o > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.12/5.32 size_s5157815400016825771nt_int: list_P5707943133018811711nt_int > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.12/5.32 size_s6639371672096860321T_VEBT: list_P7524865323317820941T_VEBT > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.12/5.32 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.12/5.32 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.12/5.32 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.12/5.32 size_size_list_real: list_real > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.32 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.12/5.32 size_size_num: num > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.12/5.32 size_size_option_nat: option_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.12/5.32 size_size_option_num: option_num > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.12/5.32 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.32 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.12/5.32 nat_list_encode: list_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.12/5.32 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.12/5.32 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.12/5.32 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.12/5.32 nat_set_decode: nat > set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.12/5.32 nat_set_encode: set_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.12/5.32 nat_triangle: nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_NthRoot_Oroot,type,
% 5.12/5.32 root: nat > real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_NthRoot_Osqrt,type,
% 5.12/5.32 sqrt: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_OBitM,type,
% 5.12/5.32 bitM: num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oinc,type,
% 5.12/5.32 inc: num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.12/5.32 neg_nu7009210354673126013omplex: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.12/5.32 neg_numeral_dbl_int: int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.12/5.32 neg_numeral_dbl_rat: rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.12/5.32 neg_numeral_dbl_real: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.12/5.32 neg_nu6511756317524482435omplex: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.12/5.32 neg_nu3811975205180677377ec_int: int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.12/5.32 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.12/5.32 neg_nu6075765906172075777c_real: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.12/5.32 neg_nu8557863876264182079omplex: complex > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.12/5.32 neg_nu5851722552734809277nc_int: int > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.12/5.32 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.12/5.32 neg_nu8295874005876285629c_real: real > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.12/5.32 neg_numeral_sub_int: num > num > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onum_OBit0,type,
% 5.12/5.32 bit0: num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onum_OBit1,type,
% 5.12/5.32 bit1: num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onum_OOne,type,
% 5.12/5.32 one: num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.12/5.32 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onum_Osize__num,type,
% 5.12/5.32 size_num: num > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onum__of__nat,type,
% 5.12/5.32 num_of_nat: nat > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 numera6620942414471956472nteger: num > code_integer ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.12/5.32 numera6690914467698888265omplex: num > complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 numera1916890842035813515d_enat: num > extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 5.12/5.32 numeral_numeral_int: num > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 5.12/5.32 numeral_numeral_nat: num > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 5.12/5.32 numeral_numeral_rat: num > rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 5.12/5.32 numeral_numeral_real: num > real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Opow,type,
% 5.12/5.32 pow: num > num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Opred__numeral,type,
% 5.12/5.32 pred_numeral: num > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Num_Osqr,type,
% 5.12/5.32 sqr: num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 5.12/5.32 none_nat: option_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 5.12/5.32 none_num: option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 5.12/5.32 some_nat: nat > option_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 5.12/5.32 some_num: num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 5.12/5.32 case_option_int_num: int > ( num > int ) > option_num > int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 5.12/5.32 case_option_num_num: num > ( num > num ) > option_num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 5.12/5.32 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 5.12/5.32 map_option_num_num: ( num > num ) > option_num > option_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Osize__option_001t__Nat__Onat,type,
% 5.12/5.32 size_option_nat: ( nat > nat ) > option_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 5.12/5.32 size_option_num: ( num > nat ) > option_num > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 5.12/5.32 the_nat: option_nat > nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
% 5.12/5.32 the_num: option_num > num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.32 the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 bot_bo4199563552545308370d_enat: extended_enat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 5.12/5.32 bot_bot_nat: nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.32 bot_bot_set_complex: set_complex ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.32 bot_bot_set_int: set_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.32 bot_bot_set_nat: set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Num__Onum_J,type,
% 5.12/5.32 bot_bot_set_num: set_num ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.12/5.32 bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Rat__Orat_J,type,
% 5.12/5.32 bot_bot_set_rat: set_rat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.32 bot_bot_set_real: set_real ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.32 bot_bot_set_set_nat: set_set_nat ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.32 bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001_Eo,type,
% 5.12/5.32 ord_less_o: $o > $o > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
% 5.12/5.32 ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Nat__Oenat,type,
% 5.12/5.32 ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 5.12/5.32 ord_less_int: int > int > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 5.12/5.32 ord_less_nat: nat > nat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 5.12/5.32 ord_less_num: num > num > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 5.12/5.32 ord_less_rat: rat > rat > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 5.12/5.32 ord_less_real: real > real > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_Eo_J,type,
% 5.12/5.32 ord_less_set_o: set_o > set_o > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 5.12/5.32 ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).
% 5.12/5.32
% 5.12/5.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.33 ord_less_set_complex: set_complex > set_complex > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.33 ord_less_set_int: set_int > set_int > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.33 ord_less_set_nat: set_nat > set_nat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Num__Onum_J,type,
% 5.12/5.33 ord_less_set_num: set_num > set_num > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Rat__Orat_J,type,
% 5.12/5.33 ord_less_set_rat: set_rat > set_rat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.33 ord_less_set_real: set_real > set_real > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.33 ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
% 5.12/5.33 ord_less_eq_o: $o > $o > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
% 5.12/5.33 ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Extended____Nat__Oenat,type,
% 5.12/5.33 ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 5.12/5.33 ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 5.12/5.33 ord_less_eq_int: int > int > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 5.12/5.33 ord_less_eq_nat: nat > nat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 5.12/5.33 ord_less_eq_num: num > num > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 5.12/5.33 ord_less_eq_rat: rat > rat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 5.12/5.33 ord_less_eq_real: real > real > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
% 5.12/5.33 ord_less_eq_set_o: set_o > set_o > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 5.12/5.33 ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.33 ord_le211207098394363844omplex: set_complex > set_complex > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.33 ord_less_eq_set_int: set_int > set_int > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.33 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
% 5.12/5.33 ord_less_eq_set_num: set_num > set_num > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Rat__Orat_J,type,
% 5.12/5.33 ord_less_eq_set_rat: set_rat > set_rat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.33 ord_less_eq_set_real: set_real > set_real > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.12/5.33 ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 5.12/5.33 ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Ointeger,type,
% 5.12/5.33 ord_max_Code_integer: code_integer > code_integer > code_integer ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Omax_001t__Extended____Nat__Oenat,type,
% 5.12/5.33 ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 5.12/5.33 ord_max_int: int > int > int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 5.12/5.33 ord_max_nat: nat > nat > nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
% 5.12/5.33 ord_max_num: num > num > num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
% 5.12/5.33 ord_max_rat: rat > rat > rat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
% 5.12/5.33 ord_max_real: real > real > real ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.33 ord_max_set_nat: set_nat > set_nat > set_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 5.12/5.33 order_Greatest_nat: ( nat > $o ) > nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.12/5.33 order_9091379641038594480t_real: ( nat > real ) > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.33 order_mono_nat_nat: ( nat > nat ) > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.12/5.33 order_mono_nat_real: ( nat > real ) > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oorder__class_Omono_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.33 order_mono_real_real: ( real > real ) > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.33 order_5726023648592871131at_nat: ( nat > nat ) > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.12/5.33 order_7092887310737990675l_real: ( real > real ) > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 5.12/5.33 top_top_set_o: set_o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.33 top_top_set_nat: set_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 5.12/5.33 top_to1996260823553986621t_unit: set_Product_unit ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.33 top_top_set_real: set_real ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
% 5.12/5.33 top_top_set_char: set_char ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 5.12/5.33 power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 5.12/5.33 power_power_complex: complex > nat > complex ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 5.12/5.33 power_power_int: int > nat > int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 5.12/5.33 power_power_nat: nat > nat > nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 5.12/5.33 power_power_rat: rat > nat > rat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 5.12/5.33 power_power_real: real > nat > real ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.12/5.33 produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.12/5.33 produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.12/5.33 produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).
% 5.12/5.33
% 5.12/5.33 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,
% 5.12/5.33 produc851828971589881931at_num: ( nat > num > num ) > produc2963631642982155120at_num > produc3368934014287244435at_num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 5.12/5.33 produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 5.12/5.33 produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.12/5.33 produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.12/5.33 produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.12/5.33 produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.12/5.33 produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 5.12/5.33 product_Pair_int_int: int > int > product_prod_int_int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
% 5.12/5.33 product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Int__Oint,type,
% 5.12/5.33 product_Pair_nat_int: nat > int > product_prod_nat_int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.33 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 5.12/5.33 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.33 produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.12/5.33 produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.33 produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 5.12/5.33 product_Pair_num_num: num > num > product_prod_num_num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.12/5.33 produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.12/5.33 produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.12/5.33 produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.12/5.33 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.12/5.33 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.12/5.33 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.12/5.33 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 5.12/5.33 produc7828578312038201481er_o_o: ( code_integer > $o > $o ) > produc6271795597528267376eger_o > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.33 produc1043322548047392435omplex: ( code_integer > $o > set_complex ) > produc6271795597528267376eger_o > set_complex ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.33 produc1253318751659547953et_int: ( code_integer > $o > set_int ) > produc6271795597528267376eger_o > set_int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.33 produc5431169771168744661et_nat: ( code_integer > $o > set_nat ) > produc6271795597528267376eger_o > set_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.33 produc242741666403216561t_real: ( code_integer > $o > set_real ) > produc6271795597528267376eger_o > set_real ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__String__Ochar,type,
% 5.12/5.33 produc4188289175737317920o_char: ( code_integer > $o > char ) > produc6271795597528267376eger_o > char ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.12/5.33 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.12/5.33 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.12/5.33 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.12/5.33 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.12/5.33 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 5.12/5.33 produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.12/5.33 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.12/5.33 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.12/5.33 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.12/5.33 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.12/5.33 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.12/5.33 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.12/5.33 produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 5.12/5.33 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.33 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.12/5.33 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.12/5.33 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.12/5.33 produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
% 5.12/5.33 produc4927758841916487424_num_o: ( nat > num > $o ) > product_prod_nat_num > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.12/5.33 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.33 produc6231982587499038204omplex: ( nat > num > set_complex ) > product_prod_nat_num > set_complex ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.33 produc1435849484188172666t_real: ( nat > num > set_real ) > product_prod_nat_num > set_real ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001_Eo,type,
% 5.12/5.33 produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.12/5.33 produc2866383454006189126omplex: ( num > num > set_complex ) > product_prod_num_num > set_complex ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Int__Oint_J,type,
% 5.12/5.33 produc6406642877701697732et_int: ( num > num > set_int ) > product_prod_num_num > set_int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.12/5.33 produc1361121860356118632et_nat: ( num > num > set_nat ) > product_prod_num_num > set_nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.12/5.33 produc8296048397933160132t_real: ( num > num > set_real ) > product_prod_num_num > set_real ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 5.12/5.33 produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.12/5.33 product_fst_int_int: product_prod_int_int > int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.33 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.12/5.33 product_snd_int_int: product_prod_int_int > int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.12/5.33 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Rat_OFract,type,
% 5.12/5.33 fract: int > int > rat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Rat_OFrct,type,
% 5.12/5.33 frct: product_prod_int_int > rat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Rat_Onormalize,type,
% 5.12/5.33 normalize: product_prod_int_int > product_prod_int_int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Rat_Oof__int,type,
% 5.12/5.33 of_int: int > rat ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Rat_Oquotient__of,type,
% 5.12/5.33 quotient_of: rat > product_prod_int_int ).
% 5.12/5.33
% 5.12/5.33 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.12/5.33 real_V2521375963428798218omplex: set_complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.15/5.33 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 5.15/5.33 real_V3694042436643373181omplex: complex > complex > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 5.15/5.33 real_V975177566351809787t_real: real > real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.15/5.33 real_V1022390504157884413omplex: complex > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.15/5.33 real_V7735802525324610683m_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.15/5.33 real_V4546457046886955230omplex: real > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 5.15/5.33 real_V1803761363581548252l_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.15/5.33 real_V2046097035970521341omplex: real > complex > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.15/5.33 real_V1485227260804924795R_real: real > real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.15/5.33 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.15/5.33 divide1717551699836669952omplex: complex > complex > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.15/5.33 divide_divide_int: int > int > int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.15/5.33 divide_divide_nat: nat > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.15/5.33 divide_divide_rat: rat > rat > rat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.15/5.33 divide_divide_real: real > real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.15/5.33 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.15/5.33 dvd_dvd_complex: complex > complex > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.15/5.33 dvd_dvd_int: int > int > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.15/5.33 dvd_dvd_nat: nat > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.15/5.33 dvd_dvd_rat: rat > rat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.15/5.33 dvd_dvd_real: real > real > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.15/5.33 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.15/5.33 modulo_modulo_int: int > int > int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.15/5.33 modulo_modulo_nat: nat > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.15/5.33 zero_n356916108424825756nteger: $o > code_integer ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.15/5.33 zero_n1201886186963655149omplex: $o > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.15/5.33 zero_n2684676970156552555ol_int: $o > int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.15/5.33 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.15/5.33 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.15/5.33 zero_n3304061248610475627l_real: $o > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.15/5.33 suminf_complex: ( nat > complex ) > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 5.15/5.33 suminf_int: ( nat > int ) > int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 5.15/5.33 suminf_nat: ( nat > nat ) > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.15/5.33 suminf_real: ( nat > real ) > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 5.15/5.33 summable_complex: ( nat > complex ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 5.15/5.33 summable_int: ( nat > int ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 5.15/5.33 summable_nat: ( nat > nat ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.15/5.33 summable_real: ( nat > real ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.15/5.33 sums_complex: ( nat > complex ) > complex > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 5.15/5.33 sums_int: ( nat > int ) > int > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 5.15/5.33 sums_nat: ( nat > nat ) > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.15/5.33 sums_real: ( nat > real ) > real > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001_Eo,type,
% 5.15/5.33 collect_o: ( $o > $o ) > set_o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 5.15/5.33 collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.15/5.33 collect_complex: ( complex > $o ) > set_complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.15/5.33 collect_int: ( int > $o ) > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 5.15/5.33 collect_list_o: ( list_o > $o ) > set_list_o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.15/5.33 collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 5.15/5.33 collect_list_int: ( list_int > $o ) > set_list_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.15/5.33 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.15/5.33 collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 5.15/5.33 collect_nat: ( nat > $o ) > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Num__Onum,type,
% 5.15/5.33 collect_num: ( num > $o ) > set_num ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.15/5.33 collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.15/5.33 collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.15/5.33 collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
% 5.15/5.33 collect_rat: ( rat > $o ) > set_rat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 5.15/5.33 collect_real: ( real > $o ) > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.15/5.33 collect_set_complex: ( set_complex > $o ) > set_set_complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 5.15/5.33 collect_set_int: ( set_int > $o ) > set_set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.15/5.33 collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OCollect_001t__VEBT____Definitions__OVEBT,type,
% 5.15/5.33 collect_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 5.15/5.33 pow_nat: set_nat > set_set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001_Eo_001t__Set__Oset_I_Eo_J,type,
% 5.15/5.33 image_o_set_o: ( $o > set_o ) > set_o > set_set_o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 5.15/5.33 image_int_int: ( int > int ) > set_int > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
% 5.15/5.33 image_int_nat: ( int > nat ) > set_int > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 5.15/5.33 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.15/5.33 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.15/5.33 image_nat_real: ( nat > real ) > set_nat > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.15/5.33 image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 5.15/5.33 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 5.15/5.33 image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 5.15/5.33 image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.15/5.33 image_real_real: ( real > real ) > set_real > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 5.15/5.33 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.15/5.33 image_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 5.15/5.33 insert_complex: complex > set_complex > set_complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 5.15/5.33 insert_int: int > set_int > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 5.15/5.33 insert_nat: nat > set_nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 5.15/5.33 insert_num: num > set_num > set_num ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.15/5.33 insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 5.15/5.33 insert_rat: rat > set_rat > set_rat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 5.15/5.33 insert_real: real > set_real > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.15/5.33 insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 5.15/5.33 insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 5.15/5.33 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 5.15/5.33 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 5.15/5.33 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 5.15/5.33 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 5.15/5.33 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 5.15/5.33 set_or1266510415728281911st_int: int > int > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 5.15/5.33 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 5.15/5.33 set_or7049704709247886629st_num: num > num > set_num ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 5.15/5.33 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.15/5.33 set_or1222579329274155063t_real: real > real > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.15/5.33 set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 5.15/5.33 set_or4662586982721622107an_int: int > int > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 5.15/5.33 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 5.15/5.33 set_ord_atLeast_nat: nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 5.15/5.33 set_ord_atLeast_real: real > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 5.15/5.33 set_ord_atMost_nat: nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 5.15/5.33 set_or6656581121297822940st_int: int > int > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 5.15/5.33 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 5.15/5.33 set_or5832277885323065728an_int: int > int > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.15/5.33 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 5.15/5.33 set_or1633881224788618240n_real: real > real > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001_Eo,type,
% 5.15/5.33 set_or6416164934427428222Than_o: $o > set_o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.15/5.33 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.15/5.33 set_or5849166863359141190n_real: real > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OlessThan_001_Eo,type,
% 5.15/5.33 set_ord_lessThan_o: $o > set_o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 5.15/5.33 set_ord_lessThan_int: int > set_int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.15/5.33 set_ord_lessThan_nat: nat > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 5.15/5.33 set_ord_lessThan_num: num > set_num ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 5.15/5.33 set_ord_lessThan_rat: rat > set_rat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.15/5.33 set_or5984915006950818249n_real: real > set_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.15/5.33 set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_String_Oascii__of,type,
% 5.15/5.33 ascii_of: char > char ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_String_Ochar_OChar,type,
% 5.15/5.33 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_String_Ochar__of__integer,type,
% 5.15/5.33 char_of_integer: code_integer > char ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.15/5.33 comm_s629917340098488124ar_nat: char > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_String_Ointeger__of__char,type,
% 5.15/5.33 integer_of_char: char > code_integer ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.15/5.33 unique3096191561947761185of_nat: nat > char ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.15/5.33 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.15/5.33 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Ogenerate__topology_001_Eo,type,
% 5.15/5.33 topolo4667128019001906403logy_o: set_set_o > set_o > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Ogenerate__topology_001t__Nat__Onat,type,
% 5.15/5.33 topolo1613498594424996677gy_nat: set_set_nat > set_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Omonoseq_001t__Code____Numeral__Ointeger,type,
% 5.15/5.33 topolo2919662092509805066nteger: ( nat > code_integer ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.15/5.33 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.15/5.33 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.15/5.33 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 5.15/5.33 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.15/5.33 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.15/5.33 topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Oopen__class_Oopen_001_Eo,type,
% 5.15/5.33 topolo9180104560040979295open_o: set_o > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Oopen__class_Oopen_001t__Complex__Ocomplex,type,
% 5.15/5.33 topolo4110288021797289639omplex: set_complex > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Oopen__class_Oopen_001t__Nat__Onat,type,
% 5.15/5.33 topolo4328251076210115529en_nat: set_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Oopen__class_Oopen_001t__Real__Oreal,type,
% 5.15/5.33 topolo4860482606490270245n_real: set_real > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.15/5.33 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.15/5.33 topolo2815343760600316023s_real: real > filter_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Complex__Ocomplex,type,
% 5.15/5.33 topolo6517432010174082258omplex: ( nat > complex ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.15/5.33 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 5.15/5.33 topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 5.15/5.33 topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oarccos,type,
% 5.15/5.33 arccos: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.15/5.33 arcosh_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oarcsin,type,
% 5.15/5.33 arcsin: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oarctan,type,
% 5.15/5.33 arctan: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.15/5.33 arsinh_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.15/5.33 artanh_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.15/5.33 cos_complex: complex > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.15/5.33 cos_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.15/5.33 cos_coeff: nat > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.15/5.33 cosh_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.15/5.33 cot_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Odiffs_001t__Code____Numeral__Ointeger,type,
% 5.15/5.33 diffs_Code_integer: ( nat > code_integer ) > nat > code_integer ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.15/5.33 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.15/5.33 diffs_int: ( nat > int ) > nat > int ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 5.15/5.33 diffs_rat: ( nat > rat ) > nat > rat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.15/5.33 diffs_real: ( nat > real ) > nat > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.15/5.33 exp_complex: complex > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.15/5.33 exp_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.15/5.33 ln_ln_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Olog,type,
% 5.15/5.33 log: real > real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Opi,type,
% 5.15/5.33 pi: real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.15/5.33 powr_real: real > real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.15/5.33 sin_complex: complex > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.15/5.33 sin_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.15/5.33 sin_coeff: nat > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.15/5.33 sinh_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.15/5.33 tan_complex: complex > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.15/5.33 tan_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.15/5.33 tanh_complex: complex > complex ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.15/5.33 tanh_real: real > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 5.15/5.33 vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H,type,
% 5.15/5.33 vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 5.15/5.33 vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 5.15/5.33 vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 5.15/5.33 vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t__rel,type,
% 5.15/5.33 vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 5.15/5.33 vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 5.15/5.33 vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 5.15/5.33 vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 5.15/5.33 vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 5.15/5.33 vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l__rel,type,
% 5.15/5.33 vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 5.15/5.33 vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 5.15/5.33 vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.15/5.33 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.15/5.33 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.15/5.33 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.15/5.33 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.15/5.33 vEBT_VEBT_high: nat > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.15/5.33 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.15/5.33 vEBT_VEBT_low: nat > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.15/5.33 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.15/5.33 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.15/5.33 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.15/5.33 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.15/5.33 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.15/5.33 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.15/5.33 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.15/5.33 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.15/5.33 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.15/5.33 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 5.15/5.33 vEBT_VEBT_height: vEBT_VEBT > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 5.15/5.33 vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.15/5.33 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.15/5.33 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.15/5.33 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.15/5.33 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.15/5.33 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.15/5.33 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.15/5.33 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.15/5.33 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.15/5.33 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.15/5.33 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.15/5.33 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.15/5.33 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.15/5.33 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.15/5.33 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.15/5.33 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.15/5.33 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.15/5.33 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.15/5.33 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.15/5.33 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.15/5.33 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.15/5.33 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.15/5.33 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.15/5.33 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.15/5.33 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.15/5.33 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.15/5.33 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.15/5.33 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.15/5.33 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.15/5.33 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.15/5.33 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.15/5.33 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.15/5.33 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.15/5.33 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.15/5.33 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.15/5.33 fChoice_real: ( real > $o ) > real ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001_Eo,type,
% 5.15/5.33 member_o: $o > set_o > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.15/5.33 member_complex: complex > set_complex > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__Int__Oint,type,
% 5.15/5.33 member_int: int > set_int > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.15/5.33 member_list_o: list_o > set_list_o > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.15/5.33 member_list_int: list_int > set_list_int > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.15/5.33 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__Nat__Onat,type,
% 5.15/5.33 member_nat: nat > set_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__Num__Onum,type,
% 5.15/5.33 member_num: num > set_num > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.15/5.33 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__Rat__Orat,type,
% 5.15/5.33 member_rat: rat > set_rat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__Real__Oreal,type,
% 5.15/5.33 member_real: real > set_real > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.15/5.33 member_set_nat: set_nat > set_set_nat > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.15/5.33 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.15/5.33
% 5.15/5.33 thf(sy_v_deg____,type,
% 5.15/5.33 deg: nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_v_m____,type,
% 5.15/5.33 m: nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_v_ma____,type,
% 5.15/5.33 ma: nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_v_mi____,type,
% 5.15/5.33 mi: nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_v_na____,type,
% 5.15/5.33 na: nat ).
% 5.15/5.33
% 5.15/5.33 thf(sy_v_summary____,type,
% 5.15/5.33 summary: vEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_v_treeList____,type,
% 5.15/5.33 treeList: list_VEBT_VEBT ).
% 5.15/5.33
% 5.15/5.33 thf(sy_v_xa____,type,
% 5.15/5.33 xa: nat ).
% 5.15/5.33
% 5.15/5.33 % Relevant facts (10205)
% 5.15/5.33 thf(fact_0_True,axiom,
% 5.15/5.33 ord_less_nat @ xa @ mi ).
% 5.15/5.33
% 5.15/5.33 % True
% 5.15/5.33 thf(fact_1_even__odd__cases,axiom,
% 5.15/5.33 ! [X: nat] :
% 5.15/5.33 ( ! [N: nat] :
% 5.15/5.33 ( X
% 5.15/5.33 != ( plus_plus_nat @ N @ N ) )
% 5.15/5.33 => ~ ! [N: nat] :
% 5.15/5.33 ( X
% 5.15/5.33 != ( plus_plus_nat @ N @ ( suc @ N ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % even_odd_cases
% 5.15/5.33 thf(fact_2_bit__split__inv,axiom,
% 5.15/5.33 ! [X: nat,D: nat] :
% 5.15/5.33 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 5.15/5.33 = X ) ).
% 5.15/5.33
% 5.15/5.33 % bit_split_inv
% 5.15/5.33 thf(fact_3__C4_Ohyps_C_I7_J,axiom,
% 5.15/5.33 ord_less_eq_nat @ mi @ ma ).
% 5.15/5.33
% 5.15/5.33 % "4.hyps"(7)
% 5.15/5.33 thf(fact_4__C4_Ohyps_C_I8_J,axiom,
% 5.15/5.33 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.15/5.33
% 5.15/5.33 % "4.hyps"(8)
% 5.15/5.33 thf(fact_5_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J,axiom,
% 5.15/5.33 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.15/5.33 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) )
% 5.15/5.33 = one_one_nat ) ).
% 5.15/5.33
% 5.15/5.33 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(5)
% 5.15/5.33 thf(fact_6_add__self__div__2,axiom,
% 5.15/5.33 ! [M: nat] :
% 5.15/5.33 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.33 = M ) ).
% 5.15/5.33
% 5.15/5.33 % add_self_div_2
% 5.15/5.33 thf(fact_7_one__add__one,axiom,
% 5.15/5.33 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.15/5.33 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_add_one
% 5.15/5.33 thf(fact_8_one__add__one,axiom,
% 5.15/5.33 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.15/5.33 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_add_one
% 5.15/5.33 thf(fact_9_one__add__one,axiom,
% 5.15/5.33 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.15/5.33 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_add_one
% 5.15/5.33 thf(fact_10_one__add__one,axiom,
% 5.15/5.33 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.15/5.33 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_add_one
% 5.15/5.33 thf(fact_11_one__add__one,axiom,
% 5.15/5.33 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.15/5.33 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_add_one
% 5.15/5.33 thf(fact_12_numeral__plus__one,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 5.15/5.33 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_one
% 5.15/5.33 thf(fact_13_numeral__plus__one,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 5.15/5.33 = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_one
% 5.15/5.33 thf(fact_14_numeral__plus__one,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 5.15/5.33 = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_one
% 5.15/5.33 thf(fact_15_numeral__plus__one,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.15/5.33 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_one
% 5.15/5.33 thf(fact_16_numeral__plus__one,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.15/5.33 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_one
% 5.15/5.33 thf(fact_17_one__plus__numeral,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.33 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_plus_numeral
% 5.15/5.33 thf(fact_18_one__plus__numeral,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_plus_numeral
% 5.15/5.33 thf(fact_19_one__plus__numeral,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_plus_numeral
% 5.15/5.33 thf(fact_20_one__plus__numeral,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_plus_numeral
% 5.15/5.33 thf(fact_21_one__plus__numeral,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_plus_numeral
% 5.15/5.33 thf(fact_22_one__less__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ one @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_less_numeral_iff
% 5.15/5.33 thf(fact_23_one__less__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ one @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_less_numeral_iff
% 5.15/5.33 thf(fact_24_one__less__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ one @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_less_numeral_iff
% 5.15/5.33 thf(fact_25_one__less__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ one @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_less_numeral_iff
% 5.15/5.33 thf(fact_26__092_060open_062T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_A_INode_A_ISome_A_Imi_M_Ama_J_J_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_J_AtreeList_Asummary_J_Ax_A_061_A19_A_L_A_Ilet_Axn_A_061_Aif_Ax_A_060_Ami_Athen_Ami_Aelse_Ax_059_Aminn_A_061_Aif_Ax_A_060_Ami_Athen_Ax_Aelse_Ami_059_Al_A_061_Alow_Axn_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_Adiv_A2_J_059_Ah_A_061_Ahigh_Axn_A_ISuc_A_ISuc_A_Ideg_A_N_A2_J_J_Adiv_A2_J_Ain_Aif_Ah_A_060_Alength_AtreeList_A_092_060and_062_A_092_060not_062_A_Ix_A_061_Ami_A_092_060or_062_Ax_A_061_Ama_J_Athen_AT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_A_ItreeList_A_B_Ah_J_Al_A_L_AT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_A_ItreeList_A_B_Ah_J_A_L_A_Iif_AminNull_A_ItreeList_A_B_Ah_J_Athen_AT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Asummary_Ah_Aelse_A1_J_Aelse_A1_J_092_060close_062,axiom,
% 5.15/5.33 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ treeList @ summary ) @ xa )
% 5.15/5.33 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.33 @ ( if_nat
% 5.15/5.33 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 5.15/5.33 & ~ ( ( xa = mi )
% 5.15/5.33 | ( xa = ma ) ) )
% 5.15/5.33 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ ( minus_minus_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.15/5.33 @ one_one_nat ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % \<open>T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t (Node (Some (mi, ma)) (Suc (Suc (deg - 2))) treeList summary) x = 19 + (let xn = if x < mi then mi else x; minn = if x < mi then x else mi; l = low xn (Suc (Suc (deg - 2)) div 2); h = high xn (Suc (Suc (deg - 2)) div 2) in if h < length treeList \<and> \<not> (x = mi \<or> x = ma) then T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t (treeList ! h) l + T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l (treeList ! h) + (if minNull (treeList ! h) then T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t summary h else 1) else 1)\<close>
% 5.15/5.33 thf(fact_27_numeral__eq__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ( numera6690914467698888265omplex @ N2 )
% 5.15/5.33 = one_one_complex )
% 5.15/5.33 = ( N2 = one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_one_iff
% 5.15/5.33 thf(fact_28_numeral__eq__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ( numeral_numeral_real @ N2 )
% 5.15/5.33 = one_one_real )
% 5.15/5.33 = ( N2 = one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_one_iff
% 5.15/5.33 thf(fact_29_numeral__eq__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ( numeral_numeral_rat @ N2 )
% 5.15/5.33 = one_one_rat )
% 5.15/5.33 = ( N2 = one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_one_iff
% 5.15/5.33 thf(fact_30_numeral__eq__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ( numeral_numeral_nat @ N2 )
% 5.15/5.33 = one_one_nat )
% 5.15/5.33 = ( N2 = one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_one_iff
% 5.15/5.33 thf(fact_31_numeral__eq__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ( numeral_numeral_int @ N2 )
% 5.15/5.33 = one_one_int )
% 5.15/5.33 = ( N2 = one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_one_iff
% 5.15/5.33 thf(fact_32_one__eq__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( one_one_complex
% 5.15/5.33 = ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.33 = ( one = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_eq_numeral_iff
% 5.15/5.33 thf(fact_33_one__eq__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( one_one_real
% 5.15/5.33 = ( numeral_numeral_real @ N2 ) )
% 5.15/5.33 = ( one = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_eq_numeral_iff
% 5.15/5.33 thf(fact_34_one__eq__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( one_one_rat
% 5.15/5.33 = ( numeral_numeral_rat @ N2 ) )
% 5.15/5.33 = ( one = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_eq_numeral_iff
% 5.15/5.33 thf(fact_35_one__eq__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( one_one_nat
% 5.15/5.33 = ( numeral_numeral_nat @ N2 ) )
% 5.15/5.33 = ( one = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_eq_numeral_iff
% 5.15/5.33 thf(fact_36_one__eq__numeral__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( one_one_int
% 5.15/5.33 = ( numeral_numeral_int @ N2 ) )
% 5.15/5.33 = ( one = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_eq_numeral_iff
% 5.15/5.33 thf(fact_37_field__less__half__sum,axiom,
% 5.15/5.33 ! [X: real,Y: real] :
% 5.15/5.33 ( ( ord_less_real @ X @ Y )
% 5.15/5.33 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % field_less_half_sum
% 5.15/5.33 thf(fact_38_field__less__half__sum,axiom,
% 5.15/5.33 ! [X: rat,Y: rat] :
% 5.15/5.33 ( ( ord_less_rat @ X @ Y )
% 5.15/5.33 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % field_less_half_sum
% 5.15/5.33 thf(fact_39_nat__add__left__cancel__less,axiom,
% 5.15/5.33 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.15/5.33 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_add_left_cancel_less
% 5.15/5.33 thf(fact_40_nat__1__add__1,axiom,
% 5.15/5.33 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.15/5.33 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_1_add_1
% 5.15/5.33 thf(fact_41_semiring__norm_I86_J,axiom,
% 5.15/5.33 ! [M: num] :
% 5.15/5.33 ( ( bit1 @ M )
% 5.15/5.33 != one ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(86)
% 5.15/5.33 thf(fact_42_max__in__set__def,axiom,
% 5.15/5.33 ( vEBT_VEBT_max_in_set
% 5.15/5.33 = ( ^ [Xs: set_nat,X2: nat] :
% 5.15/5.33 ( ( member_nat @ X2 @ Xs )
% 5.15/5.33 & ! [Y2: nat] :
% 5.15/5.33 ( ( member_nat @ Y2 @ Xs )
% 5.15/5.33 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % max_in_set_def
% 5.15/5.33 thf(fact_43_min__in__set__def,axiom,
% 5.15/5.33 ( vEBT_VEBT_min_in_set
% 5.15/5.33 = ( ^ [Xs: set_nat,X2: nat] :
% 5.15/5.33 ( ( member_nat @ X2 @ Xs )
% 5.15/5.33 & ! [Y2: nat] :
% 5.15/5.33 ( ( member_nat @ Y2 @ Xs )
% 5.15/5.33 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % min_in_set_def
% 5.15/5.33 thf(fact_44_numeral__eq__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ( numera6690914467698888265omplex @ M )
% 5.15/5.33 = ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.33 = ( M = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_iff
% 5.15/5.33 thf(fact_45_numeral__eq__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ( numeral_numeral_real @ M )
% 5.15/5.33 = ( numeral_numeral_real @ N2 ) )
% 5.15/5.33 = ( M = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_iff
% 5.15/5.33 thf(fact_46_numeral__eq__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ( numeral_numeral_rat @ M )
% 5.15/5.33 = ( numeral_numeral_rat @ N2 ) )
% 5.15/5.33 = ( M = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_iff
% 5.15/5.33 thf(fact_47_numeral__eq__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ( numeral_numeral_nat @ M )
% 5.15/5.33 = ( numeral_numeral_nat @ N2 ) )
% 5.15/5.33 = ( M = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_iff
% 5.15/5.33 thf(fact_48_numeral__eq__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ( numeral_numeral_int @ M )
% 5.15/5.33 = ( numeral_numeral_int @ N2 ) )
% 5.15/5.33 = ( M = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_eq_iff
% 5.15/5.33 thf(fact_49_semiring__norm_I87_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ( bit0 @ M )
% 5.15/5.33 = ( bit0 @ N2 ) )
% 5.15/5.33 = ( M = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(87)
% 5.15/5.33 thf(fact_50_nat_Oinject,axiom,
% 5.15/5.33 ! [X22: nat,Y22: nat] :
% 5.15/5.33 ( ( ( suc @ X22 )
% 5.15/5.33 = ( suc @ Y22 ) )
% 5.15/5.33 = ( X22 = Y22 ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat.inject
% 5.15/5.33 thf(fact_51_old_Onat_Oinject,axiom,
% 5.15/5.33 ! [Nat: nat,Nat2: nat] :
% 5.15/5.33 ( ( ( suc @ Nat )
% 5.15/5.33 = ( suc @ Nat2 ) )
% 5.15/5.33 = ( Nat = Nat2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % old.nat.inject
% 5.15/5.33 thf(fact_52_semiring__norm_I90_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ( bit1 @ M )
% 5.15/5.33 = ( bit1 @ N2 ) )
% 5.15/5.33 = ( M = N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(90)
% 5.15/5.33 thf(fact_53_pow__sum,axiom,
% 5.15/5.33 ! [A: nat,B: nat] :
% 5.15/5.33 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.15/5.33
% 5.15/5.33 % pow_sum
% 5.15/5.33 thf(fact_54_high__def,axiom,
% 5.15/5.33 ( vEBT_VEBT_high
% 5.15/5.33 = ( ^ [X2: nat,N3: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % high_def
% 5.15/5.33 thf(fact_55__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 5.15/5.33 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.15/5.33
% 5.15/5.33 % \<open>2 \<le> deg\<close>
% 5.15/5.33 thf(fact_56_power__minus__is__div,axiom,
% 5.15/5.33 ! [B: nat,A: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.33 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.15/5.33 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % power_minus_is_div
% 5.15/5.33 thf(fact_57_high__bound__aux,axiom,
% 5.15/5.33 ! [Ma: nat,N2: nat,M: nat] :
% 5.15/5.33 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.15/5.33 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % high_bound_aux
% 5.15/5.33 thf(fact_58_numeral__le__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.33 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_le_iff
% 5.15/5.33 thf(fact_59_numeral__le__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.33 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_le_iff
% 5.15/5.33 thf(fact_60_numeral__le__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.33 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_le_iff
% 5.15/5.33 thf(fact_61_numeral__le__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.33 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_le_iff
% 5.15/5.33 thf(fact_62_semiring__norm_I83_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( one
% 5.15/5.33 != ( bit0 @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(83)
% 5.15/5.33 thf(fact_63_semiring__norm_I85_J,axiom,
% 5.15/5.33 ! [M: num] :
% 5.15/5.33 ( ( bit0 @ M )
% 5.15/5.33 != one ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(85)
% 5.15/5.33 thf(fact_64_Suc__less__eq,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.15/5.33 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_less_eq
% 5.15/5.33 thf(fact_65_Suc__mono,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_mono
% 5.15/5.33 thf(fact_66_lessI,axiom,
% 5.15/5.33 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % lessI
% 5.15/5.33 thf(fact_67_semiring__norm_I88_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( bit0 @ M )
% 5.15/5.33 != ( bit1 @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(88)
% 5.15/5.33 thf(fact_68_semiring__norm_I89_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( bit1 @ M )
% 5.15/5.33 != ( bit0 @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(89)
% 5.15/5.33 thf(fact_69_semiring__norm_I84_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( one
% 5.15/5.33 != ( bit1 @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(84)
% 5.15/5.33 thf(fact_70_Suc__le__mono,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 5.15/5.33 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_le_mono
% 5.15/5.33 thf(fact_71_add__Suc__right,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 5.15/5.33 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_Suc_right
% 5.15/5.33 thf(fact_72_diff__Suc__Suc,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.15/5.33 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_Suc_Suc
% 5.15/5.33 thf(fact_73_Suc__diff__diff,axiom,
% 5.15/5.33 ! [M: nat,N2: nat,K: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 5.15/5.33 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_diff_diff
% 5.15/5.33 thf(fact_74_mem__Collect__eq,axiom,
% 5.15/5.33 ! [A: real,P: real > $o] :
% 5.15/5.33 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.15/5.33 = ( P @ A ) ) ).
% 5.15/5.33
% 5.15/5.33 % mem_Collect_eq
% 5.15/5.33 thf(fact_75_mem__Collect__eq,axiom,
% 5.15/5.33 ! [A: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.15/5.33 ( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P ) )
% 5.15/5.33 = ( P @ A ) ) ).
% 5.15/5.33
% 5.15/5.33 % mem_Collect_eq
% 5.15/5.33 thf(fact_76_mem__Collect__eq,axiom,
% 5.15/5.33 ! [A: complex,P: complex > $o] :
% 5.15/5.33 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.15/5.33 = ( P @ A ) ) ).
% 5.15/5.33
% 5.15/5.33 % mem_Collect_eq
% 5.15/5.33 thf(fact_77_mem__Collect__eq,axiom,
% 5.15/5.33 ! [A: set_nat,P: set_nat > $o] :
% 5.15/5.33 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 5.15/5.33 = ( P @ A ) ) ).
% 5.15/5.33
% 5.15/5.33 % mem_Collect_eq
% 5.15/5.33 thf(fact_78_mem__Collect__eq,axiom,
% 5.15/5.33 ! [A: nat,P: nat > $o] :
% 5.15/5.33 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.15/5.33 = ( P @ A ) ) ).
% 5.15/5.33
% 5.15/5.33 % mem_Collect_eq
% 5.15/5.33 thf(fact_79_mem__Collect__eq,axiom,
% 5.15/5.33 ! [A: int,P: int > $o] :
% 5.15/5.33 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.15/5.33 = ( P @ A ) ) ).
% 5.15/5.33
% 5.15/5.33 % mem_Collect_eq
% 5.15/5.33 thf(fact_80_Collect__mem__eq,axiom,
% 5.15/5.33 ! [A2: set_real] :
% 5.15/5.33 ( ( collect_real
% 5.15/5.33 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 5.15/5.33 = A2 ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_mem_eq
% 5.15/5.33 thf(fact_81_Collect__mem__eq,axiom,
% 5.15/5.33 ! [A2: set_Pr958786334691620121nt_int] :
% 5.15/5.33 ( ( collec213857154873943460nt_int
% 5.15/5.33 @ ^ [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ A2 ) )
% 5.15/5.33 = A2 ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_mem_eq
% 5.15/5.33 thf(fact_82_Collect__mem__eq,axiom,
% 5.15/5.33 ! [A2: set_complex] :
% 5.15/5.33 ( ( collect_complex
% 5.15/5.33 @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 5.15/5.33 = A2 ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_mem_eq
% 5.15/5.33 thf(fact_83_Collect__mem__eq,axiom,
% 5.15/5.33 ! [A2: set_set_nat] :
% 5.15/5.33 ( ( collect_set_nat
% 5.15/5.33 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A2 ) )
% 5.15/5.33 = A2 ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_mem_eq
% 5.15/5.33 thf(fact_84_Collect__mem__eq,axiom,
% 5.15/5.33 ! [A2: set_nat] :
% 5.15/5.33 ( ( collect_nat
% 5.15/5.33 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 5.15/5.33 = A2 ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_mem_eq
% 5.15/5.33 thf(fact_85_Collect__mem__eq,axiom,
% 5.15/5.33 ! [A2: set_int] :
% 5.15/5.33 ( ( collect_int
% 5.15/5.33 @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 5.15/5.33 = A2 ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_mem_eq
% 5.15/5.33 thf(fact_86_Collect__cong,axiom,
% 5.15/5.33 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.15/5.33 ( ! [X3: product_prod_int_int] :
% 5.15/5.33 ( ( P @ X3 )
% 5.15/5.33 = ( Q @ X3 ) )
% 5.15/5.33 => ( ( collec213857154873943460nt_int @ P )
% 5.15/5.33 = ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_cong
% 5.15/5.33 thf(fact_87_Collect__cong,axiom,
% 5.15/5.33 ! [P: complex > $o,Q: complex > $o] :
% 5.15/5.33 ( ! [X3: complex] :
% 5.15/5.33 ( ( P @ X3 )
% 5.15/5.33 = ( Q @ X3 ) )
% 5.15/5.33 => ( ( collect_complex @ P )
% 5.15/5.33 = ( collect_complex @ Q ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_cong
% 5.15/5.33 thf(fact_88_Collect__cong,axiom,
% 5.15/5.33 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.15/5.33 ( ! [X3: set_nat] :
% 5.15/5.33 ( ( P @ X3 )
% 5.15/5.33 = ( Q @ X3 ) )
% 5.15/5.33 => ( ( collect_set_nat @ P )
% 5.15/5.33 = ( collect_set_nat @ Q ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_cong
% 5.15/5.33 thf(fact_89_Collect__cong,axiom,
% 5.15/5.33 ! [P: nat > $o,Q: nat > $o] :
% 5.15/5.33 ( ! [X3: nat] :
% 5.15/5.33 ( ( P @ X3 )
% 5.15/5.33 = ( Q @ X3 ) )
% 5.15/5.33 => ( ( collect_nat @ P )
% 5.15/5.33 = ( collect_nat @ Q ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_cong
% 5.15/5.33 thf(fact_90_Collect__cong,axiom,
% 5.15/5.33 ! [P: int > $o,Q: int > $o] :
% 5.15/5.33 ( ! [X3: int] :
% 5.15/5.33 ( ( P @ X3 )
% 5.15/5.33 = ( Q @ X3 ) )
% 5.15/5.33 => ( ( collect_int @ P )
% 5.15/5.33 = ( collect_int @ Q ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Collect_cong
% 5.15/5.33 thf(fact_91_nat__add__left__cancel__le,axiom,
% 5.15/5.33 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.15/5.33 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_add_left_cancel_le
% 5.15/5.33 thf(fact_92_diff__diff__cancel,axiom,
% 5.15/5.33 ! [I: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ N2 )
% 5.15/5.33 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I ) )
% 5.15/5.33 = I ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_diff_cancel
% 5.15/5.33 thf(fact_93_diff__diff__left,axiom,
% 5.15/5.33 ! [I: nat,J: nat,K: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.15/5.33 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_diff_left
% 5.15/5.33 thf(fact_94_semiring__norm_I6_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(6)
% 5.15/5.33 thf(fact_95__C4_Ohyps_C_I2_J,axiom,
% 5.15/5.33 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.15/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.15/5.33
% 5.15/5.33 % "4.hyps"(2)
% 5.15/5.33 thf(fact_96_semiring__norm_I78_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(78)
% 5.15/5.33 thf(fact_97_semiring__norm_I75_J,axiom,
% 5.15/5.33 ! [M: num] :
% 5.15/5.33 ~ ( ord_less_num @ M @ one ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(75)
% 5.15/5.33 thf(fact_98_semiring__norm_I80_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(80)
% 5.15/5.33 thf(fact_99_diff__Suc__1,axiom,
% 5.15/5.33 ! [N2: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.15/5.33 = N2 ) ).
% 5.15/5.33
% 5.15/5.33 % diff_Suc_1
% 5.15/5.33 thf(fact_100_Nat_Odiff__diff__right,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.15/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.diff_diff_right
% 5.15/5.33 thf(fact_101_Nat_Oadd__diff__assoc2,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.15/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.add_diff_assoc2
% 5.15/5.33 thf(fact_102_Nat_Oadd__diff__assoc,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.15/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.add_diff_assoc
% 5.15/5.33 thf(fact_103_add__numeral__left,axiom,
% 5.15/5.33 ! [V: num,W: num,Z: complex] :
% 5.15/5.33 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.15/5.33 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_numeral_left
% 5.15/5.33 thf(fact_104_add__numeral__left,axiom,
% 5.15/5.33 ! [V: num,W: num,Z: real] :
% 5.15/5.33 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.15/5.33 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_numeral_left
% 5.15/5.33 thf(fact_105_add__numeral__left,axiom,
% 5.15/5.33 ! [V: num,W: num,Z: rat] :
% 5.15/5.33 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.15/5.33 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_numeral_left
% 5.15/5.33 thf(fact_106_add__numeral__left,axiom,
% 5.15/5.33 ! [V: num,W: num,Z: nat] :
% 5.15/5.33 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.15/5.33 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_numeral_left
% 5.15/5.33 thf(fact_107_add__numeral__left,axiom,
% 5.15/5.33 ! [V: num,W: num,Z: int] :
% 5.15/5.33 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.15/5.33 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_numeral_left
% 5.15/5.33 thf(fact_108_numeral__plus__numeral,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.33 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_numeral
% 5.15/5.33 thf(fact_109_numeral__plus__numeral,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_numeral
% 5.15/5.33 thf(fact_110_numeral__plus__numeral,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_numeral
% 5.15/5.33 thf(fact_111_numeral__plus__numeral,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_numeral
% 5.15/5.33 thf(fact_112_numeral__plus__numeral,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_plus_numeral
% 5.15/5.33 thf(fact_113_semiring__norm_I2_J,axiom,
% 5.15/5.33 ( ( plus_plus_num @ one @ one )
% 5.15/5.33 = ( bit0 @ one ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(2)
% 5.15/5.33 thf(fact_114_semiring__norm_I7_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(7)
% 5.15/5.33 thf(fact_115_semiring__norm_I9_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(9)
% 5.15/5.33 thf(fact_116_numeral__less__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_less_iff
% 5.15/5.33 thf(fact_117_numeral__less__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_less_iff
% 5.15/5.33 thf(fact_118_numeral__less__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_less_iff
% 5.15/5.33 thf(fact_119_numeral__less__iff,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_less_iff
% 5.15/5.33 thf(fact_120_semiring__norm_I76_J,axiom,
% 5.15/5.33 ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(76)
% 5.15/5.33 thf(fact_121_semiring__norm_I81_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(81)
% 5.15/5.33 thf(fact_122_semiring__norm_I77_J,axiom,
% 5.15/5.33 ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(77)
% 5.15/5.33 thf(fact_123_numeral__le__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 5.15/5.33 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_le_one_iff
% 5.15/5.33 thf(fact_124_numeral__le__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 5.15/5.33 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_le_one_iff
% 5.15/5.33 thf(fact_125_numeral__le__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.15/5.33 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_le_one_iff
% 5.15/5.33 thf(fact_126_numeral__le__one__iff,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.15/5.33 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_le_one_iff
% 5.15/5.33 thf(fact_127_diff__Suc__diff__eq2,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.15/5.33 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_Suc_diff_eq2
% 5.15/5.33 thf(fact_128_diff__Suc__diff__eq1,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.15/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_Suc_diff_eq1
% 5.15/5.33 thf(fact_129_Suc__numeral,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.33 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_numeral
% 5.15/5.33 thf(fact_130_semiring__norm_I3_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( bit1 @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(3)
% 5.15/5.33 thf(fact_131_semiring__norm_I4_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(4)
% 5.15/5.33 thf(fact_132_semiring__norm_I5_J,axiom,
% 5.15/5.33 ! [M: num] :
% 5.15/5.33 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.15/5.33 = ( bit1 @ M ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(5)
% 5.15/5.33 thf(fact_133_semiring__norm_I8_J,axiom,
% 5.15/5.33 ! [M: num] :
% 5.15/5.33 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.15/5.33 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(8)
% 5.15/5.33 thf(fact_134_semiring__norm_I10_J,axiom,
% 5.15/5.33 ! [M: num,N2: num] :
% 5.15/5.33 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % semiring_norm(10)
% 5.15/5.33 thf(fact_135_add__2__eq__Suc_H,axiom,
% 5.15/5.33 ! [N2: nat] :
% 5.15/5.33 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.33 = ( suc @ ( suc @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_2_eq_Suc'
% 5.15/5.33 thf(fact_136_add__2__eq__Suc,axiom,
% 5.15/5.33 ! [N2: nat] :
% 5.15/5.33 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.33 = ( suc @ ( suc @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_2_eq_Suc
% 5.15/5.33 thf(fact_137_Suc__1,axiom,
% 5.15/5.33 ( ( suc @ one_one_nat )
% 5.15/5.33 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_1
% 5.15/5.33 thf(fact_138_div2__Suc__Suc,axiom,
% 5.15/5.33 ! [M: nat] :
% 5.15/5.33 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.33 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % div2_Suc_Suc
% 5.15/5.33 thf(fact_139_Suc__div__eq__add3__div__numeral,axiom,
% 5.15/5.33 ! [M: nat,V: num] :
% 5.15/5.33 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.15/5.33 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_div_eq_add3_div_numeral
% 5.15/5.33 thf(fact_140_div__Suc__eq__div__add3,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.15/5.33 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % div_Suc_eq_div_add3
% 5.15/5.33 thf(fact_141_lift__Suc__mono__le,axiom,
% 5.15/5.33 ! [F: nat > set_nat,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_le
% 5.15/5.33 thf(fact_142_lift__Suc__mono__le,axiom,
% 5.15/5.33 ! [F: nat > rat,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_le
% 5.15/5.33 thf(fact_143_lift__Suc__mono__le,axiom,
% 5.15/5.33 ! [F: nat > num,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_num @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_le
% 5.15/5.33 thf(fact_144_lift__Suc__mono__le,axiom,
% 5.15/5.33 ! [F: nat > nat,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_le
% 5.15/5.33 thf(fact_145_lift__Suc__mono__le,axiom,
% 5.15/5.33 ! [F: nat > int,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_le
% 5.15/5.33 thf(fact_146_lift__Suc__antimono__le,axiom,
% 5.15/5.33 ! [F: nat > set_nat,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_set_nat @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_antimono_le
% 5.15/5.33 thf(fact_147_lift__Suc__antimono__le,axiom,
% 5.15/5.33 ! [F: nat > rat,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_rat @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_antimono_le
% 5.15/5.33 thf(fact_148_lift__Suc__antimono__le,axiom,
% 5.15/5.33 ! [F: nat > num,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_num @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_antimono_le
% 5.15/5.33 thf(fact_149_lift__Suc__antimono__le,axiom,
% 5.15/5.33 ! [F: nat > nat,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_antimono_le
% 5.15/5.33 thf(fact_150_lift__Suc__antimono__le,axiom,
% 5.15/5.33 ! [F: nat > int,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_antimono_le
% 5.15/5.33 thf(fact_151_Suc__leD,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_leD
% 5.15/5.33 thf(fact_152_le__SucE,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.33 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( M
% 5.15/5.33 = ( suc @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_SucE
% 5.15/5.33 thf(fact_153_le__SucI,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_SucI
% 5.15/5.33 thf(fact_154_le__refl,axiom,
% 5.15/5.33 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 5.15/5.33
% 5.15/5.33 % le_refl
% 5.15/5.33 thf(fact_155_Suc__le__D,axiom,
% 5.15/5.33 ! [N2: nat,M2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M2 )
% 5.15/5.33 => ? [M3: nat] :
% 5.15/5.33 ( M2
% 5.15/5.33 = ( suc @ M3 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_le_D
% 5.15/5.33 thf(fact_156_le__trans,axiom,
% 5.15/5.33 ! [I: nat,J: nat,K: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ( ord_less_eq_nat @ J @ K )
% 5.15/5.33 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_trans
% 5.15/5.33 thf(fact_157_eq__imp__le,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( M = N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % eq_imp_le
% 5.15/5.33 thf(fact_158_le__Suc__eq,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.33 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 | ( M
% 5.15/5.33 = ( suc @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_Suc_eq
% 5.15/5.33 thf(fact_159_Suc__inject,axiom,
% 5.15/5.33 ! [X: nat,Y: nat] :
% 5.15/5.33 ( ( ( suc @ X )
% 5.15/5.33 = ( suc @ Y ) )
% 5.15/5.33 => ( X = Y ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_inject
% 5.15/5.33 thf(fact_160_le__antisym,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.33 => ( M = N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_antisym
% 5.15/5.33 thf(fact_161_Suc__diff__le,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.33 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.15/5.33 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_diff_le
% 5.15/5.33 thf(fact_162_eq__diff__iff,axiom,
% 5.15/5.33 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ M )
% 5.15/5.33 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.33 => ( ( ( minus_minus_nat @ M @ K )
% 5.15/5.33 = ( minus_minus_nat @ N2 @ K ) )
% 5.15/5.33 = ( M = N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % eq_diff_iff
% 5.15/5.33 thf(fact_163_le__diff__iff,axiom,
% 5.15/5.33 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ M )
% 5.15/5.33 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.33 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.15/5.33 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_diff_iff
% 5.15/5.33 thf(fact_164_n__not__Suc__n,axiom,
% 5.15/5.33 ! [N2: nat] :
% 5.15/5.33 ( N2
% 5.15/5.33 != ( suc @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % n_not_Suc_n
% 5.15/5.33 thf(fact_165_diff__commute,axiom,
% 5.15/5.33 ! [I: nat,J: nat,K: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.15/5.33 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_commute
% 5.15/5.33 thf(fact_166_Nat_Odiff__diff__eq,axiom,
% 5.15/5.33 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ M )
% 5.15/5.33 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.33 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.15/5.33 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.diff_diff_eq
% 5.15/5.33 thf(fact_167_diff__le__mono,axiom,
% 5.15/5.33 ! [M: nat,N2: nat,L: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_le_mono
% 5.15/5.33 thf(fact_168_diff__le__self,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 5.15/5.33
% 5.15/5.33 % diff_le_self
% 5.15/5.33 thf(fact_169_le__diff__iff_H,axiom,
% 5.15/5.33 ! [A: nat,C: nat,B: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ A @ C )
% 5.15/5.33 => ( ( ord_less_eq_nat @ B @ C )
% 5.15/5.33 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.15/5.33 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_diff_iff'
% 5.15/5.33 thf(fact_170_diff__le__mono2,axiom,
% 5.15/5.33 ! [M: nat,N2: nat,L: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_le_mono2
% 5.15/5.33 thf(fact_171_nat__le__linear,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_le_linear
% 5.15/5.33 thf(fact_172_Suc__n__not__le__n,axiom,
% 5.15/5.33 ! [N2: nat] :
% 5.15/5.33 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_n_not_le_n
% 5.15/5.33 thf(fact_173_not__less__eq__eq,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 5.15/5.33 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 5.15/5.33
% 5.15/5.33 % not_less_eq_eq
% 5.15/5.33 thf(fact_174_full__nat__induct,axiom,
% 5.15/5.33 ! [P: nat > $o,N2: nat] :
% 5.15/5.33 ( ! [N: nat] :
% 5.15/5.33 ( ! [M4: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( suc @ M4 ) @ N )
% 5.15/5.33 => ( P @ M4 ) )
% 5.15/5.33 => ( P @ N ) )
% 5.15/5.33 => ( P @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % full_nat_induct
% 5.15/5.33 thf(fact_175_zero__induct__lemma,axiom,
% 5.15/5.33 ! [P: nat > $o,K: nat,I: nat] :
% 5.15/5.33 ( ( P @ K )
% 5.15/5.33 => ( ! [N: nat] :
% 5.15/5.33 ( ( P @ ( suc @ N ) )
% 5.15/5.33 => ( P @ N ) )
% 5.15/5.33 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % zero_induct_lemma
% 5.15/5.33 thf(fact_176_Nat_Oex__has__greatest__nat,axiom,
% 5.15/5.33 ! [P: nat > $o,K: nat,B: nat] :
% 5.15/5.33 ( ( P @ K )
% 5.15/5.33 => ( ! [Y3: nat] :
% 5.15/5.33 ( ( P @ Y3 )
% 5.15/5.33 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.15/5.33 => ? [X3: nat] :
% 5.15/5.33 ( ( P @ X3 )
% 5.15/5.33 & ! [Y4: nat] :
% 5.15/5.33 ( ( P @ Y4 )
% 5.15/5.33 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.ex_has_greatest_nat
% 5.15/5.33 thf(fact_177_nat__induct__at__least,axiom,
% 5.15/5.33 ! [M: nat,N2: nat,P: nat > $o] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ( P @ M )
% 5.15/5.33 => ( ! [N: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N )
% 5.15/5.33 => ( ( P @ N )
% 5.15/5.33 => ( P @ ( suc @ N ) ) ) )
% 5.15/5.33 => ( P @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_induct_at_least
% 5.15/5.33 thf(fact_178_transitive__stepwise__le,axiom,
% 5.15/5.33 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 5.15/5.33 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 5.15/5.33 ( ( R @ X3 @ Y3 )
% 5.15/5.33 => ( ( R @ Y3 @ Z2 )
% 5.15/5.33 => ( R @ X3 @ Z2 ) ) )
% 5.15/5.33 => ( ! [N: nat] : ( R @ N @ ( suc @ N ) )
% 5.15/5.33 => ( R @ M @ N2 ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % transitive_stepwise_le
% 5.15/5.33 thf(fact_179_diff__less__mono,axiom,
% 5.15/5.33 ! [A: nat,B: nat,C: nat] :
% 5.15/5.33 ( ( ord_less_nat @ A @ B )
% 5.15/5.33 => ( ( ord_less_eq_nat @ C @ A )
% 5.15/5.33 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_less_mono
% 5.15/5.33 thf(fact_180_less__diff__iff,axiom,
% 5.15/5.33 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ M )
% 5.15/5.33 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.33 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.15/5.33 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_diff_iff
% 5.15/5.33 thf(fact_181_le__imp__less__Suc,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_imp_less_Suc
% 5.15/5.33 thf(fact_182_less__eq__Suc__le,axiom,
% 5.15/5.33 ( ord_less_nat
% 5.15/5.33 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_eq_Suc_le
% 5.15/5.33 thf(fact_183_less__Suc__eq__le,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.15/5.33 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_Suc_eq_le
% 5.15/5.33 thf(fact_184_le__less__Suc__eq,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.15/5.33 = ( N2 = M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_less_Suc_eq
% 5.15/5.33 thf(fact_185_Suc__le__lessD,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.15/5.33 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_le_lessD
% 5.15/5.33 thf(fact_186_inc__induct,axiom,
% 5.15/5.33 ! [I: nat,J: nat,P: nat > $o] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ( P @ J )
% 5.15/5.33 => ( ! [N: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ N )
% 5.15/5.33 => ( ( ord_less_nat @ N @ J )
% 5.15/5.33 => ( ( P @ ( suc @ N ) )
% 5.15/5.33 => ( P @ N ) ) ) )
% 5.15/5.33 => ( P @ I ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % inc_induct
% 5.15/5.33 thf(fact_187_dec__induct,axiom,
% 5.15/5.33 ! [I: nat,J: nat,P: nat > $o] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ( P @ I )
% 5.15/5.33 => ( ! [N: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ N )
% 5.15/5.33 => ( ( ord_less_nat @ N @ J )
% 5.15/5.33 => ( ( P @ N )
% 5.15/5.33 => ( P @ ( suc @ N ) ) ) ) )
% 5.15/5.33 => ( P @ J ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % dec_induct
% 5.15/5.33 thf(fact_188_Suc__le__eq,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.15/5.33 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_le_eq
% 5.15/5.33 thf(fact_189_Suc__leI,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_leI
% 5.15/5.33 thf(fact_190_Nat_Ole__imp__diff__is__add,axiom,
% 5.15/5.33 ! [I: nat,J: nat,K: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ( ( minus_minus_nat @ J @ I )
% 5.15/5.33 = K )
% 5.15/5.33 = ( J
% 5.15/5.33 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.le_imp_diff_is_add
% 5.15/5.33 thf(fact_191_Nat_Odiff__add__assoc2,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.15/5.33 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.diff_add_assoc2
% 5.15/5.33 thf(fact_192_Nat_Odiff__add__assoc,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.15/5.33 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.diff_add_assoc
% 5.15/5.33 thf(fact_193_Nat_Ole__diff__conv2,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.15/5.33 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.le_diff_conv2
% 5.15/5.33 thf(fact_194_le__diff__conv,axiom,
% 5.15/5.33 ! [J: nat,K: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.15/5.33 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_diff_conv
% 5.15/5.33 thf(fact_195_Suc__div__le__mono,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_div_le_mono
% 5.15/5.33 thf(fact_196_add__One__commute,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( plus_plus_num @ one @ N2 )
% 5.15/5.33 = ( plus_plus_num @ N2 @ one ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_One_commute
% 5.15/5.33 thf(fact_197_le__numeral__extra_I4_J,axiom,
% 5.15/5.33 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.15/5.33
% 5.15/5.33 % le_numeral_extra(4)
% 5.15/5.33 thf(fact_198_le__numeral__extra_I4_J,axiom,
% 5.15/5.33 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.15/5.33
% 5.15/5.33 % le_numeral_extra(4)
% 5.15/5.33 thf(fact_199_le__numeral__extra_I4_J,axiom,
% 5.15/5.33 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.15/5.33
% 5.15/5.33 % le_numeral_extra(4)
% 5.15/5.33 thf(fact_200_le__numeral__extra_I4_J,axiom,
% 5.15/5.33 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.15/5.33
% 5.15/5.33 % le_numeral_extra(4)
% 5.15/5.33 thf(fact_201_less__mono__imp__le__mono,axiom,
% 5.15/5.33 ! [F: nat > nat,I: nat,J: nat] :
% 5.15/5.33 ( ! [I2: nat,J2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I2 @ J2 )
% 5.15/5.33 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 5.15/5.33 => ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_mono_imp_le_mono
% 5.15/5.33 thf(fact_202_le__neq__implies__less,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ( M != N2 )
% 5.15/5.33 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_neq_implies_less
% 5.15/5.33 thf(fact_203_less__or__eq__imp__le,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 | ( M = N2 ) )
% 5.15/5.33 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_or_eq_imp_le
% 5.15/5.33 thf(fact_204_le__eq__less__or__eq,axiom,
% 5.15/5.33 ( ord_less_eq_nat
% 5.15/5.33 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M5 @ N3 )
% 5.15/5.33 | ( M5 = N3 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_eq_less_or_eq
% 5.15/5.33 thf(fact_205_less__imp__le__nat,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_imp_le_nat
% 5.15/5.33 thf(fact_206_nat__less__le,axiom,
% 5.15/5.33 ( ord_less_nat
% 5.15/5.33 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.33 & ( M5 != N3 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_less_le
% 5.15/5.33 thf(fact_207_nat__le__iff__add,axiom,
% 5.15/5.33 ( ord_less_eq_nat
% 5.15/5.33 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.33 ? [K2: nat] :
% 5.15/5.33 ( N3
% 5.15/5.33 = ( plus_plus_nat @ M5 @ K2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_le_iff_add
% 5.15/5.33 thf(fact_208_trans__le__add2,axiom,
% 5.15/5.33 ! [I: nat,J: nat,M: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % trans_le_add2
% 5.15/5.33 thf(fact_209_trans__le__add1,axiom,
% 5.15/5.33 ! [I: nat,J: nat,M: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % trans_le_add1
% 5.15/5.33 thf(fact_210_add__le__mono1,axiom,
% 5.15/5.33 ! [I: nat,J: nat,K: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_le_mono1
% 5.15/5.33 thf(fact_211_add__le__mono,axiom,
% 5.15/5.33 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.33 => ( ( ord_less_eq_nat @ K @ L )
% 5.15/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_le_mono
% 5.15/5.33 thf(fact_212_le__Suc__ex,axiom,
% 5.15/5.33 ! [K: nat,L: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ L )
% 5.15/5.33 => ? [N: nat] :
% 5.15/5.33 ( L
% 5.15/5.33 = ( plus_plus_nat @ K @ N ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_Suc_ex
% 5.15/5.33 thf(fact_213_add__leD2,axiom,
% 5.15/5.33 ! [M: nat,K: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_leD2
% 5.15/5.33 thf(fact_214_add__leD1,axiom,
% 5.15/5.33 ! [M: nat,K: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_leD1
% 5.15/5.33 thf(fact_215_le__add2,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_add2
% 5.15/5.33 thf(fact_216_le__add1,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 5.15/5.33
% 5.15/5.33 % le_add1
% 5.15/5.33 thf(fact_217_add__leE,axiom,
% 5.15/5.33 ! [M: nat,K: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.15/5.33 => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_leE
% 5.15/5.33 thf(fact_218_div__le__dividend,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 5.15/5.33
% 5.15/5.33 % div_le_dividend
% 5.15/5.33 thf(fact_219_div__le__mono,axiom,
% 5.15/5.33 ! [M: nat,N2: nat,K: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % div_le_mono
% 5.15/5.33 thf(fact_220_numeral__code_I2_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(2)
% 5.15/5.33 thf(fact_221_numeral__code_I2_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(2)
% 5.15/5.33 thf(fact_222_numeral__code_I2_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(2)
% 5.15/5.33 thf(fact_223_numeral__code_I2_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(2)
% 5.15/5.33 thf(fact_224_numeral__code_I2_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.15/5.33 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(2)
% 5.15/5.33 thf(fact_225_diff__less__Suc,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_less_Suc
% 5.15/5.33 thf(fact_226_Suc__diff__Suc,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] :
% 5.15/5.33 ( ( ord_less_nat @ N2 @ M )
% 5.15/5.33 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.33 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_diff_Suc
% 5.15/5.33 thf(fact_227_diff__Suc__eq__diff__pred,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.15/5.33 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_Suc_eq_diff_pred
% 5.15/5.33 thf(fact_228_less__diff__conv2,axiom,
% 5.15/5.33 ! [K: nat,J: nat,I: nat] :
% 5.15/5.33 ( ( ord_less_eq_nat @ K @ J )
% 5.15/5.33 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.15/5.33 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_diff_conv2
% 5.15/5.33 thf(fact_229_one__le__numeral,axiom,
% 5.15/5.33 ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_le_numeral
% 5.15/5.33 thf(fact_230_one__le__numeral,axiom,
% 5.15/5.33 ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_le_numeral
% 5.15/5.33 thf(fact_231_one__le__numeral,axiom,
% 5.15/5.33 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_le_numeral
% 5.15/5.33 thf(fact_232_one__le__numeral,axiom,
% 5.15/5.33 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % one_le_numeral
% 5.15/5.33 thf(fact_233_numeral__code_I3_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(3)
% 5.15/5.33 thf(fact_234_numeral__code_I3_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(3)
% 5.15/5.33 thf(fact_235_numeral__code_I3_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(3)
% 5.15/5.33 thf(fact_236_numeral__code_I3_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(3)
% 5.15/5.33 thf(fact_237_numeral__code_I3_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.15/5.33 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.15/5.33
% 5.15/5.33 % numeral_code(3)
% 5.15/5.33 thf(fact_238_mono__nat__linear__lb,axiom,
% 5.15/5.33 ! [F: nat > nat,M: nat,K: nat] :
% 5.15/5.33 ( ! [M3: nat,N: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M3 @ N )
% 5.15/5.33 => ( ord_less_nat @ ( F @ M3 ) @ ( F @ N ) ) )
% 5.15/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % mono_nat_linear_lb
% 5.15/5.33 thf(fact_239_add__diff__add,axiom,
% 5.15/5.33 ! [A: complex,C: complex,B: complex,D: complex] :
% 5.15/5.33 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ D ) )
% 5.15/5.33 = ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ ( minus_minus_complex @ C @ D ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_diff_add
% 5.15/5.33 thf(fact_240_add__diff__add,axiom,
% 5.15/5.33 ! [A: real,C: real,B: real,D: real] :
% 5.15/5.33 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.15/5.33 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_diff_add
% 5.15/5.33 thf(fact_241_add__diff__add,axiom,
% 5.15/5.33 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.15/5.33 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.15/5.33 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_diff_add
% 5.15/5.33 thf(fact_242_add__diff__add,axiom,
% 5.15/5.33 ! [A: int,C: int,B: int,D: int] :
% 5.15/5.33 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.15/5.33 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_diff_add
% 5.15/5.33 thf(fact_243_less__imp__diff__less,axiom,
% 5.15/5.33 ! [J: nat,K: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ J @ K )
% 5.15/5.33 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_imp_diff_less
% 5.15/5.33 thf(fact_244_diff__less__mono2,axiom,
% 5.15/5.33 ! [M: nat,N2: nat,L: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ( ( ord_less_nat @ M @ L )
% 5.15/5.33 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_less_mono2
% 5.15/5.33 thf(fact_245_not__less__less__Suc__eq,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] :
% 5.15/5.33 ( ~ ( ord_less_nat @ N2 @ M )
% 5.15/5.33 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.15/5.33 = ( N2 = M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % not_less_less_Suc_eq
% 5.15/5.33 thf(fact_246_strict__inc__induct,axiom,
% 5.15/5.33 ! [I: nat,J: nat,P: nat > $o] :
% 5.15/5.33 ( ( ord_less_nat @ I @ J )
% 5.15/5.33 => ( ! [I2: nat] :
% 5.15/5.33 ( ( J
% 5.15/5.33 = ( suc @ I2 ) )
% 5.15/5.33 => ( P @ I2 ) )
% 5.15/5.33 => ( ! [I2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I2 @ J )
% 5.15/5.33 => ( ( P @ ( suc @ I2 ) )
% 5.15/5.33 => ( P @ I2 ) ) )
% 5.15/5.33 => ( P @ I ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % strict_inc_induct
% 5.15/5.33 thf(fact_247_less__Suc__induct,axiom,
% 5.15/5.33 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.15/5.33 ( ( ord_less_nat @ I @ J )
% 5.15/5.33 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 5.15/5.33 => ( ! [I2: nat,J2: nat,K3: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I2 @ J2 )
% 5.15/5.33 => ( ( ord_less_nat @ J2 @ K3 )
% 5.15/5.33 => ( ( P @ I2 @ J2 )
% 5.15/5.33 => ( ( P @ J2 @ K3 )
% 5.15/5.33 => ( P @ I2 @ K3 ) ) ) ) )
% 5.15/5.33 => ( P @ I @ J ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_Suc_induct
% 5.15/5.33 thf(fact_248_less__trans__Suc,axiom,
% 5.15/5.33 ! [I: nat,J: nat,K: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I @ J )
% 5.15/5.33 => ( ( ord_less_nat @ J @ K )
% 5.15/5.33 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_trans_Suc
% 5.15/5.33 thf(fact_249_Suc__less__SucD,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.15/5.33 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_less_SucD
% 5.15/5.33 thf(fact_250_less__antisym,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] :
% 5.15/5.33 ( ~ ( ord_less_nat @ N2 @ M )
% 5.15/5.33 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.15/5.33 => ( M = N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_antisym
% 5.15/5.33 thf(fact_251_Suc__less__eq2,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] :
% 5.15/5.33 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.33 = ( ? [M6: nat] :
% 5.15/5.33 ( ( M
% 5.15/5.33 = ( suc @ M6 ) )
% 5.15/5.33 & ( ord_less_nat @ N2 @ M6 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_less_eq2
% 5.15/5.33 thf(fact_252_All__less__Suc,axiom,
% 5.15/5.33 ! [N2: nat,P: nat > $o] :
% 5.15/5.33 ( ( ! [I3: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 5.15/5.33 => ( P @ I3 ) ) )
% 5.15/5.33 = ( ( P @ N2 )
% 5.15/5.33 & ! [I3: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I3 @ N2 )
% 5.15/5.33 => ( P @ I3 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % All_less_Suc
% 5.15/5.33 thf(fact_253_not__less__eq,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 5.15/5.33 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % not_less_eq
% 5.15/5.33 thf(fact_254_less__Suc__eq,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.15/5.33 = ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 | ( M = N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_Suc_eq
% 5.15/5.33 thf(fact_255_Ex__less__Suc,axiom,
% 5.15/5.33 ! [N2: nat,P: nat > $o] :
% 5.15/5.33 ( ( ? [I3: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 5.15/5.33 & ( P @ I3 ) ) )
% 5.15/5.33 = ( ( P @ N2 )
% 5.15/5.33 | ? [I3: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I3 @ N2 )
% 5.15/5.33 & ( P @ I3 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Ex_less_Suc
% 5.15/5.33 thf(fact_256_less__SucI,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_SucI
% 5.15/5.33 thf(fact_257_less__SucE,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.15/5.33 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ( M = N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_SucE
% 5.15/5.33 thf(fact_258_Suc__lessI,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ( ( ( suc @ M )
% 5.15/5.33 != N2 )
% 5.15/5.33 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_lessI
% 5.15/5.33 thf(fact_259_Suc__lessE,axiom,
% 5.15/5.33 ! [I: nat,K: nat] :
% 5.15/5.33 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.15/5.33 => ~ ! [J2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I @ J2 )
% 5.15/5.33 => ( K
% 5.15/5.33 != ( suc @ J2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_lessE
% 5.15/5.33 thf(fact_260_Suc__lessD,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 5.15/5.33 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_lessD
% 5.15/5.33 thf(fact_261_Nat_OlessE,axiom,
% 5.15/5.33 ! [I: nat,K: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I @ K )
% 5.15/5.33 => ( ( K
% 5.15/5.33 != ( suc @ I ) )
% 5.15/5.33 => ~ ! [J2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I @ J2 )
% 5.15/5.33 => ( K
% 5.15/5.33 != ( suc @ J2 ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.lessE
% 5.15/5.33 thf(fact_262_diff__add__inverse2,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 5.15/5.33 = M ) ).
% 5.15/5.33
% 5.15/5.33 % diff_add_inverse2
% 5.15/5.33 thf(fact_263_diff__add__inverse,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 5.15/5.33 = M ) ).
% 5.15/5.33
% 5.15/5.33 % diff_add_inverse
% 5.15/5.33 thf(fact_264_diff__cancel2,axiom,
% 5.15/5.33 ! [M: nat,K: nat,N2: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.15/5.33 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % diff_cancel2
% 5.15/5.33 thf(fact_265_Nat_Odiff__cancel,axiom,
% 5.15/5.33 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.15/5.33 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Nat.diff_cancel
% 5.15/5.33 thf(fact_266_add__Suc__shift,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.15/5.33 = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_Suc_shift
% 5.15/5.33 thf(fact_267_add__Suc,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.15/5.33 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_Suc
% 5.15/5.33 thf(fact_268_nat__arith_Osuc1,axiom,
% 5.15/5.33 ! [A2: nat,K: nat,A: nat] :
% 5.15/5.33 ( ( A2
% 5.15/5.33 = ( plus_plus_nat @ K @ A ) )
% 5.15/5.33 => ( ( suc @ A2 )
% 5.15/5.33 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_arith.suc1
% 5.15/5.33 thf(fact_269_Suc__nat__number__of__add,axiom,
% 5.15/5.33 ! [V: num,N2: nat] :
% 5.15/5.33 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 5.15/5.33 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_nat_number_of_add
% 5.15/5.33 thf(fact_270_minNull__bound,axiom,
% 5.15/5.33 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 5.15/5.33
% 5.15/5.33 % minNull_bound
% 5.15/5.33 thf(fact_271_is__num__normalize_I1_J,axiom,
% 5.15/5.33 ! [A: real,B: real,C: real] :
% 5.15/5.33 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.15/5.33 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % is_num_normalize(1)
% 5.15/5.33 thf(fact_272_is__num__normalize_I1_J,axiom,
% 5.15/5.33 ! [A: rat,B: rat,C: rat] :
% 5.15/5.33 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.15/5.33 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % is_num_normalize(1)
% 5.15/5.33 thf(fact_273_is__num__normalize_I1_J,axiom,
% 5.15/5.33 ! [A: int,B: int,C: int] :
% 5.15/5.33 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.33 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % is_num_normalize(1)
% 5.15/5.33 thf(fact_274_is__num__normalize_I1_J,axiom,
% 5.15/5.33 ! [A: complex,B: complex,C: complex] :
% 5.15/5.33 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.15/5.33 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % is_num_normalize(1)
% 5.15/5.33 thf(fact_275_linorder__neqE__nat,axiom,
% 5.15/5.33 ! [X: nat,Y: nat] :
% 5.15/5.33 ( ( X != Y )
% 5.15/5.33 => ( ~ ( ord_less_nat @ X @ Y )
% 5.15/5.33 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % linorder_neqE_nat
% 5.15/5.33 thf(fact_276_infinite__descent,axiom,
% 5.15/5.33 ! [P: nat > $o,N2: nat] :
% 5.15/5.33 ( ! [N: nat] :
% 5.15/5.33 ( ~ ( P @ N )
% 5.15/5.33 => ? [M4: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M4 @ N )
% 5.15/5.33 & ~ ( P @ M4 ) ) )
% 5.15/5.33 => ( P @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % infinite_descent
% 5.15/5.33 thf(fact_277_nat__less__induct,axiom,
% 5.15/5.33 ! [P: nat > $o,N2: nat] :
% 5.15/5.33 ( ! [N: nat] :
% 5.15/5.33 ( ! [M4: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M4 @ N )
% 5.15/5.33 => ( P @ M4 ) )
% 5.15/5.33 => ( P @ N ) )
% 5.15/5.33 => ( P @ N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_less_induct
% 5.15/5.33 thf(fact_278_less__irrefl__nat,axiom,
% 5.15/5.33 ! [N2: nat] :
% 5.15/5.33 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.15/5.33
% 5.15/5.33 % less_irrefl_nat
% 5.15/5.33 thf(fact_279_less__not__refl3,axiom,
% 5.15/5.33 ! [S: nat,T: nat] :
% 5.15/5.33 ( ( ord_less_nat @ S @ T )
% 5.15/5.33 => ( S != T ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_not_refl3
% 5.15/5.33 thf(fact_280_less__not__refl2,axiom,
% 5.15/5.33 ! [N2: nat,M: nat] :
% 5.15/5.33 ( ( ord_less_nat @ N2 @ M )
% 5.15/5.33 => ( M != N2 ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_not_refl2
% 5.15/5.33 thf(fact_281_less__not__refl,axiom,
% 5.15/5.33 ! [N2: nat] :
% 5.15/5.33 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.15/5.33
% 5.15/5.33 % less_not_refl
% 5.15/5.33 thf(fact_282_nat__neq__iff,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( M != N2 )
% 5.15/5.33 = ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % nat_neq_iff
% 5.15/5.33 thf(fact_283_size__neq__size__imp__neq,axiom,
% 5.15/5.33 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 5.15/5.33 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 5.15/5.33 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 5.15/5.33 => ( X != Y ) ) ).
% 5.15/5.33
% 5.15/5.33 % size_neq_size_imp_neq
% 5.15/5.33 thf(fact_284_size__neq__size__imp__neq,axiom,
% 5.15/5.33 ! [X: num,Y: num] :
% 5.15/5.33 ( ( ( size_size_num @ X )
% 5.15/5.33 != ( size_size_num @ Y ) )
% 5.15/5.33 => ( X != Y ) ) ).
% 5.15/5.33
% 5.15/5.33 % size_neq_size_imp_neq
% 5.15/5.33 thf(fact_285_size__neq__size__imp__neq,axiom,
% 5.15/5.33 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.15/5.33 ( ( ( size_size_VEBT_VEBT @ X )
% 5.15/5.33 != ( size_size_VEBT_VEBT @ Y ) )
% 5.15/5.33 => ( X != Y ) ) ).
% 5.15/5.33
% 5.15/5.33 % size_neq_size_imp_neq
% 5.15/5.33 thf(fact_286_size__neq__size__imp__neq,axiom,
% 5.15/5.33 ! [X: list_o,Y: list_o] :
% 5.15/5.33 ( ( ( size_size_list_o @ X )
% 5.15/5.33 != ( size_size_list_o @ Y ) )
% 5.15/5.33 => ( X != Y ) ) ).
% 5.15/5.33
% 5.15/5.33 % size_neq_size_imp_neq
% 5.15/5.33 thf(fact_287_size__neq__size__imp__neq,axiom,
% 5.15/5.33 ! [X: list_int,Y: list_int] :
% 5.15/5.33 ( ( ( size_size_list_int @ X )
% 5.15/5.33 != ( size_size_list_int @ Y ) )
% 5.15/5.33 => ( X != Y ) ) ).
% 5.15/5.33
% 5.15/5.33 % size_neq_size_imp_neq
% 5.15/5.33 thf(fact_288_lift__Suc__mono__less__iff,axiom,
% 5.15/5.33 ! [F: nat > real,N2: nat,M: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 5.15/5.33 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less_iff
% 5.15/5.33 thf(fact_289_lift__Suc__mono__less__iff,axiom,
% 5.15/5.33 ! [F: nat > rat,N2: nat,M: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 5.15/5.33 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less_iff
% 5.15/5.33 thf(fact_290_lift__Suc__mono__less__iff,axiom,
% 5.15/5.33 ! [F: nat > num,N2: nat,M: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_num @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 5.15/5.33 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less_iff
% 5.15/5.33 thf(fact_291_lift__Suc__mono__less__iff,axiom,
% 5.15/5.33 ! [F: nat > nat,N2: nat,M: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 5.15/5.33 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less_iff
% 5.15/5.33 thf(fact_292_lift__Suc__mono__less__iff,axiom,
% 5.15/5.33 ! [F: nat > int,N2: nat,M: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 5.15/5.33 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less_iff
% 5.15/5.33 thf(fact_293_lift__Suc__mono__less,axiom,
% 5.15/5.33 ! [F: nat > real,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_real @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less
% 5.15/5.33 thf(fact_294_lift__Suc__mono__less,axiom,
% 5.15/5.33 ! [F: nat > rat,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less
% 5.15/5.33 thf(fact_295_lift__Suc__mono__less,axiom,
% 5.15/5.33 ! [F: nat > num,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_num @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_num @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less
% 5.15/5.33 thf(fact_296_lift__Suc__mono__less,axiom,
% 5.15/5.33 ! [F: nat > nat,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less
% 5.15/5.33 thf(fact_297_lift__Suc__mono__less,axiom,
% 5.15/5.33 ! [F: nat > int,N2: nat,N4: nat] :
% 5.15/5.33 ( ! [N: nat] : ( ord_less_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.33 => ( ( ord_less_nat @ N2 @ N4 )
% 5.15/5.33 => ( ord_less_int @ ( F @ N2 ) @ ( F @ N4 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % lift_Suc_mono_less
% 5.15/5.33 thf(fact_298_add__diff__inverse__nat,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ~ ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.33 = M ) ) ).
% 5.15/5.33
% 5.15/5.33 % add_diff_inverse_nat
% 5.15/5.33 thf(fact_299_less__diff__conv,axiom,
% 5.15/5.33 ! [I: nat,J: nat,K: nat] :
% 5.15/5.33 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.15/5.33 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_diff_conv
% 5.15/5.33 thf(fact_300_less__imp__Suc__add,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ? [K3: nat] :
% 5.15/5.33 ( N2
% 5.15/5.33 = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_imp_Suc_add
% 5.15/5.33 thf(fact_301_less__iff__Suc__add,axiom,
% 5.15/5.33 ( ord_less_nat
% 5.15/5.33 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.33 ? [K2: nat] :
% 5.15/5.33 ( N3
% 5.15/5.33 = ( suc @ ( plus_plus_nat @ M5 @ K2 ) ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_iff_Suc_add
% 5.15/5.33 thf(fact_302_less__add__Suc2,axiom,
% 5.15/5.33 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_add_Suc2
% 5.15/5.33 thf(fact_303_less__add__Suc1,axiom,
% 5.15/5.33 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_add_Suc1
% 5.15/5.33 thf(fact_304_less__natE,axiom,
% 5.15/5.33 ! [M: nat,N2: nat] :
% 5.15/5.33 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.33 => ~ ! [Q2: nat] :
% 5.15/5.33 ( N2
% 5.15/5.33 != ( suc @ ( plus_plus_nat @ M @ Q2 ) ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % less_natE
% 5.15/5.33 thf(fact_305_Suc__eq__plus1__left,axiom,
% 5.15/5.33 ( suc
% 5.15/5.33 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_eq_plus1_left
% 5.15/5.33 thf(fact_306_plus__1__eq__Suc,axiom,
% 5.15/5.33 ( ( plus_plus_nat @ one_one_nat )
% 5.15/5.33 = suc ) ).
% 5.15/5.33
% 5.15/5.33 % plus_1_eq_Suc
% 5.15/5.33 thf(fact_307_Suc__eq__plus1,axiom,
% 5.15/5.33 ( suc
% 5.15/5.33 = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 5.15/5.33
% 5.15/5.33 % Suc_eq_plus1
% 5.15/5.33 thf(fact_308_eval__nat__numeral_I3_J,axiom,
% 5.15/5.33 ! [N2: num] :
% 5.15/5.33 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % eval_nat_numeral(3)
% 5.15/5.34 thf(fact_309_less__numeral__extra_I4_J,axiom,
% 5.15/5.34 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.15/5.34
% 5.15/5.34 % less_numeral_extra(4)
% 5.15/5.34 thf(fact_310_less__numeral__extra_I4_J,axiom,
% 5.15/5.34 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.15/5.34
% 5.15/5.34 % less_numeral_extra(4)
% 5.15/5.34 thf(fact_311_less__numeral__extra_I4_J,axiom,
% 5.15/5.34 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.15/5.34
% 5.15/5.34 % less_numeral_extra(4)
% 5.15/5.34 thf(fact_312_less__numeral__extra_I4_J,axiom,
% 5.15/5.34 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.15/5.34
% 5.15/5.34 % less_numeral_extra(4)
% 5.15/5.34 thf(fact_313_less__add__eq__less,axiom,
% 5.15/5.34 ! [K: nat,L: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ K @ L )
% 5.15/5.34 => ( ( ( plus_plus_nat @ M @ L )
% 5.15/5.34 = ( plus_plus_nat @ K @ N2 ) )
% 5.15/5.34 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_eq_less
% 5.15/5.34 thf(fact_314_trans__less__add2,axiom,
% 5.15/5.34 ! [I: nat,J: nat,M: nat] :
% 5.15/5.34 ( ( ord_less_nat @ I @ J )
% 5.15/5.34 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % trans_less_add2
% 5.15/5.34 thf(fact_315_trans__less__add1,axiom,
% 5.15/5.34 ! [I: nat,J: nat,M: nat] :
% 5.15/5.34 ( ( ord_less_nat @ I @ J )
% 5.15/5.34 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % trans_less_add1
% 5.15/5.34 thf(fact_316_add__less__mono1,axiom,
% 5.15/5.34 ! [I: nat,J: nat,K: nat] :
% 5.15/5.34 ( ( ord_less_nat @ I @ J )
% 5.15/5.34 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_less_mono1
% 5.15/5.34 thf(fact_317_not__add__less2,axiom,
% 5.15/5.34 ! [J: nat,I: nat] :
% 5.15/5.34 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.15/5.34
% 5.15/5.34 % not_add_less2
% 5.15/5.34 thf(fact_318_not__add__less1,axiom,
% 5.15/5.34 ! [I: nat,J: nat] :
% 5.15/5.34 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.15/5.34
% 5.15/5.34 % not_add_less1
% 5.15/5.34 thf(fact_319_add__less__mono,axiom,
% 5.15/5.34 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.34 ( ( ord_less_nat @ I @ J )
% 5.15/5.34 => ( ( ord_less_nat @ K @ L )
% 5.15/5.34 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_less_mono
% 5.15/5.34 thf(fact_320_add__lessD1,axiom,
% 5.15/5.34 ! [I: nat,J: nat,K: nat] :
% 5.15/5.34 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.15/5.34 => ( ord_less_nat @ I @ K ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_lessD1
% 5.15/5.34 thf(fact_321_Suc3__eq__add__3,axiom,
% 5.15/5.34 ! [N2: nat] :
% 5.15/5.34 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 5.15/5.34 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % Suc3_eq_add_3
% 5.15/5.34 thf(fact_322_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 5.15/5.34 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.34 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.34 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.34 @ ( if_nat
% 5.15/5.34 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.34 & ~ ( ( X = Mi )
% 5.15/5.34 | ( X = Ma ) ) )
% 5.15/5.34 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.15/5.34 @ one_one_nat ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(5)
% 5.15/5.34 thf(fact_323_Suc__div__eq__add3__div,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] :
% 5.15/5.34 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.15/5.34 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % Suc_div_eq_add3_div
% 5.15/5.34 thf(fact_324_not__numeral__less__one,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 5.15/5.34
% 5.15/5.34 % not_numeral_less_one
% 5.15/5.34 thf(fact_325_not__numeral__less__one,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 5.15/5.34
% 5.15/5.34 % not_numeral_less_one
% 5.15/5.34 thf(fact_326_not__numeral__less__one,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 5.15/5.34
% 5.15/5.34 % not_numeral_less_one
% 5.15/5.34 thf(fact_327_not__numeral__less__one,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 5.15/5.34
% 5.15/5.34 % not_numeral_less_one
% 5.15/5.34 thf(fact_328_one__plus__numeral__commute,axiom,
% 5.15/5.34 ! [X: num] :
% 5.15/5.34 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.15/5.34 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_plus_numeral_commute
% 5.15/5.34 thf(fact_329_one__plus__numeral__commute,axiom,
% 5.15/5.34 ! [X: num] :
% 5.15/5.34 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.15/5.34 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_plus_numeral_commute
% 5.15/5.34 thf(fact_330_one__plus__numeral__commute,axiom,
% 5.15/5.34 ! [X: num] :
% 5.15/5.34 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.15/5.34 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_plus_numeral_commute
% 5.15/5.34 thf(fact_331_one__plus__numeral__commute,axiom,
% 5.15/5.34 ! [X: num] :
% 5.15/5.34 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.15/5.34 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_plus_numeral_commute
% 5.15/5.34 thf(fact_332_one__plus__numeral__commute,axiom,
% 5.15/5.34 ! [X: num] :
% 5.15/5.34 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.15/5.34 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_plus_numeral_commute
% 5.15/5.34 thf(fact_333_numeral__Bit0,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 5.15/5.34 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit0
% 5.15/5.34 thf(fact_334_numeral__Bit0,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 5.15/5.34 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit0
% 5.15/5.34 thf(fact_335_numeral__Bit0,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 5.15/5.34 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit0
% 5.15/5.34 thf(fact_336_numeral__Bit0,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.15/5.34 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit0
% 5.15/5.34 thf(fact_337_numeral__Bit0,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.15/5.34 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit0
% 5.15/5.34 thf(fact_338_numeral__One,axiom,
% 5.15/5.34 ( ( numera6690914467698888265omplex @ one )
% 5.15/5.34 = one_one_complex ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_One
% 5.15/5.34 thf(fact_339_numeral__One,axiom,
% 5.15/5.34 ( ( numeral_numeral_real @ one )
% 5.15/5.34 = one_one_real ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_One
% 5.15/5.34 thf(fact_340_numeral__One,axiom,
% 5.15/5.34 ( ( numeral_numeral_rat @ one )
% 5.15/5.34 = one_one_rat ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_One
% 5.15/5.34 thf(fact_341_numeral__One,axiom,
% 5.15/5.34 ( ( numeral_numeral_nat @ one )
% 5.15/5.34 = one_one_nat ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_One
% 5.15/5.34 thf(fact_342_numeral__One,axiom,
% 5.15/5.34 ( ( numeral_numeral_int @ one )
% 5.15/5.34 = one_one_int ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_One
% 5.15/5.34 thf(fact_343_divide__numeral__1,axiom,
% 5.15/5.34 ! [A: complex] :
% 5.15/5.34 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % divide_numeral_1
% 5.15/5.34 thf(fact_344_divide__numeral__1,axiom,
% 5.15/5.34 ! [A: real] :
% 5.15/5.34 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % divide_numeral_1
% 5.15/5.34 thf(fact_345_divide__numeral__1,axiom,
% 5.15/5.34 ! [A: rat] :
% 5.15/5.34 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % divide_numeral_1
% 5.15/5.34 thf(fact_346_num_Oexhaust,axiom,
% 5.15/5.34 ! [Y: num] :
% 5.15/5.34 ( ( Y != one )
% 5.15/5.34 => ( ! [X23: num] :
% 5.15/5.34 ( Y
% 5.15/5.34 != ( bit0 @ X23 ) )
% 5.15/5.34 => ~ ! [X32: num] :
% 5.15/5.34 ( Y
% 5.15/5.34 != ( bit1 @ X32 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % num.exhaust
% 5.15/5.34 thf(fact_347_numerals_I1_J,axiom,
% 5.15/5.34 ( ( numeral_numeral_nat @ one )
% 5.15/5.34 = one_one_nat ) ).
% 5.15/5.34
% 5.15/5.34 % numerals(1)
% 5.15/5.34 thf(fact_348_numeral__Bit0__div__2,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit0_div_2
% 5.15/5.34 thf(fact_349_numeral__Bit0__div__2,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit0_div_2
% 5.15/5.34 thf(fact_350_numeral__Bit1,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit1
% 5.15/5.34 thf(fact_351_numeral__Bit1,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit1
% 5.15/5.34 thf(fact_352_numeral__Bit1,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit1
% 5.15/5.34 thf(fact_353_numeral__Bit1,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit1
% 5.15/5.34 thf(fact_354_numeral__Bit1,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit1
% 5.15/5.34 thf(fact_355_field__sum__of__halves,axiom,
% 5.15/5.34 ! [X: real] :
% 5.15/5.34 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.34 = X ) ).
% 5.15/5.34
% 5.15/5.34 % field_sum_of_halves
% 5.15/5.34 thf(fact_356_field__sum__of__halves,axiom,
% 5.15/5.34 ! [X: rat] :
% 5.15/5.34 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.15/5.34 = X ) ).
% 5.15/5.34
% 5.15/5.34 % field_sum_of_halves
% 5.15/5.34 thf(fact_357_numeral__Bit1__div__2,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit1_div_2
% 5.15/5.34 thf(fact_358_numeral__Bit1__div__2,axiom,
% 5.15/5.34 ! [N2: num] :
% 5.15/5.34 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_Bit1_div_2
% 5.15/5.34 thf(fact_359_member__inv,axiom,
% 5.15/5.34 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.34 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.34 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.34 & ( ( X = Mi )
% 5.15/5.34 | ( X = Ma )
% 5.15/5.34 | ( ( ord_less_nat @ X @ Ma )
% 5.15/5.34 & ( ord_less_nat @ Mi @ X )
% 5.15/5.34 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.34 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % member_inv
% 5.15/5.34 thf(fact_360_insert__simp__mima,axiom,
% 5.15/5.34 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.34 ( ( ( X = Mi )
% 5.15/5.34 | ( X = Ma ) )
% 5.15/5.34 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.34 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.34 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % insert_simp_mima
% 5.15/5.34 thf(fact_361_power__increasing__iff,axiom,
% 5.15/5.34 ! [B: real,X: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.34 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.15/5.34 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_increasing_iff
% 5.15/5.34 thf(fact_362_power__increasing__iff,axiom,
% 5.15/5.34 ! [B: rat,X: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ B )
% 5.15/5.34 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.15/5.34 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_increasing_iff
% 5.15/5.34 thf(fact_363_power__increasing__iff,axiom,
% 5.15/5.34 ! [B: nat,X: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ B )
% 5.15/5.34 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.15/5.34 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_increasing_iff
% 5.15/5.34 thf(fact_364_power__increasing__iff,axiom,
% 5.15/5.34 ! [B: int,X: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ B )
% 5.15/5.34 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.15/5.34 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_increasing_iff
% 5.15/5.34 thf(fact_365_power__strict__increasing__iff,axiom,
% 5.15/5.34 ! [B: real,X: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.34 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.15/5.34 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_strict_increasing_iff
% 5.15/5.34 thf(fact_366_power__strict__increasing__iff,axiom,
% 5.15/5.34 ! [B: rat,X: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ B )
% 5.15/5.34 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.15/5.34 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_strict_increasing_iff
% 5.15/5.34 thf(fact_367_power__strict__increasing__iff,axiom,
% 5.15/5.34 ! [B: nat,X: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ B )
% 5.15/5.34 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.15/5.34 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_strict_increasing_iff
% 5.15/5.34 thf(fact_368_power__strict__increasing__iff,axiom,
% 5.15/5.34 ! [B: int,X: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ B )
% 5.15/5.34 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.15/5.34 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_strict_increasing_iff
% 5.15/5.34 thf(fact_369_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.15/5.34 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.15/5.34 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.34 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.15/5.34 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.34 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % both_member_options_from_chilf_to_complete_tree
% 5.15/5.34 thf(fact_370_ex__power__ivl2,axiom,
% 5.15/5.34 ! [B: nat,K: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.15/5.34 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.15/5.34 => ? [N: nat] :
% 5.15/5.34 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.15/5.34 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ex_power_ivl2
% 5.15/5.34 thf(fact_371_ex__power__ivl1,axiom,
% 5.15/5.34 ! [B: nat,K: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.15/5.34 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.15/5.34 => ? [N: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.15/5.34 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ex_power_ivl1
% 5.15/5.34 thf(fact_372_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 5.15/5.34 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.34 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.34 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 5.15/5.34 thf(fact_373_power__inject__exp,axiom,
% 5.15/5.34 ! [A: real,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.34 => ( ( ( power_power_real @ A @ M )
% 5.15/5.34 = ( power_power_real @ A @ N2 ) )
% 5.15/5.34 = ( M = N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_inject_exp
% 5.15/5.34 thf(fact_374_power__inject__exp,axiom,
% 5.15/5.34 ! [A: rat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ( ( power_power_rat @ A @ M )
% 5.15/5.34 = ( power_power_rat @ A @ N2 ) )
% 5.15/5.34 = ( M = N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_inject_exp
% 5.15/5.34 thf(fact_375_power__inject__exp,axiom,
% 5.15/5.34 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ( ( power_power_nat @ A @ M )
% 5.15/5.34 = ( power_power_nat @ A @ N2 ) )
% 5.15/5.34 = ( M = N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_inject_exp
% 5.15/5.34 thf(fact_376_power__inject__exp,axiom,
% 5.15/5.34 ! [A: int,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ A )
% 5.15/5.34 => ( ( ( power_power_int @ A @ M )
% 5.15/5.34 = ( power_power_int @ A @ N2 ) )
% 5.15/5.34 = ( M = N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_inject_exp
% 5.15/5.34 thf(fact_377_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 5.15/5.34 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.34 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.34 = ( if_nat
% 5.15/5.34 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.34 & ~ ( ( X = Mi )
% 5.15/5.34 | ( X = Ma ) ) )
% 5.15/5.34 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.15/5.34 @ one_one_nat ) ) ).
% 5.15/5.34
% 5.15/5.34 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(5)
% 5.15/5.34 thf(fact_378_both__member__options__from__complete__tree__to__child,axiom,
% 5.15/5.34 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.15/5.34 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.34 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.34 | ( X = Mi )
% 5.15/5.34 | ( X = Ma ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % both_member_options_from_complete_tree_to_child
% 5.15/5.34 thf(fact_379_le__add__diff__inverse2,axiom,
% 5.15/5.34 ! [B: real,A: real] :
% 5.15/5.34 ( ( ord_less_eq_real @ B @ A )
% 5.15/5.34 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_add_diff_inverse2
% 5.15/5.34 thf(fact_380_le__add__diff__inverse2,axiom,
% 5.15/5.34 ! [B: rat,A: rat] :
% 5.15/5.34 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.34 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_add_diff_inverse2
% 5.15/5.34 thf(fact_381_le__add__diff__inverse2,axiom,
% 5.15/5.34 ! [B: nat,A: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.34 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_add_diff_inverse2
% 5.15/5.34 thf(fact_382_le__add__diff__inverse2,axiom,
% 5.15/5.34 ! [B: int,A: int] :
% 5.15/5.34 ( ( ord_less_eq_int @ B @ A )
% 5.15/5.34 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_add_diff_inverse2
% 5.15/5.34 thf(fact_383_not__min__Null__member,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT] :
% 5.15/5.34 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.15/5.34 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.15/5.34
% 5.15/5.34 % not_min_Null_member
% 5.15/5.34 thf(fact_384_min__Null__member,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,X: nat] :
% 5.15/5.34 ( ( vEBT_VEBT_minNull @ T )
% 5.15/5.34 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 5.15/5.34
% 5.15/5.34 % min_Null_member
% 5.15/5.34 thf(fact_385__C4_Ohyps_C_I3_J,axiom,
% 5.15/5.34 m = na ).
% 5.15/5.34
% 5.15/5.34 % "4.hyps"(3)
% 5.15/5.34 thf(fact_386__C4_Ohyps_C_I5_J,axiom,
% 5.15/5.34 ! [I4: nat] :
% 5.15/5.34 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.15/5.34 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ X4 ) )
% 5.15/5.34 = ( vEBT_V8194947554948674370ptions @ summary @ I4 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % "4.hyps"(5)
% 5.15/5.34 thf(fact_387__C4_Ohyps_C_I4_J,axiom,
% 5.15/5.34 ( deg
% 5.15/5.34 = ( plus_plus_nat @ na @ m ) ) ).
% 5.15/5.34
% 5.15/5.34 % "4.hyps"(4)
% 5.15/5.34 thf(fact_388_div__by__1,axiom,
% 5.15/5.34 ! [A: complex] :
% 5.15/5.34 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % div_by_1
% 5.15/5.34 thf(fact_389_div__by__1,axiom,
% 5.15/5.34 ! [A: real] :
% 5.15/5.34 ( ( divide_divide_real @ A @ one_one_real )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % div_by_1
% 5.15/5.34 thf(fact_390_div__by__1,axiom,
% 5.15/5.34 ! [A: rat] :
% 5.15/5.34 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % div_by_1
% 5.15/5.34 thf(fact_391_div__by__1,axiom,
% 5.15/5.34 ! [A: nat] :
% 5.15/5.34 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % div_by_1
% 5.15/5.34 thf(fact_392_div__by__1,axiom,
% 5.15/5.34 ! [A: int] :
% 5.15/5.34 ( ( divide_divide_int @ A @ one_one_int )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % div_by_1
% 5.15/5.34 thf(fact_393_power__one,axiom,
% 5.15/5.34 ! [N2: nat] :
% 5.15/5.34 ( ( power_power_rat @ one_one_rat @ N2 )
% 5.15/5.34 = one_one_rat ) ).
% 5.15/5.34
% 5.15/5.34 % power_one
% 5.15/5.34 thf(fact_394_power__one,axiom,
% 5.15/5.34 ! [N2: nat] :
% 5.15/5.34 ( ( power_power_nat @ one_one_nat @ N2 )
% 5.15/5.34 = one_one_nat ) ).
% 5.15/5.34
% 5.15/5.34 % power_one
% 5.15/5.34 thf(fact_395_power__one,axiom,
% 5.15/5.34 ! [N2: nat] :
% 5.15/5.34 ( ( power_power_real @ one_one_real @ N2 )
% 5.15/5.34 = one_one_real ) ).
% 5.15/5.34
% 5.15/5.34 % power_one
% 5.15/5.34 thf(fact_396_power__one,axiom,
% 5.15/5.34 ! [N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ one_one_complex @ N2 )
% 5.15/5.34 = one_one_complex ) ).
% 5.15/5.34
% 5.15/5.34 % power_one
% 5.15/5.34 thf(fact_397_power__one,axiom,
% 5.15/5.34 ! [N2: nat] :
% 5.15/5.34 ( ( power_power_int @ one_one_int @ N2 )
% 5.15/5.34 = one_one_int ) ).
% 5.15/5.34
% 5.15/5.34 % power_one
% 5.15/5.34 thf(fact_398_power__one__right,axiom,
% 5.15/5.34 ! [A: nat] :
% 5.15/5.34 ( ( power_power_nat @ A @ one_one_nat )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % power_one_right
% 5.15/5.34 thf(fact_399_power__one__right,axiom,
% 5.15/5.34 ! [A: real] :
% 5.15/5.34 ( ( power_power_real @ A @ one_one_nat )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % power_one_right
% 5.15/5.34 thf(fact_400_power__one__right,axiom,
% 5.15/5.34 ! [A: complex] :
% 5.15/5.34 ( ( power_power_complex @ A @ one_one_nat )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % power_one_right
% 5.15/5.34 thf(fact_401_power__one__right,axiom,
% 5.15/5.34 ! [A: int] :
% 5.15/5.34 ( ( power_power_int @ A @ one_one_nat )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % power_one_right
% 5.15/5.34 thf(fact_402_semiring__norm_I71_J,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.34 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % semiring_norm(71)
% 5.15/5.34 thf(fact_403_semiring__norm_I68_J,axiom,
% 5.15/5.34 ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 5.15/5.34
% 5.15/5.34 % semiring_norm(68)
% 5.15/5.34 thf(fact_404_semiring__norm_I73_J,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % semiring_norm(73)
% 5.15/5.34 thf(fact_405_le__add__diff__inverse,axiom,
% 5.15/5.34 ! [B: real,A: real] :
% 5.15/5.34 ( ( ord_less_eq_real @ B @ A )
% 5.15/5.34 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_add_diff_inverse
% 5.15/5.34 thf(fact_406_le__add__diff__inverse,axiom,
% 5.15/5.34 ! [B: rat,A: rat] :
% 5.15/5.34 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.34 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_add_diff_inverse
% 5.15/5.34 thf(fact_407_le__add__diff__inverse,axiom,
% 5.15/5.34 ! [B: nat,A: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.34 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_add_diff_inverse
% 5.15/5.34 thf(fact_408_le__add__diff__inverse,axiom,
% 5.15/5.34 ! [B: int,A: int] :
% 5.15/5.34 ( ( ord_less_eq_int @ B @ A )
% 5.15/5.34 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_add_diff_inverse
% 5.15/5.34 thf(fact_409_semiring__norm_I69_J,axiom,
% 5.15/5.34 ! [M: num] :
% 5.15/5.34 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.15/5.34
% 5.15/5.34 % semiring_norm(69)
% 5.15/5.34 thf(fact_410_semiring__norm_I72_J,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % semiring_norm(72)
% 5.15/5.34 thf(fact_411_semiring__norm_I70_J,axiom,
% 5.15/5.34 ! [M: num] :
% 5.15/5.34 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.15/5.34
% 5.15/5.34 % semiring_norm(70)
% 5.15/5.34 thf(fact_412_semiring__norm_I79_J,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.34 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % semiring_norm(79)
% 5.15/5.34 thf(fact_413_semiring__norm_I74_J,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.34 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % semiring_norm(74)
% 5.15/5.34 thf(fact_414__C4_Ohyps_C_I9_J,axiom,
% 5.15/5.34 ( ( mi != ma )
% 5.15/5.34 => ! [I4: nat] :
% 5.15/5.34 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.15/5.34 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.15/5.34 = I4 )
% 5.15/5.34 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.15/5.34 & ! [X5: nat] :
% 5.15/5.34 ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 5.15/5.34 = I4 )
% 5.15/5.34 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 5.15/5.34 => ( ( ord_less_nat @ mi @ X5 )
% 5.15/5.34 & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % "4.hyps"(9)
% 5.15/5.34 thf(fact_415__C4_Ohyps_C_I6_J,axiom,
% 5.15/5.34 ( ( mi = ma )
% 5.15/5.34 => ! [X5: vEBT_VEBT] :
% 5.15/5.34 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.15/5.34 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % "4.hyps"(6)
% 5.15/5.34 thf(fact_416__C4_Ohyps_C_I1_J,axiom,
% 5.15/5.34 vEBT_invar_vebt @ summary @ m ).
% 5.15/5.34
% 5.15/5.34 % "4.hyps"(1)
% 5.15/5.34 thf(fact_417_two__realpow__ge__one,axiom,
% 5.15/5.34 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % two_realpow_ge_one
% 5.15/5.34 thf(fact_418_le__num__One__iff,axiom,
% 5.15/5.34 ! [X: num] :
% 5.15/5.34 ( ( ord_less_eq_num @ X @ one )
% 5.15/5.34 = ( X = one ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_num_One_iff
% 5.15/5.34 thf(fact_419_linorder__neqE__linordered__idom,axiom,
% 5.15/5.34 ! [X: real,Y: real] :
% 5.15/5.34 ( ( X != Y )
% 5.15/5.34 => ( ~ ( ord_less_real @ X @ Y )
% 5.15/5.34 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % linorder_neqE_linordered_idom
% 5.15/5.34 thf(fact_420_linorder__neqE__linordered__idom,axiom,
% 5.15/5.34 ! [X: rat,Y: rat] :
% 5.15/5.34 ( ( X != Y )
% 5.15/5.34 => ( ~ ( ord_less_rat @ X @ Y )
% 5.15/5.34 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % linorder_neqE_linordered_idom
% 5.15/5.34 thf(fact_421_linorder__neqE__linordered__idom,axiom,
% 5.15/5.34 ! [X: int,Y: int] :
% 5.15/5.34 ( ( X != Y )
% 5.15/5.34 => ( ~ ( ord_less_int @ X @ Y )
% 5.15/5.34 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % linorder_neqE_linordered_idom
% 5.15/5.34 thf(fact_422_power__divide,axiom,
% 5.15/5.34 ! [A: complex,B: complex,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N2 )
% 5.15/5.34 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_divide
% 5.15/5.34 thf(fact_423_power__divide,axiom,
% 5.15/5.34 ! [A: real,B: real,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N2 )
% 5.15/5.34 = ( divide_divide_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_divide
% 5.15/5.34 thf(fact_424_power__divide,axiom,
% 5.15/5.34 ! [A: rat,B: rat,N2: nat] :
% 5.15/5.34 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N2 )
% 5.15/5.34 = ( divide_divide_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_divide
% 5.15/5.34 thf(fact_425_less__add__one,axiom,
% 5.15/5.34 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_one
% 5.15/5.34 thf(fact_426_less__add__one,axiom,
% 5.15/5.34 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_one
% 5.15/5.34 thf(fact_427_less__add__one,axiom,
% 5.15/5.34 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_one
% 5.15/5.34 thf(fact_428_less__add__one,axiom,
% 5.15/5.34 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_one
% 5.15/5.34 thf(fact_429_add__mono1,axiom,
% 5.15/5.34 ! [A: real,B: real] :
% 5.15/5.34 ( ( ord_less_real @ A @ B )
% 5.15/5.34 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_mono1
% 5.15/5.34 thf(fact_430_add__mono1,axiom,
% 5.15/5.34 ! [A: rat,B: rat] :
% 5.15/5.34 ( ( ord_less_rat @ A @ B )
% 5.15/5.34 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_mono1
% 5.15/5.34 thf(fact_431_add__mono1,axiom,
% 5.15/5.34 ! [A: nat,B: nat] :
% 5.15/5.34 ( ( ord_less_nat @ A @ B )
% 5.15/5.34 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_mono1
% 5.15/5.34 thf(fact_432_add__mono1,axiom,
% 5.15/5.34 ! [A: int,B: int] :
% 5.15/5.34 ( ( ord_less_int @ A @ B )
% 5.15/5.34 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_mono1
% 5.15/5.34 thf(fact_433_add__le__imp__le__diff,axiom,
% 5.15/5.34 ! [I: real,K: real,N2: real] :
% 5.15/5.34 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 5.15/5.34 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_le_imp_le_diff
% 5.15/5.34 thf(fact_434_add__le__imp__le__diff,axiom,
% 5.15/5.34 ! [I: rat,K: rat,N2: rat] :
% 5.15/5.34 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 5.15/5.34 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_le_imp_le_diff
% 5.15/5.34 thf(fact_435_add__le__imp__le__diff,axiom,
% 5.15/5.34 ! [I: nat,K: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 5.15/5.34 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_le_imp_le_diff
% 5.15/5.34 thf(fact_436_add__le__imp__le__diff,axiom,
% 5.15/5.34 ! [I: int,K: int,N2: int] :
% 5.15/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 5.15/5.34 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_le_imp_le_diff
% 5.15/5.34 thf(fact_437_add__le__add__imp__diff__le,axiom,
% 5.15/5.34 ! [I: real,K: real,N2: real,J: real] :
% 5.15/5.34 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 5.15/5.34 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 5.15/5.34 => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_le_add_imp_diff_le
% 5.15/5.34 thf(fact_438_add__le__add__imp__diff__le,axiom,
% 5.15/5.34 ! [I: rat,K: rat,N2: rat,J: rat] :
% 5.15/5.34 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 5.15/5.34 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 5.15/5.34 => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_le_add_imp_diff_le
% 5.15/5.34 thf(fact_439_add__le__add__imp__diff__le,axiom,
% 5.15/5.34 ! [I: nat,K: nat,N2: nat,J: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.15/5.34 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.15/5.34 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_le_add_imp_diff_le
% 5.15/5.34 thf(fact_440_add__le__add__imp__diff__le,axiom,
% 5.15/5.34 ! [I: int,K: int,N2: int,J: int] :
% 5.15/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.15/5.34 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.15/5.34 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_le_add_imp_diff_le
% 5.15/5.34 thf(fact_441_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.15/5.34 ! [A: real,B: real] :
% 5.15/5.34 ( ~ ( ord_less_real @ A @ B )
% 5.15/5.34 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % linordered_semidom_class.add_diff_inverse
% 5.15/5.34 thf(fact_442_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.15/5.34 ! [A: rat,B: rat] :
% 5.15/5.34 ( ~ ( ord_less_rat @ A @ B )
% 5.15/5.34 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % linordered_semidom_class.add_diff_inverse
% 5.15/5.34 thf(fact_443_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.15/5.34 ! [A: nat,B: nat] :
% 5.15/5.34 ( ~ ( ord_less_nat @ A @ B )
% 5.15/5.34 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % linordered_semidom_class.add_diff_inverse
% 5.15/5.34 thf(fact_444_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.15/5.34 ! [A: int,B: int] :
% 5.15/5.34 ( ~ ( ord_less_int @ A @ B )
% 5.15/5.34 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.15/5.34 = A ) ) ).
% 5.15/5.34
% 5.15/5.34 % linordered_semidom_class.add_diff_inverse
% 5.15/5.34 thf(fact_445_one__le__power,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.15/5.34 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_le_power
% 5.15/5.34 thf(fact_446_one__le__power,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_le_power
% 5.15/5.34 thf(fact_447_one__le__power,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_le_power
% 5.15/5.34 thf(fact_448_one__le__power,axiom,
% 5.15/5.34 ! [A: int,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.15/5.34 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % one_le_power
% 5.15/5.34 thf(fact_449_power__one__over,axiom,
% 5.15/5.34 ! [A: complex,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N2 )
% 5.15/5.34 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_one_over
% 5.15/5.34 thf(fact_450_power__one__over,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N2 )
% 5.15/5.34 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_one_over
% 5.15/5.34 thf(fact_451_power__one__over,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N2 )
% 5.15/5.34 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_one_over
% 5.15/5.34 thf(fact_452_power__gt1,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.34 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_gt1
% 5.15/5.34 thf(fact_453_power__gt1,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_gt1
% 5.15/5.34 thf(fact_454_power__gt1,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_gt1
% 5.15/5.34 thf(fact_455_power__gt1,axiom,
% 5.15/5.34 ! [A: int,N2: nat] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ A )
% 5.15/5.34 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_gt1
% 5.15/5.34 thf(fact_456_power__less__imp__less__exp,axiom,
% 5.15/5.34 ! [A: real,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.34 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 5.15/5.34 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_less_imp_less_exp
% 5.15/5.34 thf(fact_457_power__less__imp__less__exp,axiom,
% 5.15/5.34 ! [A: rat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 5.15/5.34 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_less_imp_less_exp
% 5.15/5.34 thf(fact_458_power__less__imp__less__exp,axiom,
% 5.15/5.34 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.15/5.34 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_less_imp_less_exp
% 5.15/5.34 thf(fact_459_power__less__imp__less__exp,axiom,
% 5.15/5.34 ! [A: int,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ A )
% 5.15/5.34 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.15/5.34 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_less_imp_less_exp
% 5.15/5.34 thf(fact_460_power__strict__increasing,axiom,
% 5.15/5.34 ! [N2: nat,N5: nat,A: real] :
% 5.15/5.34 ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.34 => ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.34 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_strict_increasing
% 5.15/5.34 thf(fact_461_power__strict__increasing,axiom,
% 5.15/5.34 ! [N2: nat,N5: nat,A: rat] :
% 5.15/5.34 ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.34 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_strict_increasing
% 5.15/5.34 thf(fact_462_power__strict__increasing,axiom,
% 5.15/5.34 ! [N2: nat,N5: nat,A: nat] :
% 5.15/5.34 ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.34 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_strict_increasing
% 5.15/5.34 thf(fact_463_power__strict__increasing,axiom,
% 5.15/5.34 ! [N2: nat,N5: nat,A: int] :
% 5.15/5.34 ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.34 => ( ( ord_less_int @ one_one_int @ A )
% 5.15/5.34 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_strict_increasing
% 5.15/5.34 thf(fact_464_power__increasing,axiom,
% 5.15/5.34 ! [N2: nat,N5: nat,A: real] :
% 5.15/5.34 ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.34 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.15/5.34 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_increasing
% 5.15/5.34 thf(fact_465_power__increasing,axiom,
% 5.15/5.34 ! [N2: nat,N5: nat,A: rat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.34 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_increasing
% 5.15/5.34 thf(fact_466_power__increasing,axiom,
% 5.15/5.34 ! [N2: nat,N5: nat,A: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.34 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_increasing
% 5.15/5.34 thf(fact_467_power__increasing,axiom,
% 5.15/5.34 ! [N2: nat,N5: nat,A: int] :
% 5.15/5.34 ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.34 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.15/5.34 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_increasing
% 5.15/5.34 thf(fact_468_power__le__imp__le__exp,axiom,
% 5.15/5.34 ! [A: real,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.34 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 5.15/5.34 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_le_imp_le_exp
% 5.15/5.34 thf(fact_469_power__le__imp__le__exp,axiom,
% 5.15/5.34 ! [A: rat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 5.15/5.34 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_le_imp_le_exp
% 5.15/5.34 thf(fact_470_power__le__imp__le__exp,axiom,
% 5.15/5.34 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.15/5.34 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_le_imp_le_exp
% 5.15/5.34 thf(fact_471_power__le__imp__le__exp,axiom,
% 5.15/5.34 ! [A: int,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ A )
% 5.15/5.34 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.15/5.34 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_le_imp_le_exp
% 5.15/5.34 thf(fact_472_one__power2,axiom,
% 5.15/5.34 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = one_one_rat ) ).
% 5.15/5.34
% 5.15/5.34 % one_power2
% 5.15/5.34 thf(fact_473_one__power2,axiom,
% 5.15/5.34 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = one_one_nat ) ).
% 5.15/5.34
% 5.15/5.34 % one_power2
% 5.15/5.34 thf(fact_474_one__power2,axiom,
% 5.15/5.34 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = one_one_real ) ).
% 5.15/5.34
% 5.15/5.34 % one_power2
% 5.15/5.34 thf(fact_475_one__power2,axiom,
% 5.15/5.34 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = one_one_complex ) ).
% 5.15/5.34
% 5.15/5.34 % one_power2
% 5.15/5.34 thf(fact_476_one__power2,axiom,
% 5.15/5.34 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = one_one_int ) ).
% 5.15/5.34
% 5.15/5.34 % one_power2
% 5.15/5.34 thf(fact_477_power2__commute,axiom,
% 5.15/5.34 ! [X: complex,Y: complex] :
% 5.15/5.34 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( power_power_complex @ ( minus_minus_complex @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_commute
% 5.15/5.34 thf(fact_478_power2__commute,axiom,
% 5.15/5.34 ! [X: real,Y: real] :
% 5.15/5.34 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( power_power_real @ ( minus_minus_real @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_commute
% 5.15/5.34 thf(fact_479_power2__commute,axiom,
% 5.15/5.34 ! [X: rat,Y: rat] :
% 5.15/5.34 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( power_power_rat @ ( minus_minus_rat @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_commute
% 5.15/5.34 thf(fact_480_power2__commute,axiom,
% 5.15/5.34 ! [X: int,Y: int] :
% 5.15/5.34 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( power_power_int @ ( minus_minus_int @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_commute
% 5.15/5.34 thf(fact_481_less__exp,axiom,
% 5.15/5.34 ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_exp
% 5.15/5.34 thf(fact_482_self__le__ge2__pow,axiom,
% 5.15/5.34 ! [K: nat,M: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.15/5.34 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % self_le_ge2_pow
% 5.15/5.34 thf(fact_483_power2__nat__le__eq__le,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.34 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_nat_le_eq_le
% 5.15/5.34 thf(fact_484_power2__nat__le__imp__le,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 5.15/5.34 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_nat_le_imp_le
% 5.15/5.34 thf(fact_485_diff__le__diff__pow,axiom,
% 5.15/5.34 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.15/5.34 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % diff_le_diff_pow
% 5.15/5.34 thf(fact_486_in__children__def,axiom,
% 5.15/5.34 ( vEBT_V5917875025757280293ildren
% 5.15/5.34 = ( ^ [N3: nat,TreeList2: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ N3 ) ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % in_children_def
% 5.15/5.34 thf(fact_487_vebt__member_Osimps_I5_J,axiom,
% 5.15/5.34 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.34 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.34 = ( ( X != Mi )
% 5.15/5.34 => ( ( X != Ma )
% 5.15/5.34 => ( ~ ( ord_less_nat @ X @ Mi )
% 5.15/5.34 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.15/5.34 => ( ~ ( ord_less_nat @ Ma @ X )
% 5.15/5.34 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.15/5.34 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.34 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.34 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % vebt_member.simps(5)
% 5.15/5.34 thf(fact_488_set__vebt_H__def,axiom,
% 5.15/5.34 ( vEBT_VEBT_set_vebt
% 5.15/5.34 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % set_vebt'_def
% 5.15/5.34 thf(fact_489_both__member__options__ding,axiom,
% 5.15/5.34 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N2 )
% 5.15/5.34 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.15/5.34 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.34 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % both_member_options_ding
% 5.15/5.34 thf(fact_490_div__exp__eq,axiom,
% 5.15/5.34 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % div_exp_eq
% 5.15/5.34 thf(fact_491_div__exp__eq,axiom,
% 5.15/5.34 ! [A: int,M: nat,N2: nat] :
% 5.15/5.34 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % div_exp_eq
% 5.15/5.34 thf(fact_492_bit__concat__def,axiom,
% 5.15/5.34 ( vEBT_VEBT_bit_concat
% 5.15/5.34 = ( ^ [H: nat,L2: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % bit_concat_def
% 5.15/5.34 thf(fact_493_low__inv,axiom,
% 5.15/5.34 ! [X: nat,N2: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
% 5.15/5.34 = X ) ) ).
% 5.15/5.34
% 5.15/5.34 % low_inv
% 5.15/5.34 thf(fact_494_high__inv,axiom,
% 5.15/5.34 ! [X: nat,N2: nat,Y: nat] :
% 5.15/5.34 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
% 5.15/5.34 = Y ) ) ).
% 5.15/5.34
% 5.15/5.34 % high_inv
% 5.15/5.34 thf(fact_495_mi__ma__2__deg,axiom,
% 5.15/5.34 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.15/5.34 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.15/5.34 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mi_ma_2_deg
% 5.15/5.34 thf(fact_496_height__compose__summary,axiom,
% 5.15/5.34 ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % height_compose_summary
% 5.15/5.34 thf(fact_497_enat__ord__number_I1_J,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.15/5.34 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % enat_ord_number(1)
% 5.15/5.34 thf(fact_498_deg__deg__n,axiom,
% 5.15/5.34 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N2 )
% 5.15/5.34 => ( Deg = N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % deg_deg_n
% 5.15/5.34 thf(fact_499_deg__SUcn__Node,axiom,
% 5.15/5.34 ! [Tree: vEBT_VEBT,N2: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N2 ) ) )
% 5.15/5.34 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.34 ( Tree
% 5.15/5.34 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N2 ) ) @ TreeList3 @ S2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % deg_SUcn_Node
% 5.15/5.34 thf(fact_500_both__member__options__equiv__member,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.15/5.34 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % both_member_options_equiv_member
% 5.15/5.34 thf(fact_501_valid__member__both__member__options,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.15/5.34 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % valid_member_both_member_options
% 5.15/5.34 thf(fact_502_inthall,axiom,
% 5.15/5.34 ! [Xs2: list_complex,P: complex > $o,N2: nat] :
% 5.15/5.34 ( ! [X3: complex] :
% 5.15/5.34 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 5.15/5.34 => ( P @ X3 ) )
% 5.15/5.34 => ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.15/5.34 => ( P @ ( nth_complex @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % inthall
% 5.15/5.34 thf(fact_503_inthall,axiom,
% 5.15/5.34 ! [Xs2: list_real,P: real > $o,N2: nat] :
% 5.15/5.34 ( ! [X3: real] :
% 5.15/5.34 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 5.15/5.34 => ( P @ X3 ) )
% 5.15/5.34 => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.15/5.34 => ( P @ ( nth_real @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % inthall
% 5.15/5.34 thf(fact_504_inthall,axiom,
% 5.15/5.34 ! [Xs2: list_set_nat,P: set_nat > $o,N2: nat] :
% 5.15/5.34 ( ! [X3: set_nat] :
% 5.15/5.34 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 5.15/5.34 => ( P @ X3 ) )
% 5.15/5.34 => ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.15/5.34 => ( P @ ( nth_set_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % inthall
% 5.15/5.34 thf(fact_505_inthall,axiom,
% 5.15/5.34 ! [Xs2: list_nat,P: nat > $o,N2: nat] :
% 5.15/5.34 ( ! [X3: nat] :
% 5.15/5.34 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.15/5.34 => ( P @ X3 ) )
% 5.15/5.34 => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.34 => ( P @ ( nth_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % inthall
% 5.15/5.34 thf(fact_506_inthall,axiom,
% 5.15/5.34 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 5.15/5.34 ( ! [X3: vEBT_VEBT] :
% 5.15/5.34 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.34 => ( P @ X3 ) )
% 5.15/5.34 => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.34 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % inthall
% 5.15/5.34 thf(fact_507_inthall,axiom,
% 5.15/5.34 ! [Xs2: list_o,P: $o > $o,N2: nat] :
% 5.15/5.34 ( ! [X3: $o] :
% 5.15/5.34 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.15/5.34 => ( P @ X3 ) )
% 5.15/5.34 => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.34 => ( P @ ( nth_o @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % inthall
% 5.15/5.34 thf(fact_508_inthall,axiom,
% 5.15/5.34 ! [Xs2: list_int,P: int > $o,N2: nat] :
% 5.15/5.34 ( ! [X3: int] :
% 5.15/5.34 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.15/5.34 => ( P @ X3 ) )
% 5.15/5.34 => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.34 => ( P @ ( nth_int @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % inthall
% 5.15/5.34 thf(fact_509_height__compose__child,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 5.15/5.34 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.34 => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % height_compose_child
% 5.15/5.34 thf(fact_510_mi__eq__ma__no__ch,axiom,
% 5.15/5.34 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.15/5.34 => ( ( Mi = Ma )
% 5.15/5.34 => ( ! [X5: vEBT_VEBT] :
% 5.15/5.34 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.34 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.15/5.34 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mi_eq_ma_no_ch
% 5.15/5.34 thf(fact_511_member__bound,axiom,
% 5.15/5.34 ! [Tree: vEBT_VEBT,X: nat,N2: nat] :
% 5.15/5.34 ( ( vEBT_vebt_member @ Tree @ X )
% 5.15/5.34 => ( ( vEBT_invar_vebt @ Tree @ N2 )
% 5.15/5.34 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % member_bound
% 5.15/5.34 thf(fact_512_numeral__times__numeral,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.34 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_times_numeral
% 5.15/5.34 thf(fact_513_numeral__times__numeral,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.34 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_times_numeral
% 5.15/5.34 thf(fact_514_numeral__times__numeral,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.34 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_times_numeral
% 5.15/5.34 thf(fact_515_numeral__times__numeral,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.34 = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_times_numeral
% 5.15/5.34 thf(fact_516_numeral__times__numeral,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.34 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % numeral_times_numeral
% 5.15/5.34 thf(fact_517_mult__numeral__left__semiring__numeral,axiom,
% 5.15/5.34 ! [V: num,W: num,Z: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.15/5.34 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_left_semiring_numeral
% 5.15/5.34 thf(fact_518_mult__numeral__left__semiring__numeral,axiom,
% 5.15/5.34 ! [V: num,W: num,Z: real] :
% 5.15/5.34 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.15/5.34 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_left_semiring_numeral
% 5.15/5.34 thf(fact_519_mult__numeral__left__semiring__numeral,axiom,
% 5.15/5.34 ! [V: num,W: num,Z: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.15/5.34 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_left_semiring_numeral
% 5.15/5.34 thf(fact_520_mult__numeral__left__semiring__numeral,axiom,
% 5.15/5.34 ! [V: num,W: num,Z: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.15/5.34 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_left_semiring_numeral
% 5.15/5.34 thf(fact_521_mult__numeral__left__semiring__numeral,axiom,
% 5.15/5.34 ! [V: num,W: num,Z: int] :
% 5.15/5.34 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.15/5.34 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_left_semiring_numeral
% 5.15/5.34 thf(fact_522_bits__div__by__1,axiom,
% 5.15/5.34 ! [A: nat] :
% 5.15/5.34 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % bits_div_by_1
% 5.15/5.34 thf(fact_523_bits__div__by__1,axiom,
% 5.15/5.34 ! [A: int] :
% 5.15/5.34 ( ( divide_divide_int @ A @ one_one_int )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % bits_div_by_1
% 5.15/5.34 thf(fact_524_two__powr__height__bound__deg,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % two_powr_height_bound_deg
% 5.15/5.34 thf(fact_525_valid__insert__both__member__options__pres,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.15/5.34 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % valid_insert_both_member_options_pres
% 5.15/5.34 thf(fact_526_valid__insert__both__member__options__add,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % valid_insert_both_member_options_add
% 5.15/5.34 thf(fact_527_post__member__pre__member,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 5.15/5.34 => ( ( vEBT_vebt_member @ T @ Y )
% 5.15/5.34 | ( X = Y ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % post_member_pre_member
% 5.15/5.34 thf(fact_528_nat__mult__eq__1__iff,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] :
% 5.15/5.34 ( ( ( times_times_nat @ M @ N2 )
% 5.15/5.34 = one_one_nat )
% 5.15/5.34 = ( ( M = one_one_nat )
% 5.15/5.34 & ( N2 = one_one_nat ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % nat_mult_eq_1_iff
% 5.15/5.34 thf(fact_529_nat__1__eq__mult__iff,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] :
% 5.15/5.34 ( ( one_one_nat
% 5.15/5.34 = ( times_times_nat @ M @ N2 ) )
% 5.15/5.34 = ( ( M = one_one_nat )
% 5.15/5.34 & ( N2 = one_one_nat ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % nat_1_eq_mult_iff
% 5.15/5.34 thf(fact_530__C4_OIH_C_I1_J,axiom,
% 5.15/5.34 ! [X5: vEBT_VEBT] :
% 5.15/5.34 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.15/5.34 => ( ( vEBT_invar_vebt @ X5 @ na )
% 5.15/5.34 & ! [Xa: nat] : ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ X5 @ Xa ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ X5 ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % "4.IH"(1)
% 5.15/5.34 thf(fact_531_member__correct,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ( vEBT_vebt_member @ T @ X )
% 5.15/5.34 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % member_correct
% 5.15/5.34 thf(fact_532_set__vebt__set__vebt_H__valid,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ( vEBT_set_vebt @ T )
% 5.15/5.34 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % set_vebt_set_vebt'_valid
% 5.15/5.34 thf(fact_533_set__n__deg__not__0,axiom,
% 5.15/5.34 ! [TreeList: list_VEBT_VEBT,N2: nat,M: nat] :
% 5.15/5.34 ( ! [X3: vEBT_VEBT] :
% 5.15/5.34 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.34 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.15/5.34 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.15/5.34 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.34 => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % set_n_deg_not_0
% 5.15/5.34 thf(fact_534_distrib__right__numeral,axiom,
% 5.15/5.34 ! [A: complex,B: complex,V: num] :
% 5.15/5.34 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right_numeral
% 5.15/5.34 thf(fact_535_distrib__right__numeral,axiom,
% 5.15/5.34 ! [A: real,B: real,V: num] :
% 5.15/5.34 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right_numeral
% 5.15/5.34 thf(fact_536_distrib__right__numeral,axiom,
% 5.15/5.34 ! [A: rat,B: rat,V: num] :
% 5.15/5.34 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right_numeral
% 5.15/5.34 thf(fact_537_distrib__right__numeral,axiom,
% 5.15/5.34 ! [A: nat,B: nat,V: num] :
% 5.15/5.34 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right_numeral
% 5.15/5.34 thf(fact_538_distrib__right__numeral,axiom,
% 5.15/5.34 ! [A: int,B: int,V: num] :
% 5.15/5.34 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right_numeral
% 5.15/5.34 thf(fact_539_distrib__left__numeral,axiom,
% 5.15/5.34 ! [V: num,B: complex,C: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left_numeral
% 5.15/5.34 thf(fact_540_distrib__left__numeral,axiom,
% 5.15/5.34 ! [V: num,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left_numeral
% 5.15/5.34 thf(fact_541_distrib__left__numeral,axiom,
% 5.15/5.34 ! [V: num,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left_numeral
% 5.15/5.34 thf(fact_542_distrib__left__numeral,axiom,
% 5.15/5.34 ! [V: num,B: nat,C: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left_numeral
% 5.15/5.34 thf(fact_543_distrib__left__numeral,axiom,
% 5.15/5.34 ! [V: num,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left_numeral
% 5.15/5.34 thf(fact_544_right__diff__distrib__numeral,axiom,
% 5.15/5.34 ! [V: num,B: complex,C: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.15/5.34 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib_numeral
% 5.15/5.34 thf(fact_545_right__diff__distrib__numeral,axiom,
% 5.15/5.34 ! [V: num,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.15/5.34 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib_numeral
% 5.15/5.34 thf(fact_546_right__diff__distrib__numeral,axiom,
% 5.15/5.34 ! [V: num,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.15/5.34 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib_numeral
% 5.15/5.34 thf(fact_547_right__diff__distrib__numeral,axiom,
% 5.15/5.34 ! [V: num,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.15/5.34 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib_numeral
% 5.15/5.34 thf(fact_548_left__diff__distrib__numeral,axiom,
% 5.15/5.34 ! [A: complex,B: complex,V: num] :
% 5.15/5.34 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.15/5.34 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib_numeral
% 5.15/5.34 thf(fact_549_left__diff__distrib__numeral,axiom,
% 5.15/5.34 ! [A: real,B: real,V: num] :
% 5.15/5.34 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.34 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib_numeral
% 5.15/5.34 thf(fact_550_left__diff__distrib__numeral,axiom,
% 5.15/5.34 ! [A: rat,B: rat,V: num] :
% 5.15/5.34 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.34 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib_numeral
% 5.15/5.34 thf(fact_551_left__diff__distrib__numeral,axiom,
% 5.15/5.34 ! [A: int,B: int,V: num] :
% 5.15/5.34 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.34 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib_numeral
% 5.15/5.34 thf(fact_552_mult__Suc__right,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] :
% 5.15/5.34 ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 5.15/5.34 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_Suc_right
% 5.15/5.34 thf(fact_553__C4_OIH_C_I2_J,axiom,
% 5.15/5.34 ! [X: nat] : ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ summary @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ summary ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % "4.IH"(2)
% 5.15/5.34 thf(fact_554_enat__ord__number_I2_J,axiom,
% 5.15/5.34 ! [M: num,N2: num] :
% 5.15/5.34 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.15/5.34 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % enat_ord_number(2)
% 5.15/5.34 thf(fact_555_le__divide__eq__numeral1_I1_J,axiom,
% 5.15/5.34 ! [A: real,B: real,W: num] :
% 5.15/5.34 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.34 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_divide_eq_numeral1(1)
% 5.15/5.34 thf(fact_556_le__divide__eq__numeral1_I1_J,axiom,
% 5.15/5.34 ! [A: rat,B: rat,W: num] :
% 5.15/5.34 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.15/5.34 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_divide_eq_numeral1(1)
% 5.15/5.34 thf(fact_557_divide__le__eq__numeral1_I1_J,axiom,
% 5.15/5.34 ! [B: real,W: num,A: real] :
% 5.15/5.34 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.15/5.34 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % divide_le_eq_numeral1(1)
% 5.15/5.34 thf(fact_558_divide__le__eq__numeral1_I1_J,axiom,
% 5.15/5.34 ! [B: rat,W: num,A: rat] :
% 5.15/5.34 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.15/5.34 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % divide_le_eq_numeral1(1)
% 5.15/5.34 thf(fact_559_less__divide__eq__numeral1_I1_J,axiom,
% 5.15/5.34 ! [A: real,B: real,W: num] :
% 5.15/5.34 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.34 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_divide_eq_numeral1(1)
% 5.15/5.34 thf(fact_560_less__divide__eq__numeral1_I1_J,axiom,
% 5.15/5.34 ! [A: rat,B: rat,W: num] :
% 5.15/5.34 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.15/5.34 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_divide_eq_numeral1(1)
% 5.15/5.34 thf(fact_561_divide__less__eq__numeral1_I1_J,axiom,
% 5.15/5.34 ! [B: real,W: num,A: real] :
% 5.15/5.34 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.15/5.34 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % divide_less_eq_numeral1(1)
% 5.15/5.34 thf(fact_562_divide__less__eq__numeral1_I1_J,axiom,
% 5.15/5.34 ! [B: rat,W: num,A: rat] :
% 5.15/5.34 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.15/5.34 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % divide_less_eq_numeral1(1)
% 5.15/5.34 thf(fact_563_power__add__numeral,axiom,
% 5.15/5.34 ! [A: complex,M: num,N2: num] :
% 5.15/5.34 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.15/5.34 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral
% 5.15/5.34 thf(fact_564_power__add__numeral,axiom,
% 5.15/5.34 ! [A: real,M: num,N2: num] :
% 5.15/5.34 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.15/5.34 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral
% 5.15/5.34 thf(fact_565_power__add__numeral,axiom,
% 5.15/5.34 ! [A: rat,M: num,N2: num] :
% 5.15/5.34 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.15/5.34 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral
% 5.15/5.34 thf(fact_566_power__add__numeral,axiom,
% 5.15/5.34 ! [A: nat,M: num,N2: num] :
% 5.15/5.34 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.15/5.34 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral
% 5.15/5.34 thf(fact_567_power__add__numeral,axiom,
% 5.15/5.34 ! [A: int,M: num,N2: num] :
% 5.15/5.34 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.15/5.34 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral
% 5.15/5.34 thf(fact_568_power__add__numeral2,axiom,
% 5.15/5.34 ! [A: complex,M: num,N2: num,B: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.15/5.34 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral2
% 5.15/5.34 thf(fact_569_power__add__numeral2,axiom,
% 5.15/5.34 ! [A: real,M: num,N2: num,B: real] :
% 5.15/5.34 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.15/5.34 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral2
% 5.15/5.34 thf(fact_570_power__add__numeral2,axiom,
% 5.15/5.34 ! [A: rat,M: num,N2: num,B: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.15/5.34 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral2
% 5.15/5.34 thf(fact_571_power__add__numeral2,axiom,
% 5.15/5.34 ! [A: nat,M: num,N2: num,B: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.15/5.34 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral2
% 5.15/5.34 thf(fact_572_power__add__numeral2,axiom,
% 5.15/5.34 ! [A: int,M: num,N2: num,B: int] :
% 5.15/5.34 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.15/5.34 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add_numeral2
% 5.15/5.34 thf(fact_573_succ__member,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.15/5.34 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.15/5.34 = ( ( vEBT_vebt_member @ T @ Y )
% 5.15/5.34 & ( ord_less_nat @ X @ Y )
% 5.15/5.34 & ! [Z3: nat] :
% 5.15/5.34 ( ( ( vEBT_vebt_member @ T @ Z3 )
% 5.15/5.34 & ( ord_less_nat @ X @ Z3 ) )
% 5.15/5.34 => ( ord_less_eq_nat @ Y @ Z3 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % succ_member
% 5.15/5.34 thf(fact_574_pred__member,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.15/5.34 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.15/5.34 = ( ( vEBT_vebt_member @ T @ Y )
% 5.15/5.34 & ( ord_less_nat @ Y @ X )
% 5.15/5.34 & ! [Z3: nat] :
% 5.15/5.34 ( ( ( vEBT_vebt_member @ T @ Z3 )
% 5.15/5.34 & ( ord_less_nat @ Z3 @ X ) )
% 5.15/5.34 => ( ord_less_eq_nat @ Z3 @ Y ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % pred_member
% 5.15/5.34 thf(fact_575_complete__real,axiom,
% 5.15/5.34 ! [S3: set_real] :
% 5.15/5.34 ( ? [X5: real] : ( member_real @ X5 @ S3 )
% 5.15/5.34 => ( ? [Z4: real] :
% 5.15/5.34 ! [X3: real] :
% 5.15/5.34 ( ( member_real @ X3 @ S3 )
% 5.15/5.34 => ( ord_less_eq_real @ X3 @ Z4 ) )
% 5.15/5.34 => ? [Y3: real] :
% 5.15/5.34 ( ! [X5: real] :
% 5.15/5.34 ( ( member_real @ X5 @ S3 )
% 5.15/5.34 => ( ord_less_eq_real @ X5 @ Y3 ) )
% 5.15/5.34 & ! [Z4: real] :
% 5.15/5.34 ( ! [X3: real] :
% 5.15/5.34 ( ( member_real @ X3 @ S3 )
% 5.15/5.34 => ( ord_less_eq_real @ X3 @ Z4 ) )
% 5.15/5.34 => ( ord_less_eq_real @ Y3 @ Z4 ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % complete_real
% 5.15/5.34 thf(fact_576_real__arch__pow,axiom,
% 5.15/5.34 ! [X: real,Y: real] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.34 => ? [N: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % real_arch_pow
% 5.15/5.34 thf(fact_577_less__eq__real__def,axiom,
% 5.15/5.34 ( ord_less_eq_real
% 5.15/5.34 = ( ^ [X2: real,Y2: real] :
% 5.15/5.34 ( ( ord_less_real @ X2 @ Y2 )
% 5.15/5.34 | ( X2 = Y2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_eq_real_def
% 5.15/5.34 thf(fact_578_add__diff__assoc__enat,axiom,
% 5.15/5.34 ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 5.15/5.34 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 5.15/5.34 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 5.15/5.34 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_diff_assoc_enat
% 5.15/5.34 thf(fact_579_combine__common__factor,axiom,
% 5.15/5.34 ! [A: complex,E: complex,B: complex,C: complex] :
% 5.15/5.34 ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ C ) )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E ) @ C ) ) ).
% 5.15/5.34
% 5.15/5.34 % combine_common_factor
% 5.15/5.34 thf(fact_580_combine__common__factor,axiom,
% 5.15/5.34 ! [A: real,E: real,B: real,C: real] :
% 5.15/5.34 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.15/5.34
% 5.15/5.34 % combine_common_factor
% 5.15/5.34 thf(fact_581_combine__common__factor,axiom,
% 5.15/5.34 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.15/5.34
% 5.15/5.34 % combine_common_factor
% 5.15/5.34 thf(fact_582_combine__common__factor,axiom,
% 5.15/5.34 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.15/5.34 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.15/5.34
% 5.15/5.34 % combine_common_factor
% 5.15/5.34 thf(fact_583_combine__common__factor,axiom,
% 5.15/5.34 ! [A: int,E: int,B: int,C: int] :
% 5.15/5.34 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.15/5.34
% 5.15/5.34 % combine_common_factor
% 5.15/5.34 thf(fact_584_distrib__right,axiom,
% 5.15/5.34 ! [A: complex,B: complex,C: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right
% 5.15/5.34 thf(fact_585_distrib__right,axiom,
% 5.15/5.34 ! [A: real,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right
% 5.15/5.34 thf(fact_586_distrib__right,axiom,
% 5.15/5.34 ! [A: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right
% 5.15/5.34 thf(fact_587_distrib__right,axiom,
% 5.15/5.34 ! [A: nat,B: nat,C: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right
% 5.15/5.34 thf(fact_588_distrib__right,axiom,
% 5.15/5.34 ! [A: int,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_right
% 5.15/5.34 thf(fact_589_distrib__left,axiom,
% 5.15/5.34 ! [A: complex,B: complex,C: complex] :
% 5.15/5.34 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left
% 5.15/5.34 thf(fact_590_distrib__left,axiom,
% 5.15/5.34 ! [A: real,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left
% 5.15/5.34 thf(fact_591_distrib__left,axiom,
% 5.15/5.34 ! [A: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left
% 5.15/5.34 thf(fact_592_distrib__left,axiom,
% 5.15/5.34 ! [A: nat,B: nat,C: nat] :
% 5.15/5.34 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left
% 5.15/5.34 thf(fact_593_distrib__left,axiom,
% 5.15/5.34 ! [A: int,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % distrib_left
% 5.15/5.34 thf(fact_594_comm__semiring__class_Odistrib,axiom,
% 5.15/5.34 ! [A: complex,B: complex,C: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % comm_semiring_class.distrib
% 5.15/5.34 thf(fact_595_comm__semiring__class_Odistrib,axiom,
% 5.15/5.34 ! [A: real,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % comm_semiring_class.distrib
% 5.15/5.34 thf(fact_596_comm__semiring__class_Odistrib,axiom,
% 5.15/5.34 ! [A: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % comm_semiring_class.distrib
% 5.15/5.34 thf(fact_597_comm__semiring__class_Odistrib,axiom,
% 5.15/5.34 ! [A: nat,B: nat,C: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % comm_semiring_class.distrib
% 5.15/5.34 thf(fact_598_comm__semiring__class_Odistrib,axiom,
% 5.15/5.34 ! [A: int,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % comm_semiring_class.distrib
% 5.15/5.34 thf(fact_599_ring__class_Oring__distribs_I1_J,axiom,
% 5.15/5.34 ! [A: complex,B: complex,C: complex] :
% 5.15/5.34 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ring_class.ring_distribs(1)
% 5.15/5.34 thf(fact_600_ring__class_Oring__distribs_I1_J,axiom,
% 5.15/5.34 ! [A: real,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ring_class.ring_distribs(1)
% 5.15/5.34 thf(fact_601_ring__class_Oring__distribs_I1_J,axiom,
% 5.15/5.34 ! [A: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ring_class.ring_distribs(1)
% 5.15/5.34 thf(fact_602_ring__class_Oring__distribs_I1_J,axiom,
% 5.15/5.34 ! [A: int,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ring_class.ring_distribs(1)
% 5.15/5.34 thf(fact_603_ring__class_Oring__distribs_I2_J,axiom,
% 5.15/5.34 ! [A: complex,B: complex,C: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ring_class.ring_distribs(2)
% 5.15/5.34 thf(fact_604_ring__class_Oring__distribs_I2_J,axiom,
% 5.15/5.34 ! [A: real,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ring_class.ring_distribs(2)
% 5.15/5.34 thf(fact_605_ring__class_Oring__distribs_I2_J,axiom,
% 5.15/5.34 ! [A: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ring_class.ring_distribs(2)
% 5.15/5.34 thf(fact_606_ring__class_Oring__distribs_I2_J,axiom,
% 5.15/5.34 ! [A: int,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ring_class.ring_distribs(2)
% 5.15/5.34 thf(fact_607_left__diff__distrib,axiom,
% 5.15/5.34 ! [A: real,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.15/5.34 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib
% 5.15/5.34 thf(fact_608_left__diff__distrib,axiom,
% 5.15/5.34 ! [A: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.15/5.34 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib
% 5.15/5.34 thf(fact_609_left__diff__distrib,axiom,
% 5.15/5.34 ! [A: int,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.15/5.34 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib
% 5.15/5.34 thf(fact_610_right__diff__distrib,axiom,
% 5.15/5.34 ! [A: real,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.15/5.34 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib
% 5.15/5.34 thf(fact_611_right__diff__distrib,axiom,
% 5.15/5.34 ! [A: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.15/5.34 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib
% 5.15/5.34 thf(fact_612_right__diff__distrib,axiom,
% 5.15/5.34 ! [A: int,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.15/5.34 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib
% 5.15/5.34 thf(fact_613_left__diff__distrib_H,axiom,
% 5.15/5.34 ! [B: real,C: real,A: real] :
% 5.15/5.34 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.15/5.34 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib'
% 5.15/5.34 thf(fact_614_left__diff__distrib_H,axiom,
% 5.15/5.34 ! [B: rat,C: rat,A: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.15/5.34 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib'
% 5.15/5.34 thf(fact_615_left__diff__distrib_H,axiom,
% 5.15/5.34 ! [B: nat,C: nat,A: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.15/5.34 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib'
% 5.15/5.34 thf(fact_616_left__diff__distrib_H,axiom,
% 5.15/5.34 ! [B: int,C: int,A: int] :
% 5.15/5.34 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.15/5.34 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_diff_distrib'
% 5.15/5.34 thf(fact_617_right__diff__distrib_H,axiom,
% 5.15/5.34 ! [A: real,B: real,C: real] :
% 5.15/5.34 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.15/5.34 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib'
% 5.15/5.34 thf(fact_618_right__diff__distrib_H,axiom,
% 5.15/5.34 ! [A: rat,B: rat,C: rat] :
% 5.15/5.34 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.15/5.34 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib'
% 5.15/5.34 thf(fact_619_right__diff__distrib_H,axiom,
% 5.15/5.34 ! [A: nat,B: nat,C: nat] :
% 5.15/5.34 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.15/5.34 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib'
% 5.15/5.34 thf(fact_620_right__diff__distrib_H,axiom,
% 5.15/5.34 ! [A: int,B: int,C: int] :
% 5.15/5.34 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.15/5.34 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % right_diff_distrib'
% 5.15/5.34 thf(fact_621_power__commutes,axiom,
% 5.15/5.34 ! [A: complex,N2: nat] :
% 5.15/5.34 ( ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A )
% 5.15/5.34 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commutes
% 5.15/5.34 thf(fact_622_power__commutes,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( times_times_real @ ( power_power_real @ A @ N2 ) @ A )
% 5.15/5.34 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commutes
% 5.15/5.34 thf(fact_623_power__commutes,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ A )
% 5.15/5.34 = ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commutes
% 5.15/5.34 thf(fact_624_power__commutes,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
% 5.15/5.34 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commutes
% 5.15/5.34 thf(fact_625_power__commutes,axiom,
% 5.15/5.34 ! [A: int,N2: nat] :
% 5.15/5.34 ( ( times_times_int @ ( power_power_int @ A @ N2 ) @ A )
% 5.15/5.34 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commutes
% 5.15/5.34 thf(fact_626_power__mult__distrib,axiom,
% 5.15/5.34 ! [A: complex,B: complex,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N2 )
% 5.15/5.34 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult_distrib
% 5.15/5.34 thf(fact_627_power__mult__distrib,axiom,
% 5.15/5.34 ! [A: real,B: real,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N2 )
% 5.15/5.34 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult_distrib
% 5.15/5.34 thf(fact_628_power__mult__distrib,axiom,
% 5.15/5.34 ! [A: rat,B: rat,N2: nat] :
% 5.15/5.34 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N2 )
% 5.15/5.34 = ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult_distrib
% 5.15/5.34 thf(fact_629_power__mult__distrib,axiom,
% 5.15/5.34 ! [A: nat,B: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
% 5.15/5.34 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult_distrib
% 5.15/5.34 thf(fact_630_power__mult__distrib,axiom,
% 5.15/5.34 ! [A: int,B: int,N2: nat] :
% 5.15/5.34 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N2 )
% 5.15/5.34 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult_distrib
% 5.15/5.34 thf(fact_631_power__commuting__commutes,axiom,
% 5.15/5.34 ! [X: complex,Y: complex,N2: nat] :
% 5.15/5.34 ( ( ( times_times_complex @ X @ Y )
% 5.15/5.34 = ( times_times_complex @ Y @ X ) )
% 5.15/5.34 => ( ( times_times_complex @ ( power_power_complex @ X @ N2 ) @ Y )
% 5.15/5.34 = ( times_times_complex @ Y @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commuting_commutes
% 5.15/5.34 thf(fact_632_power__commuting__commutes,axiom,
% 5.15/5.34 ! [X: real,Y: real,N2: nat] :
% 5.15/5.34 ( ( ( times_times_real @ X @ Y )
% 5.15/5.34 = ( times_times_real @ Y @ X ) )
% 5.15/5.34 => ( ( times_times_real @ ( power_power_real @ X @ N2 ) @ Y )
% 5.15/5.34 = ( times_times_real @ Y @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commuting_commutes
% 5.15/5.34 thf(fact_633_power__commuting__commutes,axiom,
% 5.15/5.34 ! [X: rat,Y: rat,N2: nat] :
% 5.15/5.34 ( ( ( times_times_rat @ X @ Y )
% 5.15/5.34 = ( times_times_rat @ Y @ X ) )
% 5.15/5.34 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ Y )
% 5.15/5.34 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commuting_commutes
% 5.15/5.34 thf(fact_634_power__commuting__commutes,axiom,
% 5.15/5.34 ! [X: nat,Y: nat,N2: nat] :
% 5.15/5.34 ( ( ( times_times_nat @ X @ Y )
% 5.15/5.34 = ( times_times_nat @ Y @ X ) )
% 5.15/5.34 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ Y )
% 5.15/5.34 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commuting_commutes
% 5.15/5.34 thf(fact_635_power__commuting__commutes,axiom,
% 5.15/5.34 ! [X: int,Y: int,N2: nat] :
% 5.15/5.34 ( ( ( times_times_int @ X @ Y )
% 5.15/5.34 = ( times_times_int @ Y @ X ) )
% 5.15/5.34 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ Y )
% 5.15/5.34 = ( times_times_int @ Y @ ( power_power_int @ X @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_commuting_commutes
% 5.15/5.34 thf(fact_636_Suc__mult__cancel1,axiom,
% 5.15/5.34 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.15/5.34 = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.15/5.34 = ( M = N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % Suc_mult_cancel1
% 5.15/5.34 thf(fact_637_power__mult,axiom,
% 5.15/5.34 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.34 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult
% 5.15/5.34 thf(fact_638_power__mult,axiom,
% 5.15/5.34 ! [A: real,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.34 = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult
% 5.15/5.34 thf(fact_639_power__mult,axiom,
% 5.15/5.34 ! [A: complex,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.34 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult
% 5.15/5.34 thf(fact_640_power__mult,axiom,
% 5.15/5.34 ! [A: int,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.34 = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_mult
% 5.15/5.34 thf(fact_641_le__cube,axiom,
% 5.15/5.34 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_cube
% 5.15/5.34 thf(fact_642_le__square,axiom,
% 5.15/5.34 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.15/5.34
% 5.15/5.34 % le_square
% 5.15/5.34 thf(fact_643_mult__le__mono,axiom,
% 5.15/5.34 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.34 => ( ( ord_less_eq_nat @ K @ L )
% 5.15/5.34 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_le_mono
% 5.15/5.34 thf(fact_644_mult__le__mono1,axiom,
% 5.15/5.34 ! [I: nat,J: nat,K: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.34 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_le_mono1
% 5.15/5.34 thf(fact_645_mult__le__mono2,axiom,
% 5.15/5.34 ! [I: nat,J: nat,K: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.34 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_le_mono2
% 5.15/5.34 thf(fact_646_left__add__mult__distrib,axiom,
% 5.15/5.34 ! [I: nat,U: nat,J: nat,K: nat] :
% 5.15/5.34 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_add_mult_distrib
% 5.15/5.34 thf(fact_647_add__mult__distrib2,axiom,
% 5.15/5.34 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_mult_distrib2
% 5.15/5.34 thf(fact_648_add__mult__distrib,axiom,
% 5.15/5.34 ! [M: nat,N2: nat,K: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % add_mult_distrib
% 5.15/5.34 thf(fact_649_nat__mult__1__right,axiom,
% 5.15/5.34 ! [N2: nat] :
% 5.15/5.34 ( ( times_times_nat @ N2 @ one_one_nat )
% 5.15/5.34 = N2 ) ).
% 5.15/5.34
% 5.15/5.34 % nat_mult_1_right
% 5.15/5.34 thf(fact_650_nat__mult__1,axiom,
% 5.15/5.34 ! [N2: nat] :
% 5.15/5.34 ( ( times_times_nat @ one_one_nat @ N2 )
% 5.15/5.34 = N2 ) ).
% 5.15/5.34
% 5.15/5.34 % nat_mult_1
% 5.15/5.34 thf(fact_651_diff__mult__distrib,axiom,
% 5.15/5.34 ! [M: nat,N2: nat,K: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 5.15/5.34 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % diff_mult_distrib
% 5.15/5.34 thf(fact_652_diff__mult__distrib2,axiom,
% 5.15/5.34 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.34 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % diff_mult_distrib2
% 5.15/5.34 thf(fact_653_div__mult2__eq,axiom,
% 5.15/5.34 ! [M: nat,N2: nat,Q3: nat] :
% 5.15/5.34 ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q3 ) )
% 5.15/5.34 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q3 ) ) ).
% 5.15/5.34
% 5.15/5.34 % div_mult2_eq
% 5.15/5.34 thf(fact_654_lambda__one,axiom,
% 5.15/5.34 ( ( ^ [X2: complex] : X2 )
% 5.15/5.34 = ( times_times_complex @ one_one_complex ) ) ).
% 5.15/5.34
% 5.15/5.34 % lambda_one
% 5.15/5.34 thf(fact_655_lambda__one,axiom,
% 5.15/5.34 ( ( ^ [X2: real] : X2 )
% 5.15/5.34 = ( times_times_real @ one_one_real ) ) ).
% 5.15/5.34
% 5.15/5.34 % lambda_one
% 5.15/5.34 thf(fact_656_lambda__one,axiom,
% 5.15/5.34 ( ( ^ [X2: rat] : X2 )
% 5.15/5.34 = ( times_times_rat @ one_one_rat ) ) ).
% 5.15/5.34
% 5.15/5.34 % lambda_one
% 5.15/5.34 thf(fact_657_lambda__one,axiom,
% 5.15/5.34 ( ( ^ [X2: nat] : X2 )
% 5.15/5.34 = ( times_times_nat @ one_one_nat ) ) ).
% 5.15/5.34
% 5.15/5.34 % lambda_one
% 5.15/5.34 thf(fact_658_lambda__one,axiom,
% 5.15/5.34 ( ( ^ [X2: int] : X2 )
% 5.15/5.34 = ( times_times_int @ one_one_int ) ) ).
% 5.15/5.34
% 5.15/5.34 % lambda_one
% 5.15/5.34 thf(fact_659_less__1__mult,axiom,
% 5.15/5.34 ! [M: real,N2: real] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ M )
% 5.15/5.34 => ( ( ord_less_real @ one_one_real @ N2 )
% 5.15/5.34 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_1_mult
% 5.15/5.34 thf(fact_660_less__1__mult,axiom,
% 5.15/5.34 ! [M: rat,N2: rat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ M )
% 5.15/5.34 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 5.15/5.34 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_1_mult
% 5.15/5.34 thf(fact_661_less__1__mult,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ M )
% 5.15/5.34 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.15/5.34 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_1_mult
% 5.15/5.34 thf(fact_662_less__1__mult,axiom,
% 5.15/5.34 ! [M: int,N2: int] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ M )
% 5.15/5.34 => ( ( ord_less_int @ one_one_int @ N2 )
% 5.15/5.34 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_1_mult
% 5.15/5.34 thf(fact_663_mult__numeral__1__right,axiom,
% 5.15/5.34 ! [A: complex] :
% 5.15/5.34 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1_right
% 5.15/5.34 thf(fact_664_mult__numeral__1__right,axiom,
% 5.15/5.34 ! [A: real] :
% 5.15/5.34 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1_right
% 5.15/5.34 thf(fact_665_mult__numeral__1__right,axiom,
% 5.15/5.34 ! [A: rat] :
% 5.15/5.34 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1_right
% 5.15/5.34 thf(fact_666_mult__numeral__1__right,axiom,
% 5.15/5.34 ! [A: nat] :
% 5.15/5.34 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1_right
% 5.15/5.34 thf(fact_667_mult__numeral__1__right,axiom,
% 5.15/5.34 ! [A: int] :
% 5.15/5.34 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1_right
% 5.15/5.34 thf(fact_668_mult__numeral__1,axiom,
% 5.15/5.34 ! [A: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1
% 5.15/5.34 thf(fact_669_mult__numeral__1,axiom,
% 5.15/5.34 ! [A: real] :
% 5.15/5.34 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1
% 5.15/5.34 thf(fact_670_mult__numeral__1,axiom,
% 5.15/5.34 ! [A: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1
% 5.15/5.34 thf(fact_671_mult__numeral__1,axiom,
% 5.15/5.34 ! [A: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1
% 5.15/5.34 thf(fact_672_mult__numeral__1,axiom,
% 5.15/5.34 ! [A: int] :
% 5.15/5.34 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.15/5.34 = A ) ).
% 5.15/5.34
% 5.15/5.34 % mult_numeral_1
% 5.15/5.34 thf(fact_673_mult__diff__mult,axiom,
% 5.15/5.34 ! [X: complex,Y: complex,A: complex,B: complex] :
% 5.15/5.34 ( ( minus_minus_complex @ ( times_times_complex @ X @ Y ) @ ( times_times_complex @ A @ B ) )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ X @ ( minus_minus_complex @ Y @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X @ A ) @ B ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_diff_mult
% 5.15/5.34 thf(fact_674_mult__diff__mult,axiom,
% 5.15/5.34 ! [X: real,Y: real,A: real,B: real] :
% 5.15/5.34 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_diff_mult
% 5.15/5.34 thf(fact_675_mult__diff__mult,axiom,
% 5.15/5.34 ! [X: rat,Y: rat,A: rat,B: rat] :
% 5.15/5.34 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_diff_mult
% 5.15/5.34 thf(fact_676_mult__diff__mult,axiom,
% 5.15/5.34 ! [X: int,Y: int,A: int,B: int] :
% 5.15/5.34 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_diff_mult
% 5.15/5.34 thf(fact_677_square__diff__square__factored,axiom,
% 5.15/5.34 ! [X: complex,Y: complex] :
% 5.15/5.34 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ ( times_times_complex @ Y @ Y ) )
% 5.15/5.34 = ( times_times_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_complex @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % square_diff_square_factored
% 5.15/5.34 thf(fact_678_square__diff__square__factored,axiom,
% 5.15/5.34 ! [X: real,Y: real] :
% 5.15/5.34 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.15/5.34 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % square_diff_square_factored
% 5.15/5.34 thf(fact_679_square__diff__square__factored,axiom,
% 5.15/5.34 ! [X: rat,Y: rat] :
% 5.15/5.34 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.15/5.34 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % square_diff_square_factored
% 5.15/5.34 thf(fact_680_square__diff__square__factored,axiom,
% 5.15/5.34 ! [X: int,Y: int] :
% 5.15/5.34 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.15/5.34 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % square_diff_square_factored
% 5.15/5.34 thf(fact_681_eq__add__iff2,axiom,
% 5.15/5.34 ! [A: complex,E: complex,C: complex,B: complex,D: complex] :
% 5.15/5.34 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D ) )
% 5.15/5.34 = ( C
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % eq_add_iff2
% 5.15/5.34 thf(fact_682_eq__add__iff2,axiom,
% 5.15/5.34 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.15/5.34 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.15/5.34 = ( C
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % eq_add_iff2
% 5.15/5.34 thf(fact_683_eq__add__iff2,axiom,
% 5.15/5.34 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.15/5.34 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.15/5.34 = ( C
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % eq_add_iff2
% 5.15/5.34 thf(fact_684_eq__add__iff2,axiom,
% 5.15/5.34 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.15/5.34 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.15/5.34 = ( C
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % eq_add_iff2
% 5.15/5.34 thf(fact_685_eq__add__iff1,axiom,
% 5.15/5.34 ! [A: complex,E: complex,C: complex,B: complex,D: complex] :
% 5.15/5.34 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D ) )
% 5.15/5.34 = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E ) @ C )
% 5.15/5.34 = D ) ) ).
% 5.15/5.34
% 5.15/5.34 % eq_add_iff1
% 5.15/5.34 thf(fact_686_eq__add__iff1,axiom,
% 5.15/5.34 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.15/5.34 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.15/5.34 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.15/5.34 = D ) ) ).
% 5.15/5.34
% 5.15/5.34 % eq_add_iff1
% 5.15/5.34 thf(fact_687_eq__add__iff1,axiom,
% 5.15/5.34 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.15/5.34 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.15/5.34 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.15/5.34 = D ) ) ).
% 5.15/5.34
% 5.15/5.34 % eq_add_iff1
% 5.15/5.34 thf(fact_688_eq__add__iff1,axiom,
% 5.15/5.34 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.15/5.34 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.15/5.34 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.15/5.34 = D ) ) ).
% 5.15/5.34
% 5.15/5.34 % eq_add_iff1
% 5.15/5.34 thf(fact_689_left__right__inverse__power,axiom,
% 5.15/5.34 ! [X: complex,Y: complex,N2: nat] :
% 5.15/5.34 ( ( ( times_times_complex @ X @ Y )
% 5.15/5.34 = one_one_complex )
% 5.15/5.34 => ( ( times_times_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.15/5.34 = one_one_complex ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_right_inverse_power
% 5.15/5.34 thf(fact_690_left__right__inverse__power,axiom,
% 5.15/5.34 ! [X: real,Y: real,N2: nat] :
% 5.15/5.34 ( ( ( times_times_real @ X @ Y )
% 5.15/5.34 = one_one_real )
% 5.15/5.34 => ( ( times_times_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.15/5.34 = one_one_real ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_right_inverse_power
% 5.15/5.34 thf(fact_691_left__right__inverse__power,axiom,
% 5.15/5.34 ! [X: rat,Y: rat,N2: nat] :
% 5.15/5.34 ( ( ( times_times_rat @ X @ Y )
% 5.15/5.34 = one_one_rat )
% 5.15/5.34 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.15/5.34 = one_one_rat ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_right_inverse_power
% 5.15/5.34 thf(fact_692_left__right__inverse__power,axiom,
% 5.15/5.34 ! [X: nat,Y: nat,N2: nat] :
% 5.15/5.34 ( ( ( times_times_nat @ X @ Y )
% 5.15/5.34 = one_one_nat )
% 5.15/5.34 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 5.15/5.34 = one_one_nat ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_right_inverse_power
% 5.15/5.34 thf(fact_693_left__right__inverse__power,axiom,
% 5.15/5.34 ! [X: int,Y: int,N2: nat] :
% 5.15/5.34 ( ( ( times_times_int @ X @ Y )
% 5.15/5.34 = one_one_int )
% 5.15/5.34 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.15/5.34 = one_one_int ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_right_inverse_power
% 5.15/5.34 thf(fact_694_power__Suc,axiom,
% 5.15/5.34 ! [A: complex,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc
% 5.15/5.34 thf(fact_695_power__Suc,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc
% 5.15/5.34 thf(fact_696_power__Suc,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc
% 5.15/5.34 thf(fact_697_power__Suc,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc
% 5.15/5.34 thf(fact_698_power__Suc,axiom,
% 5.15/5.34 ! [A: int,N2: nat] :
% 5.15/5.34 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc
% 5.15/5.34 thf(fact_699_power__Suc2,axiom,
% 5.15/5.34 ! [A: complex,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc2
% 5.15/5.34 thf(fact_700_power__Suc2,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc2
% 5.15/5.34 thf(fact_701_power__Suc2,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc2
% 5.15/5.34 thf(fact_702_power__Suc2,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc2
% 5.15/5.34 thf(fact_703_power__Suc2,axiom,
% 5.15/5.34 ! [A: int,N2: nat] :
% 5.15/5.34 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.15/5.34 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_Suc2
% 5.15/5.34 thf(fact_704_Suc__mult__less__cancel1,axiom,
% 5.15/5.34 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.15/5.34 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % Suc_mult_less_cancel1
% 5.15/5.34 thf(fact_705_power__add,axiom,
% 5.15/5.34 ! [A: complex,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.34 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add
% 5.15/5.34 thf(fact_706_power__add,axiom,
% 5.15/5.34 ! [A: real,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.34 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add
% 5.15/5.34 thf(fact_707_power__add,axiom,
% 5.15/5.34 ! [A: rat,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.34 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add
% 5.15/5.34 thf(fact_708_power__add,axiom,
% 5.15/5.34 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.34 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add
% 5.15/5.34 thf(fact_709_power__add,axiom,
% 5.15/5.34 ! [A: int,M: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.34 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_add
% 5.15/5.34 thf(fact_710_Suc__mult__le__cancel1,axiom,
% 5.15/5.34 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.15/5.34 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.34
% 5.15/5.34 % Suc_mult_le_cancel1
% 5.15/5.34 thf(fact_711_mult__Suc,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 5.15/5.34 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_Suc
% 5.15/5.34 thf(fact_712_less__mult__imp__div__less,axiom,
% 5.15/5.34 ! [M: nat,I: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N2 ) )
% 5.15/5.34 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_mult_imp_div_less
% 5.15/5.34 thf(fact_713_div__times__less__eq__dividend,axiom,
% 5.15/5.34 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 5.15/5.34
% 5.15/5.34 % div_times_less_eq_dividend
% 5.15/5.34 thf(fact_714_times__div__less__eq__dividend,axiom,
% 5.15/5.34 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 5.15/5.34
% 5.15/5.34 % times_div_less_eq_dividend
% 5.15/5.34 thf(fact_715_member__bound__height,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % member_bound_height
% 5.15/5.34 thf(fact_716_power__odd__eq,axiom,
% 5.15/5.34 ! [A: complex,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.34 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_odd_eq
% 5.15/5.34 thf(fact_717_power__odd__eq,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.34 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_odd_eq
% 5.15/5.34 thf(fact_718_power__odd__eq,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.34 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_odd_eq
% 5.15/5.34 thf(fact_719_power__odd__eq,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.34 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_odd_eq
% 5.15/5.34 thf(fact_720_power__odd__eq,axiom,
% 5.15/5.34 ! [A: int,N2: nat] :
% 5.15/5.34 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.34 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_odd_eq
% 5.15/5.34 thf(fact_721_height__node,axiom,
% 5.15/5.34 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.15/5.34 => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % height_node
% 5.15/5.34 thf(fact_722_ordered__ring__class_Ole__add__iff1,axiom,
% 5.15/5.34 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.15/5.34 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.15/5.34
% 5.15/5.34 % ordered_ring_class.le_add_iff1
% 5.15/5.34 thf(fact_723_ordered__ring__class_Ole__add__iff1,axiom,
% 5.15/5.34 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.15/5.34 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.15/5.34
% 5.15/5.34 % ordered_ring_class.le_add_iff1
% 5.15/5.34 thf(fact_724_ordered__ring__class_Ole__add__iff1,axiom,
% 5.15/5.34 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.15/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.15/5.34
% 5.15/5.34 % ordered_ring_class.le_add_iff1
% 5.15/5.34 thf(fact_725_ordered__ring__class_Ole__add__iff2,axiom,
% 5.15/5.34 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.15/5.34 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ordered_ring_class.le_add_iff2
% 5.15/5.34 thf(fact_726_ordered__ring__class_Ole__add__iff2,axiom,
% 5.15/5.34 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.15/5.34 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ordered_ring_class.le_add_iff2
% 5.15/5.34 thf(fact_727_ordered__ring__class_Ole__add__iff2,axiom,
% 5.15/5.34 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.15/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % ordered_ring_class.le_add_iff2
% 5.15/5.34 thf(fact_728_less__add__iff2,axiom,
% 5.15/5.34 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.15/5.34 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_iff2
% 5.15/5.34 thf(fact_729_less__add__iff2,axiom,
% 5.15/5.34 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.15/5.34 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_iff2
% 5.15/5.34 thf(fact_730_less__add__iff2,axiom,
% 5.15/5.34 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.15/5.34 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_iff2
% 5.15/5.34 thf(fact_731_less__add__iff1,axiom,
% 5.15/5.34 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.15/5.34 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_iff1
% 5.15/5.34 thf(fact_732_less__add__iff1,axiom,
% 5.15/5.34 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.15/5.34 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_iff1
% 5.15/5.34 thf(fact_733_less__add__iff1,axiom,
% 5.15/5.34 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.15/5.34 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.15/5.34 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.15/5.34
% 5.15/5.34 % less_add_iff1
% 5.15/5.34 thf(fact_734_power__less__power__Suc,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.34 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_less_power_Suc
% 5.15/5.34 thf(fact_735_power__less__power__Suc,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_less_power_Suc
% 5.15/5.34 thf(fact_736_power__less__power__Suc,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_less_power_Suc
% 5.15/5.34 thf(fact_737_power__less__power__Suc,axiom,
% 5.15/5.34 ! [A: int,N2: nat] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ A )
% 5.15/5.34 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_less_power_Suc
% 5.15/5.34 thf(fact_738_power__gt1__lemma,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.34 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_gt1_lemma
% 5.15/5.34 thf(fact_739_power__gt1__lemma,axiom,
% 5.15/5.34 ! [A: rat,N2: nat] :
% 5.15/5.34 ( ( ord_less_rat @ one_one_rat @ A )
% 5.15/5.34 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_gt1_lemma
% 5.15/5.34 thf(fact_740_power__gt1__lemma,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_nat @ one_one_nat @ A )
% 5.15/5.34 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_gt1_lemma
% 5.15/5.34 thf(fact_741_power__gt1__lemma,axiom,
% 5.15/5.34 ! [A: int,N2: nat] :
% 5.15/5.34 ( ( ord_less_int @ one_one_int @ A )
% 5.15/5.34 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_gt1_lemma
% 5.15/5.34 thf(fact_742_square__diff__one__factored,axiom,
% 5.15/5.34 ! [X: complex] :
% 5.15/5.34 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.15/5.34 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % square_diff_one_factored
% 5.15/5.34 thf(fact_743_square__diff__one__factored,axiom,
% 5.15/5.34 ! [X: real] :
% 5.15/5.34 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.15/5.34 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % square_diff_one_factored
% 5.15/5.34 thf(fact_744_square__diff__one__factored,axiom,
% 5.15/5.34 ! [X: rat] :
% 5.15/5.34 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.15/5.34 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % square_diff_one_factored
% 5.15/5.34 thf(fact_745_square__diff__one__factored,axiom,
% 5.15/5.34 ! [X: int] :
% 5.15/5.34 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.15/5.34 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % square_diff_one_factored
% 5.15/5.34 thf(fact_746_nat__eq__add__iff1,axiom,
% 5.15/5.34 ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ J @ I )
% 5.15/5.34 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.15/5.34 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.15/5.34 = N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % nat_eq_add_iff1
% 5.15/5.34 thf(fact_747_nat__eq__add__iff2,axiom,
% 5.15/5.34 ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.34 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.15/5.34 = ( M
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % nat_eq_add_iff2
% 5.15/5.34 thf(fact_748_nat__le__add__iff1,axiom,
% 5.15/5.34 ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ J @ I )
% 5.15/5.34 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.15/5.34 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % nat_le_add_iff1
% 5.15/5.34 thf(fact_749_nat__le__add__iff2,axiom,
% 5.15/5.34 ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.34 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.15/5.34 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % nat_le_add_iff2
% 5.15/5.34 thf(fact_750_nat__diff__add__eq1,axiom,
% 5.15/5.34 ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ J @ I )
% 5.15/5.34 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.15/5.34 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % nat_diff_add_eq1
% 5.15/5.34 thf(fact_751_nat__diff__add__eq2,axiom,
% 5.15/5.34 ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.15/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.34 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.15/5.34 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % nat_diff_add_eq2
% 5.15/5.34 thf(fact_752_power__numeral__even,axiom,
% 5.15/5.34 ! [Z: complex,W: num] :
% 5.15/5.34 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.15/5.34 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_even
% 5.15/5.34 thf(fact_753_power__numeral__even,axiom,
% 5.15/5.34 ! [Z: real,W: num] :
% 5.15/5.34 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.15/5.34 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_even
% 5.15/5.34 thf(fact_754_power__numeral__even,axiom,
% 5.15/5.34 ! [Z: rat,W: num] :
% 5.15/5.34 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.15/5.34 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_even
% 5.15/5.34 thf(fact_755_power__numeral__even,axiom,
% 5.15/5.34 ! [Z: nat,W: num] :
% 5.15/5.34 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.15/5.34 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_even
% 5.15/5.34 thf(fact_756_power__numeral__even,axiom,
% 5.15/5.34 ! [Z: int,W: num] :
% 5.15/5.34 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.15/5.34 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_even
% 5.15/5.34 thf(fact_757_power__numeral__odd,axiom,
% 5.15/5.34 ! [Z: complex,W: num] :
% 5.15/5.34 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.15/5.34 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_odd
% 5.15/5.34 thf(fact_758_power__numeral__odd,axiom,
% 5.15/5.34 ! [Z: real,W: num] :
% 5.15/5.34 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.15/5.34 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_odd
% 5.15/5.34 thf(fact_759_power__numeral__odd,axiom,
% 5.15/5.34 ! [Z: rat,W: num] :
% 5.15/5.34 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.15/5.34 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_odd
% 5.15/5.34 thf(fact_760_power__numeral__odd,axiom,
% 5.15/5.34 ! [Z: nat,W: num] :
% 5.15/5.34 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.15/5.34 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_odd
% 5.15/5.34 thf(fact_761_power__numeral__odd,axiom,
% 5.15/5.34 ! [Z: int,W: num] :
% 5.15/5.34 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.15/5.34 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_numeral_odd
% 5.15/5.34 thf(fact_762_left__add__twice,axiom,
% 5.15/5.34 ! [A: complex,B: complex] :
% 5.15/5.34 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.15/5.34 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_add_twice
% 5.15/5.34 thf(fact_763_left__add__twice,axiom,
% 5.15/5.34 ! [A: real,B: real] :
% 5.15/5.34 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.15/5.34 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_add_twice
% 5.15/5.34 thf(fact_764_left__add__twice,axiom,
% 5.15/5.34 ! [A: rat,B: rat] :
% 5.15/5.34 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.15/5.34 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_add_twice
% 5.15/5.34 thf(fact_765_left__add__twice,axiom,
% 5.15/5.34 ! [A: nat,B: nat] :
% 5.15/5.34 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.15/5.34 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_add_twice
% 5.15/5.34 thf(fact_766_left__add__twice,axiom,
% 5.15/5.34 ! [A: int,B: int] :
% 5.15/5.34 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.15/5.34 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.15/5.34
% 5.15/5.34 % left_add_twice
% 5.15/5.34 thf(fact_767_mult__2__right,axiom,
% 5.15/5.34 ! [Z: complex] :
% 5.15/5.34 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2_right
% 5.15/5.34 thf(fact_768_mult__2__right,axiom,
% 5.15/5.34 ! [Z: real] :
% 5.15/5.34 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2_right
% 5.15/5.34 thf(fact_769_mult__2__right,axiom,
% 5.15/5.34 ! [Z: rat] :
% 5.15/5.34 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2_right
% 5.15/5.34 thf(fact_770_mult__2__right,axiom,
% 5.15/5.34 ! [Z: nat] :
% 5.15/5.34 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2_right
% 5.15/5.34 thf(fact_771_mult__2__right,axiom,
% 5.15/5.34 ! [Z: int] :
% 5.15/5.34 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2_right
% 5.15/5.34 thf(fact_772_mult__2,axiom,
% 5.15/5.34 ! [Z: complex] :
% 5.15/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.15/5.34 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2
% 5.15/5.34 thf(fact_773_mult__2,axiom,
% 5.15/5.34 ! [Z: real] :
% 5.15/5.34 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.15/5.34 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2
% 5.15/5.34 thf(fact_774_mult__2,axiom,
% 5.15/5.34 ! [Z: rat] :
% 5.15/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.15/5.34 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2
% 5.15/5.34 thf(fact_775_mult__2,axiom,
% 5.15/5.34 ! [Z: nat] :
% 5.15/5.34 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.15/5.34 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2
% 5.15/5.34 thf(fact_776_mult__2,axiom,
% 5.15/5.34 ! [Z: int] :
% 5.15/5.34 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.15/5.34 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.15/5.34
% 5.15/5.34 % mult_2
% 5.15/5.34 thf(fact_777_power2__eq__square,axiom,
% 5.15/5.34 ! [A: complex] :
% 5.15/5.34 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( times_times_complex @ A @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_eq_square
% 5.15/5.34 thf(fact_778_power2__eq__square,axiom,
% 5.15/5.34 ! [A: real] :
% 5.15/5.34 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( times_times_real @ A @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_eq_square
% 5.15/5.34 thf(fact_779_power2__eq__square,axiom,
% 5.15/5.34 ! [A: rat] :
% 5.15/5.34 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( times_times_rat @ A @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_eq_square
% 5.15/5.34 thf(fact_780_power2__eq__square,axiom,
% 5.15/5.34 ! [A: nat] :
% 5.15/5.34 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( times_times_nat @ A @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_eq_square
% 5.15/5.34 thf(fact_781_power2__eq__square,axiom,
% 5.15/5.34 ! [A: int] :
% 5.15/5.34 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.34 = ( times_times_int @ A @ A ) ) ).
% 5.15/5.34
% 5.15/5.34 % power2_eq_square
% 5.15/5.34 thf(fact_782_power4__eq__xxxx,axiom,
% 5.15/5.34 ! [X: complex] :
% 5.15/5.34 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.34 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 5.15/5.34
% 5.15/5.34 % power4_eq_xxxx
% 5.15/5.34 thf(fact_783_power4__eq__xxxx,axiom,
% 5.15/5.34 ! [X: real] :
% 5.15/5.34 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.34 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 5.15/5.34
% 5.15/5.34 % power4_eq_xxxx
% 5.15/5.34 thf(fact_784_power4__eq__xxxx,axiom,
% 5.15/5.34 ! [X: rat] :
% 5.15/5.34 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.34 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 5.15/5.34
% 5.15/5.34 % power4_eq_xxxx
% 5.15/5.34 thf(fact_785_power4__eq__xxxx,axiom,
% 5.15/5.34 ! [X: nat] :
% 5.15/5.34 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.34 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.15/5.34
% 5.15/5.34 % power4_eq_xxxx
% 5.15/5.34 thf(fact_786_power4__eq__xxxx,axiom,
% 5.15/5.34 ! [X: int] :
% 5.15/5.34 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.34 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.15/5.34
% 5.15/5.34 % power4_eq_xxxx
% 5.15/5.34 thf(fact_787_insersimp_H,axiom,
% 5.15/5.34 ! [T: vEBT_VEBT,N2: nat,Y: nat] :
% 5.15/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.34 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 5.15/5.34 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y ) @ one_one_nat ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % insersimp'
% 5.15/5.34 thf(fact_788_power__even__eq,axiom,
% 5.15/5.34 ! [A: nat,N2: nat] :
% 5.15/5.34 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_even_eq
% 5.15/5.34 thf(fact_789_power__even__eq,axiom,
% 5.15/5.34 ! [A: real,N2: nat] :
% 5.15/5.34 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_even_eq
% 5.15/5.34 thf(fact_790_power__even__eq,axiom,
% 5.15/5.34 ! [A: complex,N2: nat] :
% 5.15/5.34 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.34 = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.34
% 5.15/5.34 % power_even_eq
% 5.15/5.34 thf(fact_791_power__even__eq,axiom,
% 5.15/5.35 ! [A: int,N2: nat] :
% 5.15/5.35 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.35 = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power_even_eq
% 5.15/5.35 thf(fact_792_power3__eq__cube,axiom,
% 5.15/5.35 ! [A: complex] :
% 5.15/5.35 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.15/5.35 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.15/5.35
% 5.15/5.35 % power3_eq_cube
% 5.15/5.35 thf(fact_793_power3__eq__cube,axiom,
% 5.15/5.35 ! [A: real] :
% 5.15/5.35 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.15/5.35 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.15/5.35
% 5.15/5.35 % power3_eq_cube
% 5.15/5.35 thf(fact_794_power3__eq__cube,axiom,
% 5.15/5.35 ! [A: rat] :
% 5.15/5.35 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.15/5.35 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.15/5.35
% 5.15/5.35 % power3_eq_cube
% 5.15/5.35 thf(fact_795_power3__eq__cube,axiom,
% 5.15/5.35 ! [A: nat] :
% 5.15/5.35 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.15/5.35 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.15/5.35
% 5.15/5.35 % power3_eq_cube
% 5.15/5.35 thf(fact_796_power3__eq__cube,axiom,
% 5.15/5.35 ! [A: int] :
% 5.15/5.35 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.15/5.35 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.15/5.35
% 5.15/5.35 % power3_eq_cube
% 5.15/5.35 thf(fact_797_div__nat__eqI,axiom,
% 5.15/5.35 ! [N2: nat,Q3: nat,M: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q3 ) @ M )
% 5.15/5.35 => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q3 ) ) )
% 5.15/5.35 => ( ( divide_divide_nat @ M @ N2 )
% 5.15/5.35 = Q3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % div_nat_eqI
% 5.15/5.35 thf(fact_798_insertsimp_H,axiom,
% 5.15/5.35 ! [T: vEBT_VEBT,N2: nat,L: nat] :
% 5.15/5.35 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.35 => ( ( vEBT_VEBT_minNull @ T )
% 5.15/5.35 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L ) @ one_one_nat ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % insertsimp'
% 5.15/5.35 thf(fact_799_nat__less__add__iff2,axiom,
% 5.15/5.35 ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.35 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.15/5.35 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nat_less_add_iff2
% 5.15/5.35 thf(fact_800_nat__less__add__iff1,axiom,
% 5.15/5.35 ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ J @ I )
% 5.15/5.35 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.15/5.35 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nat_less_add_iff1
% 5.15/5.35 thf(fact_801_insersimp,axiom,
% 5.15/5.35 ! [T: vEBT_VEBT,N2: nat,Y: nat] :
% 5.15/5.35 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.35 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 5.15/5.35 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % insersimp
% 5.15/5.35 thf(fact_802_insertsimp,axiom,
% 5.15/5.35 ! [T: vEBT_VEBT,N2: nat,L: nat] :
% 5.15/5.35 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.35 => ( ( vEBT_VEBT_minNull @ T )
% 5.15/5.35 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % insertsimp
% 5.15/5.35 thf(fact_803_power2__sum,axiom,
% 5.15/5.35 ! [X: complex,Y: complex] :
% 5.15/5.35 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_sum
% 5.15/5.35 thf(fact_804_power2__sum,axiom,
% 5.15/5.35 ! [X: real,Y: real] :
% 5.15/5.35 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_sum
% 5.15/5.35 thf(fact_805_power2__sum,axiom,
% 5.15/5.35 ! [X: rat,Y: rat] :
% 5.15/5.35 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_sum
% 5.15/5.35 thf(fact_806_power2__sum,axiom,
% 5.15/5.35 ! [X: nat,Y: nat] :
% 5.15/5.35 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_sum
% 5.15/5.35 thf(fact_807_power2__sum,axiom,
% 5.15/5.35 ! [X: int,Y: int] :
% 5.15/5.35 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_sum
% 5.15/5.35 thf(fact_808_power2__diff,axiom,
% 5.15/5.35 ! [X: complex,Y: complex] :
% 5.15/5.35 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_diff
% 5.15/5.35 thf(fact_809_power2__diff,axiom,
% 5.15/5.35 ! [X: real,Y: real] :
% 5.15/5.35 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_diff
% 5.15/5.35 thf(fact_810_power2__diff,axiom,
% 5.15/5.35 ! [X: rat,Y: rat] :
% 5.15/5.35 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_diff
% 5.15/5.35 thf(fact_811_power2__diff,axiom,
% 5.15/5.35 ! [X: int,Y: int] :
% 5.15/5.35 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.35 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power2_diff
% 5.15/5.35 thf(fact_812_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.15/5.35 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.15/5.35 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.15/5.35
% 5.15/5.35 % VEBT_internal.minNull.simps(5)
% 5.15/5.35 thf(fact_813_invar__vebt_Ointros_I5_J,axiom,
% 5.15/5.35 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.15/5.35 ( ! [X3: vEBT_VEBT] :
% 5.15/5.35 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.35 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.15/5.35 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.15/5.35 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.15/5.35 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.35 => ( ( M
% 5.15/5.35 = ( suc @ N2 ) )
% 5.15/5.35 => ( ( Deg
% 5.15/5.35 = ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.35 => ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.35 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X4 ) )
% 5.15/5.35 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.15/5.35 => ( ( ( Mi = Ma )
% 5.15/5.35 => ! [X3: vEBT_VEBT] :
% 5.15/5.35 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.35 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.15/5.35 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.15/5.35 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.15/5.35 => ( ( ( Mi != Ma )
% 5.15/5.35 => ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.35 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 5.15/5.35 = I2 )
% 5.15/5.35 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 5.15/5.35 & ! [X3: nat] :
% 5.15/5.35 ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 5.15/5.35 = I2 )
% 5.15/5.35 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 5.15/5.35 => ( ( ord_less_nat @ Mi @ X3 )
% 5.15/5.35 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.15/5.35 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % invar_vebt.intros(5)
% 5.15/5.35 thf(fact_814_invar__vebt_Ointros_I4_J,axiom,
% 5.15/5.35 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.15/5.35 ( ! [X3: vEBT_VEBT] :
% 5.15/5.35 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.35 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.15/5.35 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.15/5.35 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.15/5.35 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.35 => ( ( M = N2 )
% 5.15/5.35 => ( ( Deg
% 5.15/5.35 = ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.35 => ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.35 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X4 ) )
% 5.15/5.35 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.15/5.35 => ( ( ( Mi = Ma )
% 5.15/5.35 => ! [X3: vEBT_VEBT] :
% 5.15/5.35 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.35 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.15/5.35 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.15/5.35 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.15/5.35 => ( ( ( Mi != Ma )
% 5.15/5.35 => ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.35 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 5.15/5.35 = I2 )
% 5.15/5.35 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 5.15/5.35 & ! [X3: nat] :
% 5.15/5.35 ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 5.15/5.35 = I2 )
% 5.15/5.35 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 5.15/5.35 => ( ( ord_less_nat @ Mi @ X3 )
% 5.15/5.35 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.15/5.35 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % invar_vebt.intros(4)
% 5.15/5.35 thf(fact_815_sum__squares__bound,axiom,
% 5.15/5.35 ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % sum_squares_bound
% 5.15/5.35 thf(fact_816_sum__squares__bound,axiom,
% 5.15/5.35 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % sum_squares_bound
% 5.15/5.35 thf(fact_817_real__average__minus__first,axiom,
% 5.15/5.35 ! [A: real,B: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.15/5.35 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % real_average_minus_first
% 5.15/5.35 thf(fact_818_real__average__minus__second,axiom,
% 5.15/5.35 ! [B: real,A: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.15/5.35 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % real_average_minus_second
% 5.15/5.35 thf(fact_819_zdiv__numeral__Bit1,axiom,
% 5.15/5.35 ! [V: num,W: num] :
% 5.15/5.35 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.15/5.35 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % zdiv_numeral_Bit1
% 5.15/5.35 thf(fact_820_double__not__eq__Suc__double,axiom,
% 5.15/5.35 ! [M: nat,N2: nat] :
% 5.15/5.35 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.15/5.35 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % double_not_eq_Suc_double
% 5.15/5.35 thf(fact_821_Suc__double__not__eq__double,axiom,
% 5.15/5.35 ! [M: nat,N2: nat] :
% 5.15/5.35 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.35 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.35
% 5.15/5.35 % Suc_double_not_eq_double
% 5.15/5.35 thf(fact_822_add__diff__cancel__right_H,axiom,
% 5.15/5.35 ! [A: complex,B: complex] :
% 5.15/5.35 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right'
% 5.15/5.35 thf(fact_823_add__diff__cancel__right_H,axiom,
% 5.15/5.35 ! [A: real,B: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right'
% 5.15/5.35 thf(fact_824_add__diff__cancel__right_H,axiom,
% 5.15/5.35 ! [A: rat,B: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right'
% 5.15/5.35 thf(fact_825_add__diff__cancel__right_H,axiom,
% 5.15/5.35 ! [A: nat,B: nat] :
% 5.15/5.35 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right'
% 5.15/5.35 thf(fact_826_add__diff__cancel__right_H,axiom,
% 5.15/5.35 ! [A: int,B: int] :
% 5.15/5.35 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right'
% 5.15/5.35 thf(fact_827_add__diff__cancel__right,axiom,
% 5.15/5.35 ! [A: complex,C: complex,B: complex] :
% 5.15/5.35 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ C ) )
% 5.15/5.35 = ( minus_minus_complex @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right
% 5.15/5.35 thf(fact_828_add__diff__cancel__right,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.15/5.35 = ( minus_minus_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right
% 5.15/5.35 thf(fact_829_add__diff__cancel__right,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.35 = ( minus_minus_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right
% 5.15/5.35 thf(fact_830_add__diff__cancel__right,axiom,
% 5.15/5.35 ! [A: nat,C: nat,B: nat] :
% 5.15/5.35 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.35 = ( minus_minus_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right
% 5.15/5.35 thf(fact_831_add__diff__cancel__right,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.15/5.35 = ( minus_minus_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_right
% 5.15/5.35 thf(fact_832_add__diff__cancel__left_H,axiom,
% 5.15/5.35 ! [A: complex,B: complex] :
% 5.15/5.35 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ A )
% 5.15/5.35 = B ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left'
% 5.15/5.35 thf(fact_833_add__diff__cancel__left_H,axiom,
% 5.15/5.35 ! [A: real,B: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.15/5.35 = B ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left'
% 5.15/5.35 thf(fact_834_add__diff__cancel__left_H,axiom,
% 5.15/5.35 ! [A: rat,B: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.15/5.35 = B ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left'
% 5.15/5.35 thf(fact_835_add__diff__cancel__left_H,axiom,
% 5.15/5.35 ! [A: nat,B: nat] :
% 5.15/5.35 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.15/5.35 = B ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left'
% 5.15/5.35 thf(fact_836_add__diff__cancel__left_H,axiom,
% 5.15/5.35 ! [A: int,B: int] :
% 5.15/5.35 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.15/5.35 = B ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left'
% 5.15/5.35 thf(fact_837_add__left__cancel,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ( plus_plus_real @ A @ B )
% 5.15/5.35 = ( plus_plus_real @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_cancel
% 5.15/5.35 thf(fact_838_add__left__cancel,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ( plus_plus_rat @ A @ B )
% 5.15/5.35 = ( plus_plus_rat @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_cancel
% 5.15/5.35 thf(fact_839_add__left__cancel,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ( plus_plus_nat @ A @ B )
% 5.15/5.35 = ( plus_plus_nat @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_cancel
% 5.15/5.35 thf(fact_840_add__left__cancel,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ( plus_plus_int @ A @ B )
% 5.15/5.35 = ( plus_plus_int @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_cancel
% 5.15/5.35 thf(fact_841_add__left__cancel,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( ( plus_plus_complex @ A @ B )
% 5.15/5.35 = ( plus_plus_complex @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_cancel
% 5.15/5.35 thf(fact_842_add__right__cancel,axiom,
% 5.15/5.35 ! [B: real,A: real,C: real] :
% 5.15/5.35 ( ( ( plus_plus_real @ B @ A )
% 5.15/5.35 = ( plus_plus_real @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_cancel
% 5.15/5.35 thf(fact_843_add__right__cancel,axiom,
% 5.15/5.35 ! [B: rat,A: rat,C: rat] :
% 5.15/5.35 ( ( ( plus_plus_rat @ B @ A )
% 5.15/5.35 = ( plus_plus_rat @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_cancel
% 5.15/5.35 thf(fact_844_add__right__cancel,axiom,
% 5.15/5.35 ! [B: nat,A: nat,C: nat] :
% 5.15/5.35 ( ( ( plus_plus_nat @ B @ A )
% 5.15/5.35 = ( plus_plus_nat @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_cancel
% 5.15/5.35 thf(fact_845_add__right__cancel,axiom,
% 5.15/5.35 ! [B: int,A: int,C: int] :
% 5.15/5.35 ( ( ( plus_plus_int @ B @ A )
% 5.15/5.35 = ( plus_plus_int @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_cancel
% 5.15/5.35 thf(fact_846_add__right__cancel,axiom,
% 5.15/5.35 ! [B: complex,A: complex,C: complex] :
% 5.15/5.35 ( ( ( plus_plus_complex @ B @ A )
% 5.15/5.35 = ( plus_plus_complex @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_cancel
% 5.15/5.35 thf(fact_847_VEBT_Oinject_I1_J,axiom,
% 5.15/5.35 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.15/5.35 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.15/5.35 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.15/5.35 = ( ( X11 = Y11 )
% 5.15/5.35 & ( X12 = Y12 )
% 5.15/5.35 & ( X13 = Y13 )
% 5.15/5.35 & ( X14 = Y14 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % VEBT.inject(1)
% 5.15/5.35 thf(fact_848_real__divide__square__eq,axiom,
% 5.15/5.35 ! [R2: real,A: real] :
% 5.15/5.35 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 5.15/5.35 = ( divide_divide_real @ A @ R2 ) ) ).
% 5.15/5.35
% 5.15/5.35 % real_divide_square_eq
% 5.15/5.35 thf(fact_849_add__le__cancel__left,axiom,
% 5.15/5.35 ! [C: real,A: real,B: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.15/5.35 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_cancel_left
% 5.15/5.35 thf(fact_850_add__le__cancel__left,axiom,
% 5.15/5.35 ! [C: rat,A: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.15/5.35 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_cancel_left
% 5.15/5.35 thf(fact_851_add__le__cancel__left,axiom,
% 5.15/5.35 ! [C: nat,A: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.15/5.35 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_cancel_left
% 5.15/5.35 thf(fact_852_add__le__cancel__left,axiom,
% 5.15/5.35 ! [C: int,A: int,B: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.15/5.35 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_cancel_left
% 5.15/5.35 thf(fact_853_add__le__cancel__right,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.15/5.35 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_cancel_right
% 5.15/5.35 thf(fact_854_add__le__cancel__right,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.35 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_cancel_right
% 5.15/5.35 thf(fact_855_add__le__cancel__right,axiom,
% 5.15/5.35 ! [A: nat,C: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.35 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_cancel_right
% 5.15/5.35 thf(fact_856_add__le__cancel__right,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.15/5.35 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_cancel_right
% 5.15/5.35 thf(fact_857_add__less__cancel__left,axiom,
% 5.15/5.35 ! [C: real,A: real,B: real] :
% 5.15/5.35 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.15/5.35 = ( ord_less_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_cancel_left
% 5.15/5.35 thf(fact_858_add__less__cancel__left,axiom,
% 5.15/5.35 ! [C: rat,A: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.15/5.35 = ( ord_less_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_cancel_left
% 5.15/5.35 thf(fact_859_add__less__cancel__left,axiom,
% 5.15/5.35 ! [C: nat,A: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.15/5.35 = ( ord_less_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_cancel_left
% 5.15/5.35 thf(fact_860_add__less__cancel__left,axiom,
% 5.15/5.35 ! [C: int,A: int,B: int] :
% 5.15/5.35 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.15/5.35 = ( ord_less_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_cancel_left
% 5.15/5.35 thf(fact_861_add__less__cancel__right,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.15/5.35 = ( ord_less_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_cancel_right
% 5.15/5.35 thf(fact_862_add__less__cancel__right,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.35 = ( ord_less_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_cancel_right
% 5.15/5.35 thf(fact_863_add__less__cancel__right,axiom,
% 5.15/5.35 ! [A: nat,C: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.35 = ( ord_less_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_cancel_right
% 5.15/5.35 thf(fact_864_add__less__cancel__right,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.15/5.35 = ( ord_less_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_cancel_right
% 5.15/5.35 thf(fact_865_mult_Oright__neutral,axiom,
% 5.15/5.35 ! [A: complex] :
% 5.15/5.35 ( ( times_times_complex @ A @ one_one_complex )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.right_neutral
% 5.15/5.35 thf(fact_866_mult_Oright__neutral,axiom,
% 5.15/5.35 ! [A: real] :
% 5.15/5.35 ( ( times_times_real @ A @ one_one_real )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.right_neutral
% 5.15/5.35 thf(fact_867_mult_Oright__neutral,axiom,
% 5.15/5.35 ! [A: rat] :
% 5.15/5.35 ( ( times_times_rat @ A @ one_one_rat )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.right_neutral
% 5.15/5.35 thf(fact_868_mult_Oright__neutral,axiom,
% 5.15/5.35 ! [A: nat] :
% 5.15/5.35 ( ( times_times_nat @ A @ one_one_nat )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.right_neutral
% 5.15/5.35 thf(fact_869_mult_Oright__neutral,axiom,
% 5.15/5.35 ! [A: int] :
% 5.15/5.35 ( ( times_times_int @ A @ one_one_int )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.right_neutral
% 5.15/5.35 thf(fact_870_mult__1,axiom,
% 5.15/5.35 ! [A: complex] :
% 5.15/5.35 ( ( times_times_complex @ one_one_complex @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult_1
% 5.15/5.35 thf(fact_871_mult__1,axiom,
% 5.15/5.35 ! [A: real] :
% 5.15/5.35 ( ( times_times_real @ one_one_real @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult_1
% 5.15/5.35 thf(fact_872_mult__1,axiom,
% 5.15/5.35 ! [A: rat] :
% 5.15/5.35 ( ( times_times_rat @ one_one_rat @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult_1
% 5.15/5.35 thf(fact_873_mult__1,axiom,
% 5.15/5.35 ! [A: nat] :
% 5.15/5.35 ( ( times_times_nat @ one_one_nat @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult_1
% 5.15/5.35 thf(fact_874_mult__1,axiom,
% 5.15/5.35 ! [A: int] :
% 5.15/5.35 ( ( times_times_int @ one_one_int @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult_1
% 5.15/5.35 thf(fact_875_add__diff__cancel,axiom,
% 5.15/5.35 ! [A: complex,B: complex] :
% 5.15/5.35 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel
% 5.15/5.35 thf(fact_876_add__diff__cancel,axiom,
% 5.15/5.35 ! [A: real,B: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel
% 5.15/5.35 thf(fact_877_add__diff__cancel,axiom,
% 5.15/5.35 ! [A: rat,B: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel
% 5.15/5.35 thf(fact_878_add__diff__cancel,axiom,
% 5.15/5.35 ! [A: int,B: int] :
% 5.15/5.35 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel
% 5.15/5.35 thf(fact_879_diff__add__cancel,axiom,
% 5.15/5.35 ! [A: complex,B: complex] :
% 5.15/5.35 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_cancel
% 5.15/5.35 thf(fact_880_diff__add__cancel,axiom,
% 5.15/5.35 ! [A: real,B: real] :
% 5.15/5.35 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_cancel
% 5.15/5.35 thf(fact_881_diff__add__cancel,axiom,
% 5.15/5.35 ! [A: rat,B: rat] :
% 5.15/5.35 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_cancel
% 5.15/5.35 thf(fact_882_diff__add__cancel,axiom,
% 5.15/5.35 ! [A: int,B: int] :
% 5.15/5.35 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_cancel
% 5.15/5.35 thf(fact_883_add__diff__cancel__left,axiom,
% 5.15/5.35 ! [C: complex,A: complex,B: complex] :
% 5.15/5.35 ( ( minus_minus_complex @ ( plus_plus_complex @ C @ A ) @ ( plus_plus_complex @ C @ B ) )
% 5.15/5.35 = ( minus_minus_complex @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left
% 5.15/5.35 thf(fact_884_add__diff__cancel__left,axiom,
% 5.15/5.35 ! [C: real,A: real,B: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.15/5.35 = ( minus_minus_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left
% 5.15/5.35 thf(fact_885_add__diff__cancel__left,axiom,
% 5.15/5.35 ! [C: rat,A: rat,B: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.15/5.35 = ( minus_minus_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left
% 5.15/5.35 thf(fact_886_add__diff__cancel__left,axiom,
% 5.15/5.35 ! [C: nat,A: nat,B: nat] :
% 5.15/5.35 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.15/5.35 = ( minus_minus_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left
% 5.15/5.35 thf(fact_887_add__diff__cancel__left,axiom,
% 5.15/5.35 ! [C: int,A: int,B: int] :
% 5.15/5.35 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.15/5.35 = ( minus_minus_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_cancel_left
% 5.15/5.35 thf(fact_888_semiring__norm_I13_J,axiom,
% 5.15/5.35 ! [M: num,N2: num] :
% 5.15/5.35 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.35 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % semiring_norm(13)
% 5.15/5.35 thf(fact_889_semiring__norm_I12_J,axiom,
% 5.15/5.35 ! [N2: num] :
% 5.15/5.35 ( ( times_times_num @ one @ N2 )
% 5.15/5.35 = N2 ) ).
% 5.15/5.35
% 5.15/5.35 % semiring_norm(12)
% 5.15/5.35 thf(fact_890_semiring__norm_I11_J,axiom,
% 5.15/5.35 ! [M: num] :
% 5.15/5.35 ( ( times_times_num @ M @ one )
% 5.15/5.35 = M ) ).
% 5.15/5.35
% 5.15/5.35 % semiring_norm(11)
% 5.15/5.35 thf(fact_891_zdiv__numeral__Bit0,axiom,
% 5.15/5.35 ! [V: num,W: num] :
% 5.15/5.35 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.15/5.35 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % zdiv_numeral_Bit0
% 5.15/5.35 thf(fact_892_num__double,axiom,
% 5.15/5.35 ! [N2: num] :
% 5.15/5.35 ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 5.15/5.35 = ( bit0 @ N2 ) ) ).
% 5.15/5.35
% 5.15/5.35 % num_double
% 5.15/5.35 thf(fact_893_power__mult__numeral,axiom,
% 5.15/5.35 ! [A: nat,M: num,N2: num] :
% 5.15/5.35 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.35 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power_mult_numeral
% 5.15/5.35 thf(fact_894_power__mult__numeral,axiom,
% 5.15/5.35 ! [A: real,M: num,N2: num] :
% 5.15/5.35 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.35 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power_mult_numeral
% 5.15/5.35 thf(fact_895_power__mult__numeral,axiom,
% 5.15/5.35 ! [A: complex,M: num,N2: num] :
% 5.15/5.35 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.35 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power_mult_numeral
% 5.15/5.35 thf(fact_896_power__mult__numeral,axiom,
% 5.15/5.35 ! [A: int,M: num,N2: num] :
% 5.15/5.35 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.35 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % power_mult_numeral
% 5.15/5.35 thf(fact_897_semiring__norm_I15_J,axiom,
% 5.15/5.35 ! [M: num,N2: num] :
% 5.15/5.35 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.35 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % semiring_norm(15)
% 5.15/5.35 thf(fact_898_semiring__norm_I14_J,axiom,
% 5.15/5.35 ! [M: num,N2: num] :
% 5.15/5.35 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.35 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % semiring_norm(14)
% 5.15/5.35 thf(fact_899_semiring__norm_I16_J,axiom,
% 5.15/5.35 ! [M: num,N2: num] :
% 5.15/5.35 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.35 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % semiring_norm(16)
% 5.15/5.35 thf(fact_900_enat__less__induct,axiom,
% 5.15/5.35 ! [P: extended_enat > $o,N2: extended_enat] :
% 5.15/5.35 ( ! [N: extended_enat] :
% 5.15/5.35 ( ! [M4: extended_enat] :
% 5.15/5.35 ( ( ord_le72135733267957522d_enat @ M4 @ N )
% 5.15/5.35 => ( P @ M4 ) )
% 5.15/5.35 => ( P @ N ) )
% 5.15/5.35 => ( P @ N2 ) ) ).
% 5.15/5.35
% 5.15/5.35 % enat_less_induct
% 5.15/5.35 thf(fact_901_set__vebt__def,axiom,
% 5.15/5.35 ( vEBT_set_vebt
% 5.15/5.35 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % set_vebt_def
% 5.15/5.35 thf(fact_902_div__mult2__numeral__eq,axiom,
% 5.15/5.35 ! [A: nat,K: num,L: num] :
% 5.15/5.35 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 5.15/5.35 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % div_mult2_numeral_eq
% 5.15/5.35 thf(fact_903_div__mult2__numeral__eq,axiom,
% 5.15/5.35 ! [A: int,K: num,L: num] :
% 5.15/5.35 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 5.15/5.35 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % div_mult2_numeral_eq
% 5.15/5.35 thf(fact_904_mult_Oleft__commute,axiom,
% 5.15/5.35 ! [B: real,A: real,C: real] :
% 5.15/5.35 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.15/5.35 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.left_commute
% 5.15/5.35 thf(fact_905_mult_Oleft__commute,axiom,
% 5.15/5.35 ! [B: rat,A: rat,C: rat] :
% 5.15/5.35 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.15/5.35 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.left_commute
% 5.15/5.35 thf(fact_906_mult_Oleft__commute,axiom,
% 5.15/5.35 ! [B: nat,A: nat,C: nat] :
% 5.15/5.35 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.15/5.35 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.left_commute
% 5.15/5.35 thf(fact_907_mult_Oleft__commute,axiom,
% 5.15/5.35 ! [B: int,A: int,C: int] :
% 5.15/5.35 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.15/5.35 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.left_commute
% 5.15/5.35 thf(fact_908_mult_Ocommute,axiom,
% 5.15/5.35 ( times_times_real
% 5.15/5.35 = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.commute
% 5.15/5.35 thf(fact_909_mult_Ocommute,axiom,
% 5.15/5.35 ( times_times_rat
% 5.15/5.35 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.commute
% 5.15/5.35 thf(fact_910_mult_Ocommute,axiom,
% 5.15/5.35 ( times_times_nat
% 5.15/5.35 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.commute
% 5.15/5.35 thf(fact_911_mult_Ocommute,axiom,
% 5.15/5.35 ( times_times_int
% 5.15/5.35 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.commute
% 5.15/5.35 thf(fact_912_mult_Oassoc,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.15/5.35 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.assoc
% 5.15/5.35 thf(fact_913_mult_Oassoc,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.15/5.35 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.assoc
% 5.15/5.35 thf(fact_914_mult_Oassoc,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.15/5.35 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.assoc
% 5.15/5.35 thf(fact_915_mult_Oassoc,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.15/5.35 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult.assoc
% 5.15/5.35 thf(fact_916_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.15/5.35 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_mult_class.mult_ac(1)
% 5.15/5.35 thf(fact_917_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.15/5.35 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_mult_class.mult_ac(1)
% 5.15/5.35 thf(fact_918_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.15/5.35 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_mult_class.mult_ac(1)
% 5.15/5.35 thf(fact_919_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.15/5.35 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_mult_class.mult_ac(1)
% 5.15/5.35 thf(fact_920_one__reorient,axiom,
% 5.15/5.35 ! [X: complex] :
% 5.15/5.35 ( ( one_one_complex = X )
% 5.15/5.35 = ( X = one_one_complex ) ) ).
% 5.15/5.35
% 5.15/5.35 % one_reorient
% 5.15/5.35 thf(fact_921_one__reorient,axiom,
% 5.15/5.35 ! [X: real] :
% 5.15/5.35 ( ( one_one_real = X )
% 5.15/5.35 = ( X = one_one_real ) ) ).
% 5.15/5.35
% 5.15/5.35 % one_reorient
% 5.15/5.35 thf(fact_922_one__reorient,axiom,
% 5.15/5.35 ! [X: rat] :
% 5.15/5.35 ( ( one_one_rat = X )
% 5.15/5.35 = ( X = one_one_rat ) ) ).
% 5.15/5.35
% 5.15/5.35 % one_reorient
% 5.15/5.35 thf(fact_923_one__reorient,axiom,
% 5.15/5.35 ! [X: nat] :
% 5.15/5.35 ( ( one_one_nat = X )
% 5.15/5.35 = ( X = one_one_nat ) ) ).
% 5.15/5.35
% 5.15/5.35 % one_reorient
% 5.15/5.35 thf(fact_924_one__reorient,axiom,
% 5.15/5.35 ! [X: int] :
% 5.15/5.35 ( ( one_one_int = X )
% 5.15/5.35 = ( X = one_one_int ) ) ).
% 5.15/5.35
% 5.15/5.35 % one_reorient
% 5.15/5.35 thf(fact_925_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_add_class.add_ac(1)
% 5.15/5.35 thf(fact_926_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_add_class.add_ac(1)
% 5.15/5.35 thf(fact_927_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_add_class.add_ac(1)
% 5.15/5.35 thf(fact_928_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_add_class.add_ac(1)
% 5.15/5.35 thf(fact_929_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ab_semigroup_add_class.add_ac(1)
% 5.15/5.35 thf(fact_930_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ( plus_plus_real @ I @ K )
% 5.15/5.35 = ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(4)
% 5.15/5.35 thf(fact_931_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ( plus_plus_rat @ I @ K )
% 5.15/5.35 = ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(4)
% 5.15/5.35 thf(fact_932_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ( plus_plus_nat @ I @ K )
% 5.15/5.35 = ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(4)
% 5.15/5.35 thf(fact_933_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ( plus_plus_int @ I @ K )
% 5.15/5.35 = ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(4)
% 5.15/5.35 thf(fact_934_group__cancel_Oadd1,axiom,
% 5.15/5.35 ! [A2: real,K: real,A: real,B: real] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_real @ K @ A ) )
% 5.15/5.35 => ( ( plus_plus_real @ A2 @ B )
% 5.15/5.35 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add1
% 5.15/5.35 thf(fact_935_group__cancel_Oadd1,axiom,
% 5.15/5.35 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_rat @ K @ A ) )
% 5.15/5.35 => ( ( plus_plus_rat @ A2 @ B )
% 5.15/5.35 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add1
% 5.15/5.35 thf(fact_936_group__cancel_Oadd1,axiom,
% 5.15/5.35 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_nat @ K @ A ) )
% 5.15/5.35 => ( ( plus_plus_nat @ A2 @ B )
% 5.15/5.35 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add1
% 5.15/5.35 thf(fact_937_group__cancel_Oadd1,axiom,
% 5.15/5.35 ! [A2: int,K: int,A: int,B: int] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_int @ K @ A ) )
% 5.15/5.35 => ( ( plus_plus_int @ A2 @ B )
% 5.15/5.35 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add1
% 5.15/5.35 thf(fact_938_group__cancel_Oadd1,axiom,
% 5.15/5.35 ! [A2: complex,K: complex,A: complex,B: complex] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_complex @ K @ A ) )
% 5.15/5.35 => ( ( plus_plus_complex @ A2 @ B )
% 5.15/5.35 = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add1
% 5.15/5.35 thf(fact_939_group__cancel_Oadd2,axiom,
% 5.15/5.35 ! [B3: real,K: real,B: real,A: real] :
% 5.15/5.35 ( ( B3
% 5.15/5.35 = ( plus_plus_real @ K @ B ) )
% 5.15/5.35 => ( ( plus_plus_real @ A @ B3 )
% 5.15/5.35 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add2
% 5.15/5.35 thf(fact_940_group__cancel_Oadd2,axiom,
% 5.15/5.35 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.15/5.35 ( ( B3
% 5.15/5.35 = ( plus_plus_rat @ K @ B ) )
% 5.15/5.35 => ( ( plus_plus_rat @ A @ B3 )
% 5.15/5.35 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add2
% 5.15/5.35 thf(fact_941_group__cancel_Oadd2,axiom,
% 5.15/5.35 ! [B3: nat,K: nat,B: nat,A: nat] :
% 5.15/5.35 ( ( B3
% 5.15/5.35 = ( plus_plus_nat @ K @ B ) )
% 5.15/5.35 => ( ( plus_plus_nat @ A @ B3 )
% 5.15/5.35 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add2
% 5.15/5.35 thf(fact_942_group__cancel_Oadd2,axiom,
% 5.15/5.35 ! [B3: int,K: int,B: int,A: int] :
% 5.15/5.35 ( ( B3
% 5.15/5.35 = ( plus_plus_int @ K @ B ) )
% 5.15/5.35 => ( ( plus_plus_int @ A @ B3 )
% 5.15/5.35 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add2
% 5.15/5.35 thf(fact_943_group__cancel_Oadd2,axiom,
% 5.15/5.35 ! [B3: complex,K: complex,B: complex,A: complex] :
% 5.15/5.35 ( ( B3
% 5.15/5.35 = ( plus_plus_complex @ K @ B ) )
% 5.15/5.35 => ( ( plus_plus_complex @ A @ B3 )
% 5.15/5.35 = ( plus_plus_complex @ K @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.add2
% 5.15/5.35 thf(fact_944_add_Oassoc,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.assoc
% 5.15/5.35 thf(fact_945_add_Oassoc,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.assoc
% 5.15/5.35 thf(fact_946_add_Oassoc,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.assoc
% 5.15/5.35 thf(fact_947_add_Oassoc,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.assoc
% 5.15/5.35 thf(fact_948_add_Oassoc,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( plus_plus_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.assoc
% 5.15/5.35 thf(fact_949_add_Oleft__cancel,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ( plus_plus_real @ A @ B )
% 5.15/5.35 = ( plus_plus_real @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_cancel
% 5.15/5.35 thf(fact_950_add_Oleft__cancel,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ( plus_plus_rat @ A @ B )
% 5.15/5.35 = ( plus_plus_rat @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_cancel
% 5.15/5.35 thf(fact_951_add_Oleft__cancel,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ( plus_plus_int @ A @ B )
% 5.15/5.35 = ( plus_plus_int @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_cancel
% 5.15/5.35 thf(fact_952_add_Oleft__cancel,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( ( plus_plus_complex @ A @ B )
% 5.15/5.35 = ( plus_plus_complex @ A @ C ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_cancel
% 5.15/5.35 thf(fact_953_add_Oright__cancel,axiom,
% 5.15/5.35 ! [B: real,A: real,C: real] :
% 5.15/5.35 ( ( ( plus_plus_real @ B @ A )
% 5.15/5.35 = ( plus_plus_real @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.right_cancel
% 5.15/5.35 thf(fact_954_add_Oright__cancel,axiom,
% 5.15/5.35 ! [B: rat,A: rat,C: rat] :
% 5.15/5.35 ( ( ( plus_plus_rat @ B @ A )
% 5.15/5.35 = ( plus_plus_rat @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.right_cancel
% 5.15/5.35 thf(fact_955_add_Oright__cancel,axiom,
% 5.15/5.35 ! [B: int,A: int,C: int] :
% 5.15/5.35 ( ( ( plus_plus_int @ B @ A )
% 5.15/5.35 = ( plus_plus_int @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.right_cancel
% 5.15/5.35 thf(fact_956_add_Oright__cancel,axiom,
% 5.15/5.35 ! [B: complex,A: complex,C: complex] :
% 5.15/5.35 ( ( ( plus_plus_complex @ B @ A )
% 5.15/5.35 = ( plus_plus_complex @ C @ A ) )
% 5.15/5.35 = ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.right_cancel
% 5.15/5.35 thf(fact_957_add_Ocommute,axiom,
% 5.15/5.35 ( plus_plus_real
% 5.15/5.35 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.commute
% 5.15/5.35 thf(fact_958_add_Ocommute,axiom,
% 5.15/5.35 ( plus_plus_rat
% 5.15/5.35 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.commute
% 5.15/5.35 thf(fact_959_add_Ocommute,axiom,
% 5.15/5.35 ( plus_plus_nat
% 5.15/5.35 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.commute
% 5.15/5.35 thf(fact_960_add_Ocommute,axiom,
% 5.15/5.35 ( plus_plus_int
% 5.15/5.35 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.commute
% 5.15/5.35 thf(fact_961_add_Ocommute,axiom,
% 5.15/5.35 ( plus_plus_complex
% 5.15/5.35 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ B2 @ A3 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.commute
% 5.15/5.35 thf(fact_962_add_Oleft__commute,axiom,
% 5.15/5.35 ! [B: real,A: real,C: real] :
% 5.15/5.35 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.15/5.35 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_commute
% 5.15/5.35 thf(fact_963_add_Oleft__commute,axiom,
% 5.15/5.35 ! [B: rat,A: rat,C: rat] :
% 5.15/5.35 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.15/5.35 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_commute
% 5.15/5.35 thf(fact_964_add_Oleft__commute,axiom,
% 5.15/5.35 ! [B: nat,A: nat,C: nat] :
% 5.15/5.35 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.15/5.35 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_commute
% 5.15/5.35 thf(fact_965_add_Oleft__commute,axiom,
% 5.15/5.35 ! [B: int,A: int,C: int] :
% 5.15/5.35 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.15/5.35 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_commute
% 5.15/5.35 thf(fact_966_add_Oleft__commute,axiom,
% 5.15/5.35 ! [B: complex,A: complex,C: complex] :
% 5.15/5.35 ( ( plus_plus_complex @ B @ ( plus_plus_complex @ A @ C ) )
% 5.15/5.35 = ( plus_plus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add.left_commute
% 5.15/5.35 thf(fact_967_add__left__imp__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ( plus_plus_real @ A @ B )
% 5.15/5.35 = ( plus_plus_real @ A @ C ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_imp_eq
% 5.15/5.35 thf(fact_968_add__left__imp__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ( plus_plus_rat @ A @ B )
% 5.15/5.35 = ( plus_plus_rat @ A @ C ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_imp_eq
% 5.15/5.35 thf(fact_969_add__left__imp__eq,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ( plus_plus_nat @ A @ B )
% 5.15/5.35 = ( plus_plus_nat @ A @ C ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_imp_eq
% 5.15/5.35 thf(fact_970_add__left__imp__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ( plus_plus_int @ A @ B )
% 5.15/5.35 = ( plus_plus_int @ A @ C ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_imp_eq
% 5.15/5.35 thf(fact_971_add__left__imp__eq,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( ( plus_plus_complex @ A @ B )
% 5.15/5.35 = ( plus_plus_complex @ A @ C ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_imp_eq
% 5.15/5.35 thf(fact_972_add__right__imp__eq,axiom,
% 5.15/5.35 ! [B: real,A: real,C: real] :
% 5.15/5.35 ( ( ( plus_plus_real @ B @ A )
% 5.15/5.35 = ( plus_plus_real @ C @ A ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_imp_eq
% 5.15/5.35 thf(fact_973_add__right__imp__eq,axiom,
% 5.15/5.35 ! [B: rat,A: rat,C: rat] :
% 5.15/5.35 ( ( ( plus_plus_rat @ B @ A )
% 5.15/5.35 = ( plus_plus_rat @ C @ A ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_imp_eq
% 5.15/5.35 thf(fact_974_add__right__imp__eq,axiom,
% 5.15/5.35 ! [B: nat,A: nat,C: nat] :
% 5.15/5.35 ( ( ( plus_plus_nat @ B @ A )
% 5.15/5.35 = ( plus_plus_nat @ C @ A ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_imp_eq
% 5.15/5.35 thf(fact_975_add__right__imp__eq,axiom,
% 5.15/5.35 ! [B: int,A: int,C: int] :
% 5.15/5.35 ( ( ( plus_plus_int @ B @ A )
% 5.15/5.35 = ( plus_plus_int @ C @ A ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_imp_eq
% 5.15/5.35 thf(fact_976_add__right__imp__eq,axiom,
% 5.15/5.35 ! [B: complex,A: complex,C: complex] :
% 5.15/5.35 ( ( ( plus_plus_complex @ B @ A )
% 5.15/5.35 = ( plus_plus_complex @ C @ A ) )
% 5.15/5.35 => ( B = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_imp_eq
% 5.15/5.35 thf(fact_977_diff__right__commute,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.15/5.35 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_right_commute
% 5.15/5.35 thf(fact_978_diff__right__commute,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.15/5.35 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_right_commute
% 5.15/5.35 thf(fact_979_diff__right__commute,axiom,
% 5.15/5.35 ! [A: nat,C: nat,B: nat] :
% 5.15/5.35 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.15/5.35 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_right_commute
% 5.15/5.35 thf(fact_980_diff__right__commute,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.15/5.35 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_right_commute
% 5.15/5.35 thf(fact_981_diff__eq__diff__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.35 ( ( ( minus_minus_real @ A @ B )
% 5.15/5.35 = ( minus_minus_real @ C @ D ) )
% 5.15/5.35 => ( ( A = B )
% 5.15/5.35 = ( C = D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_eq
% 5.15/5.35 thf(fact_982_diff__eq__diff__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.35 ( ( ( minus_minus_rat @ A @ B )
% 5.15/5.35 = ( minus_minus_rat @ C @ D ) )
% 5.15/5.35 => ( ( A = B )
% 5.15/5.35 = ( C = D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_eq
% 5.15/5.35 thf(fact_983_diff__eq__diff__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.35 ( ( ( minus_minus_int @ A @ B )
% 5.15/5.35 = ( minus_minus_int @ C @ D ) )
% 5.15/5.35 => ( ( A = B )
% 5.15/5.35 = ( C = D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_eq
% 5.15/5.35 thf(fact_984_four__x__squared,axiom,
% 5.15/5.35 ! [X: real] :
% 5.15/5.35 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.35 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % four_x_squared
% 5.15/5.35 thf(fact_985_L2__set__mult__ineq__lemma,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % L2_set_mult_ineq_lemma
% 5.15/5.35 thf(fact_986_mult__commute__abs,axiom,
% 5.15/5.35 ! [C: real] :
% 5.15/5.35 ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 5.15/5.35 = ( times_times_real @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult_commute_abs
% 5.15/5.35 thf(fact_987_mult__commute__abs,axiom,
% 5.15/5.35 ! [C: rat] :
% 5.15/5.35 ( ( ^ [X2: rat] : ( times_times_rat @ X2 @ C ) )
% 5.15/5.35 = ( times_times_rat @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult_commute_abs
% 5.15/5.35 thf(fact_988_mult__commute__abs,axiom,
% 5.15/5.35 ! [C: nat] :
% 5.15/5.35 ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 5.15/5.35 = ( times_times_nat @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult_commute_abs
% 5.15/5.35 thf(fact_989_mult__commute__abs,axiom,
% 5.15/5.35 ! [C: int] :
% 5.15/5.35 ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 5.15/5.35 = ( times_times_int @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % mult_commute_abs
% 5.15/5.35 thf(fact_990_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( ord_less_eq_real @ I @ J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(3)
% 5.15/5.35 thf(fact_991_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( ord_less_eq_rat @ I @ J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(3)
% 5.15/5.35 thf(fact_992_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(3)
% 5.15/5.35 thf(fact_993_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( ord_less_eq_int @ I @ J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(3)
% 5.15/5.35 thf(fact_994_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( ord_less_eq_real @ K @ L ) )
% 5.15/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(2)
% 5.15/5.35 thf(fact_995_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( ord_less_eq_rat @ K @ L ) )
% 5.15/5.35 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(2)
% 5.15/5.35 thf(fact_996_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( ord_less_eq_nat @ K @ L ) )
% 5.15/5.35 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(2)
% 5.15/5.35 thf(fact_997_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( ord_less_eq_int @ K @ L ) )
% 5.15/5.35 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(2)
% 5.15/5.35 thf(fact_998_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( ord_less_eq_real @ I @ J )
% 5.15/5.35 & ( ord_less_eq_real @ K @ L ) )
% 5.15/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(1)
% 5.15/5.35 thf(fact_999_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( ord_less_eq_rat @ I @ J )
% 5.15/5.35 & ( ord_less_eq_rat @ K @ L ) )
% 5.15/5.35 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(1)
% 5.15/5.35 thf(fact_1000_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.35 & ( ord_less_eq_nat @ K @ L ) )
% 5.15/5.35 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(1)
% 5.15/5.35 thf(fact_1001_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( ord_less_eq_int @ I @ J )
% 5.15/5.35 & ( ord_less_eq_int @ K @ L ) )
% 5.15/5.35 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_semiring(1)
% 5.15/5.35 thf(fact_1002_add__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_real @ C @ D )
% 5.15/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono
% 5.15/5.35 thf(fact_1003_add__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_rat @ C @ D )
% 5.15/5.35 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono
% 5.15/5.35 thf(fact_1004_add__mono,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_nat @ C @ D )
% 5.15/5.35 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono
% 5.15/5.35 thf(fact_1005_add__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_int @ C @ D )
% 5.15/5.35 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono
% 5.15/5.35 thf(fact_1006_add__left__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_mono
% 5.15/5.35 thf(fact_1007_add__left__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.35 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_mono
% 5.15/5.35 thf(fact_1008_add__left__mono,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_mono
% 5.15/5.35 thf(fact_1009_add__left__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.35 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_left_mono
% 5.15/5.35 thf(fact_1010_less__eqE,axiom,
% 5.15/5.35 ! [A: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ~ ! [C2: nat] :
% 5.15/5.35 ( B
% 5.15/5.35 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % less_eqE
% 5.15/5.35 thf(fact_1011_add__right__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_mono
% 5.15/5.35 thf(fact_1012_add__right__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.35 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_mono
% 5.15/5.35 thf(fact_1013_add__right__mono,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_mono
% 5.15/5.35 thf(fact_1014_add__right__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.35 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_right_mono
% 5.15/5.35 thf(fact_1015_le__iff__add,axiom,
% 5.15/5.35 ( ord_less_eq_nat
% 5.15/5.35 = ( ^ [A3: nat,B2: nat] :
% 5.15/5.35 ? [C3: nat] :
% 5.15/5.35 ( B2
% 5.15/5.35 = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % le_iff_add
% 5.15/5.35 thf(fact_1016_add__le__imp__le__left,axiom,
% 5.15/5.35 ! [C: real,A: real,B: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.15/5.35 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_imp_le_left
% 5.15/5.35 thf(fact_1017_add__le__imp__le__left,axiom,
% 5.15/5.35 ! [C: rat,A: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.15/5.35 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_imp_le_left
% 5.15/5.35 thf(fact_1018_add__le__imp__le__left,axiom,
% 5.15/5.35 ! [C: nat,A: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.15/5.35 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_imp_le_left
% 5.15/5.35 thf(fact_1019_add__le__imp__le__left,axiom,
% 5.15/5.35 ! [C: int,A: int,B: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.15/5.35 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_imp_le_left
% 5.15/5.35 thf(fact_1020_add__le__imp__le__right,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.15/5.35 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_imp_le_right
% 5.15/5.35 thf(fact_1021_add__le__imp__le__right,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.35 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_imp_le_right
% 5.15/5.35 thf(fact_1022_add__le__imp__le__right,axiom,
% 5.15/5.35 ! [A: nat,C: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.35 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_imp_le_right
% 5.15/5.35 thf(fact_1023_add__le__imp__le__right,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.15/5.35 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_imp_le_right
% 5.15/5.35 thf(fact_1024_add__mono__thms__linordered__field_I5_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( ord_less_real @ I @ J )
% 5.15/5.35 & ( ord_less_real @ K @ L ) )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(5)
% 5.15/5.35 thf(fact_1025_add__mono__thms__linordered__field_I5_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( ord_less_rat @ I @ J )
% 5.15/5.35 & ( ord_less_rat @ K @ L ) )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(5)
% 5.15/5.35 thf(fact_1026_add__mono__thms__linordered__field_I5_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( ord_less_nat @ I @ J )
% 5.15/5.35 & ( ord_less_nat @ K @ L ) )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(5)
% 5.15/5.35 thf(fact_1027_add__mono__thms__linordered__field_I5_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( ord_less_int @ I @ J )
% 5.15/5.35 & ( ord_less_int @ K @ L ) )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(5)
% 5.15/5.35 thf(fact_1028_add__mono__thms__linordered__field_I2_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( ord_less_real @ K @ L ) )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(2)
% 5.15/5.35 thf(fact_1029_add__mono__thms__linordered__field_I2_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( ord_less_rat @ K @ L ) )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(2)
% 5.15/5.35 thf(fact_1030_add__mono__thms__linordered__field_I2_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( ord_less_nat @ K @ L ) )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(2)
% 5.15/5.35 thf(fact_1031_add__mono__thms__linordered__field_I2_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( I = J )
% 5.15/5.35 & ( ord_less_int @ K @ L ) )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(2)
% 5.15/5.35 thf(fact_1032_add__mono__thms__linordered__field_I1_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( ord_less_real @ I @ J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(1)
% 5.15/5.35 thf(fact_1033_add__mono__thms__linordered__field_I1_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( ord_less_rat @ I @ J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(1)
% 5.15/5.35 thf(fact_1034_add__mono__thms__linordered__field_I1_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( ord_less_nat @ I @ J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(1)
% 5.15/5.35 thf(fact_1035_add__mono__thms__linordered__field_I1_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( ord_less_int @ I @ J )
% 5.15/5.35 & ( K = L ) )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(1)
% 5.15/5.35 thf(fact_1036_add__strict__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.35 ( ( ord_less_real @ A @ B )
% 5.15/5.35 => ( ( ord_less_real @ C @ D )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_mono
% 5.15/5.35 thf(fact_1037_add__strict__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.35 ( ( ord_less_rat @ A @ B )
% 5.15/5.35 => ( ( ord_less_rat @ C @ D )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_mono
% 5.15/5.35 thf(fact_1038_add__strict__mono,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.35 ( ( ord_less_nat @ A @ B )
% 5.15/5.35 => ( ( ord_less_nat @ C @ D )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_mono
% 5.15/5.35 thf(fact_1039_add__strict__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.35 ( ( ord_less_int @ A @ B )
% 5.15/5.35 => ( ( ord_less_int @ C @ D )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_mono
% 5.15/5.35 thf(fact_1040_add__strict__left__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ord_less_real @ A @ B )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_left_mono
% 5.15/5.35 thf(fact_1041_add__strict__left__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_rat @ A @ B )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_left_mono
% 5.15/5.35 thf(fact_1042_add__strict__left__mono,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_nat @ A @ B )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_left_mono
% 5.15/5.35 thf(fact_1043_add__strict__left__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ord_less_int @ A @ B )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_left_mono
% 5.15/5.35 thf(fact_1044_add__strict__right__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ord_less_real @ A @ B )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_right_mono
% 5.15/5.35 thf(fact_1045_add__strict__right__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_rat @ A @ B )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_right_mono
% 5.15/5.35 thf(fact_1046_add__strict__right__mono,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_nat @ A @ B )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_right_mono
% 5.15/5.35 thf(fact_1047_add__strict__right__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ord_less_int @ A @ B )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_strict_right_mono
% 5.15/5.35 thf(fact_1048_add__less__imp__less__left,axiom,
% 5.15/5.35 ! [C: real,A: real,B: real] :
% 5.15/5.35 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.15/5.35 => ( ord_less_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_imp_less_left
% 5.15/5.35 thf(fact_1049_add__less__imp__less__left,axiom,
% 5.15/5.35 ! [C: rat,A: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.15/5.35 => ( ord_less_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_imp_less_left
% 5.15/5.35 thf(fact_1050_add__less__imp__less__left,axiom,
% 5.15/5.35 ! [C: nat,A: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.15/5.35 => ( ord_less_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_imp_less_left
% 5.15/5.35 thf(fact_1051_add__less__imp__less__left,axiom,
% 5.15/5.35 ! [C: int,A: int,B: int] :
% 5.15/5.35 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.15/5.35 => ( ord_less_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_imp_less_left
% 5.15/5.35 thf(fact_1052_add__less__imp__less__right,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.15/5.35 => ( ord_less_real @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_imp_less_right
% 5.15/5.35 thf(fact_1053_add__less__imp__less__right,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.35 => ( ord_less_rat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_imp_less_right
% 5.15/5.35 thf(fact_1054_add__less__imp__less__right,axiom,
% 5.15/5.35 ! [A: nat,C: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.35 => ( ord_less_nat @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_imp_less_right
% 5.15/5.35 thf(fact_1055_add__less__imp__less__right,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.15/5.35 => ( ord_less_int @ A @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_imp_less_right
% 5.15/5.35 thf(fact_1056_diff__eq__diff__less__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.35 ( ( ( minus_minus_real @ A @ B )
% 5.15/5.35 = ( minus_minus_real @ C @ D ) )
% 5.15/5.35 => ( ( ord_less_eq_real @ A @ B )
% 5.15/5.35 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_less_eq
% 5.15/5.35 thf(fact_1057_diff__eq__diff__less__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.35 ( ( ( minus_minus_rat @ A @ B )
% 5.15/5.35 = ( minus_minus_rat @ C @ D ) )
% 5.15/5.35 => ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.35 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_less_eq
% 5.15/5.35 thf(fact_1058_diff__eq__diff__less__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.35 ( ( ( minus_minus_int @ A @ B )
% 5.15/5.35 = ( minus_minus_int @ C @ D ) )
% 5.15/5.35 => ( ( ord_less_eq_int @ A @ B )
% 5.15/5.35 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_less_eq
% 5.15/5.35 thf(fact_1059_diff__right__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.35 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_right_mono
% 5.15/5.35 thf(fact_1060_diff__right__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.35 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_right_mono
% 5.15/5.35 thf(fact_1061_diff__right__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.35 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_right_mono
% 5.15/5.35 thf(fact_1062_diff__left__mono,axiom,
% 5.15/5.35 ! [B: real,A: real,C: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ B @ A )
% 5.15/5.35 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_left_mono
% 5.15/5.35 thf(fact_1063_diff__left__mono,axiom,
% 5.15/5.35 ! [B: rat,A: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.35 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_left_mono
% 5.15/5.35 thf(fact_1064_diff__left__mono,axiom,
% 5.15/5.35 ! [B: int,A: int,C: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ B @ A )
% 5.15/5.35 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_left_mono
% 5.15/5.35 thf(fact_1065_diff__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,D: real,C: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_real @ D @ C )
% 5.15/5.35 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_mono
% 5.15/5.35 thf(fact_1066_diff__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_rat @ D @ C )
% 5.15/5.35 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_mono
% 5.15/5.35 thf(fact_1067_diff__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,D: int,C: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_int @ D @ C )
% 5.15/5.35 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_mono
% 5.15/5.35 thf(fact_1068_diff__strict__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,D: real,C: real] :
% 5.15/5.35 ( ( ord_less_real @ A @ B )
% 5.15/5.35 => ( ( ord_less_real @ D @ C )
% 5.15/5.35 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_mono
% 5.15/5.35 thf(fact_1069_diff__strict__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_rat @ A @ B )
% 5.15/5.35 => ( ( ord_less_rat @ D @ C )
% 5.15/5.35 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_mono
% 5.15/5.35 thf(fact_1070_diff__strict__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,D: int,C: int] :
% 5.15/5.35 ( ( ord_less_int @ A @ B )
% 5.15/5.35 => ( ( ord_less_int @ D @ C )
% 5.15/5.35 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_mono
% 5.15/5.35 thf(fact_1071_diff__eq__diff__less,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.35 ( ( ( minus_minus_real @ A @ B )
% 5.15/5.35 = ( minus_minus_real @ C @ D ) )
% 5.15/5.35 => ( ( ord_less_real @ A @ B )
% 5.15/5.35 = ( ord_less_real @ C @ D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_less
% 5.15/5.35 thf(fact_1072_diff__eq__diff__less,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.35 ( ( ( minus_minus_rat @ A @ B )
% 5.15/5.35 = ( minus_minus_rat @ C @ D ) )
% 5.15/5.35 => ( ( ord_less_rat @ A @ B )
% 5.15/5.35 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_less
% 5.15/5.35 thf(fact_1073_diff__eq__diff__less,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.35 ( ( ( minus_minus_int @ A @ B )
% 5.15/5.35 = ( minus_minus_int @ C @ D ) )
% 5.15/5.35 => ( ( ord_less_int @ A @ B )
% 5.15/5.35 = ( ord_less_int @ C @ D ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_diff_less
% 5.15/5.35 thf(fact_1074_diff__strict__left__mono,axiom,
% 5.15/5.35 ! [B: real,A: real,C: real] :
% 5.15/5.35 ( ( ord_less_real @ B @ A )
% 5.15/5.35 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_left_mono
% 5.15/5.35 thf(fact_1075_diff__strict__left__mono,axiom,
% 5.15/5.35 ! [B: rat,A: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_rat @ B @ A )
% 5.15/5.35 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_left_mono
% 5.15/5.35 thf(fact_1076_diff__strict__left__mono,axiom,
% 5.15/5.35 ! [B: int,A: int,C: int] :
% 5.15/5.35 ( ( ord_less_int @ B @ A )
% 5.15/5.35 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_left_mono
% 5.15/5.35 thf(fact_1077_diff__strict__right__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ord_less_real @ A @ B )
% 5.15/5.35 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_right_mono
% 5.15/5.35 thf(fact_1078_diff__strict__right__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_rat @ A @ B )
% 5.15/5.35 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_right_mono
% 5.15/5.35 thf(fact_1079_diff__strict__right__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ord_less_int @ A @ B )
% 5.15/5.35 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_strict_right_mono
% 5.15/5.35 thf(fact_1080_comm__monoid__mult__class_Omult__1,axiom,
% 5.15/5.35 ! [A: complex] :
% 5.15/5.35 ( ( times_times_complex @ one_one_complex @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % comm_monoid_mult_class.mult_1
% 5.15/5.35 thf(fact_1081_comm__monoid__mult__class_Omult__1,axiom,
% 5.15/5.35 ! [A: real] :
% 5.15/5.35 ( ( times_times_real @ one_one_real @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % comm_monoid_mult_class.mult_1
% 5.15/5.35 thf(fact_1082_comm__monoid__mult__class_Omult__1,axiom,
% 5.15/5.35 ! [A: rat] :
% 5.15/5.35 ( ( times_times_rat @ one_one_rat @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % comm_monoid_mult_class.mult_1
% 5.15/5.35 thf(fact_1083_comm__monoid__mult__class_Omult__1,axiom,
% 5.15/5.35 ! [A: nat] :
% 5.15/5.35 ( ( times_times_nat @ one_one_nat @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % comm_monoid_mult_class.mult_1
% 5.15/5.35 thf(fact_1084_comm__monoid__mult__class_Omult__1,axiom,
% 5.15/5.35 ! [A: int] :
% 5.15/5.35 ( ( times_times_int @ one_one_int @ A )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % comm_monoid_mult_class.mult_1
% 5.15/5.35 thf(fact_1085_mult_Ocomm__neutral,axiom,
% 5.15/5.35 ! [A: complex] :
% 5.15/5.35 ( ( times_times_complex @ A @ one_one_complex )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.comm_neutral
% 5.15/5.35 thf(fact_1086_mult_Ocomm__neutral,axiom,
% 5.15/5.35 ! [A: real] :
% 5.15/5.35 ( ( times_times_real @ A @ one_one_real )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.comm_neutral
% 5.15/5.35 thf(fact_1087_mult_Ocomm__neutral,axiom,
% 5.15/5.35 ! [A: rat] :
% 5.15/5.35 ( ( times_times_rat @ A @ one_one_rat )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.comm_neutral
% 5.15/5.35 thf(fact_1088_mult_Ocomm__neutral,axiom,
% 5.15/5.35 ! [A: nat] :
% 5.15/5.35 ( ( times_times_nat @ A @ one_one_nat )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.comm_neutral
% 5.15/5.35 thf(fact_1089_mult_Ocomm__neutral,axiom,
% 5.15/5.35 ! [A: int] :
% 5.15/5.35 ( ( times_times_int @ A @ one_one_int )
% 5.15/5.35 = A ) ).
% 5.15/5.35
% 5.15/5.35 % mult.comm_neutral
% 5.15/5.35 thf(fact_1090_group__cancel_Osub1,axiom,
% 5.15/5.35 ! [A2: complex,K: complex,A: complex,B: complex] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_complex @ K @ A ) )
% 5.15/5.35 => ( ( minus_minus_complex @ A2 @ B )
% 5.15/5.35 = ( plus_plus_complex @ K @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.sub1
% 5.15/5.35 thf(fact_1091_group__cancel_Osub1,axiom,
% 5.15/5.35 ! [A2: real,K: real,A: real,B: real] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_real @ K @ A ) )
% 5.15/5.35 => ( ( minus_minus_real @ A2 @ B )
% 5.15/5.35 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.sub1
% 5.15/5.35 thf(fact_1092_group__cancel_Osub1,axiom,
% 5.15/5.35 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_rat @ K @ A ) )
% 5.15/5.35 => ( ( minus_minus_rat @ A2 @ B )
% 5.15/5.35 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.sub1
% 5.15/5.35 thf(fact_1093_group__cancel_Osub1,axiom,
% 5.15/5.35 ! [A2: int,K: int,A: int,B: int] :
% 5.15/5.35 ( ( A2
% 5.15/5.35 = ( plus_plus_int @ K @ A ) )
% 5.15/5.35 => ( ( minus_minus_int @ A2 @ B )
% 5.15/5.35 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % group_cancel.sub1
% 5.15/5.35 thf(fact_1094_diff__eq__eq,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( ( minus_minus_complex @ A @ B )
% 5.15/5.35 = C )
% 5.15/5.35 = ( A
% 5.15/5.35 = ( plus_plus_complex @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_eq
% 5.15/5.35 thf(fact_1095_diff__eq__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ( minus_minus_real @ A @ B )
% 5.15/5.35 = C )
% 5.15/5.35 = ( A
% 5.15/5.35 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_eq
% 5.15/5.35 thf(fact_1096_diff__eq__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ( minus_minus_rat @ A @ B )
% 5.15/5.35 = C )
% 5.15/5.35 = ( A
% 5.15/5.35 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_eq
% 5.15/5.35 thf(fact_1097_diff__eq__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ( minus_minus_int @ A @ B )
% 5.15/5.35 = C )
% 5.15/5.35 = ( A
% 5.15/5.35 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_eq_eq
% 5.15/5.35 thf(fact_1098_eq__diff__eq,axiom,
% 5.15/5.35 ! [A: complex,C: complex,B: complex] :
% 5.15/5.35 ( ( A
% 5.15/5.35 = ( minus_minus_complex @ C @ B ) )
% 5.15/5.35 = ( ( plus_plus_complex @ A @ B )
% 5.15/5.35 = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % eq_diff_eq
% 5.15/5.35 thf(fact_1099_eq__diff__eq,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( A
% 5.15/5.35 = ( minus_minus_real @ C @ B ) )
% 5.15/5.35 = ( ( plus_plus_real @ A @ B )
% 5.15/5.35 = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % eq_diff_eq
% 5.15/5.35 thf(fact_1100_eq__diff__eq,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( A
% 5.15/5.35 = ( minus_minus_rat @ C @ B ) )
% 5.15/5.35 = ( ( plus_plus_rat @ A @ B )
% 5.15/5.35 = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % eq_diff_eq
% 5.15/5.35 thf(fact_1101_eq__diff__eq,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( A
% 5.15/5.35 = ( minus_minus_int @ C @ B ) )
% 5.15/5.35 = ( ( plus_plus_int @ A @ B )
% 5.15/5.35 = C ) ) ).
% 5.15/5.35
% 5.15/5.35 % eq_diff_eq
% 5.15/5.35 thf(fact_1102_add__diff__eq,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( plus_plus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.15/5.35 = ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_eq
% 5.15/5.35 thf(fact_1103_add__diff__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.15/5.35 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_eq
% 5.15/5.35 thf(fact_1104_add__diff__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.15/5.35 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_eq
% 5.15/5.35 thf(fact_1105_add__diff__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.15/5.35 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_diff_eq
% 5.15/5.35 thf(fact_1106_diff__diff__eq2,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( minus_minus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.15/5.35 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq2
% 5.15/5.35 thf(fact_1107_diff__diff__eq2,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.15/5.35 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq2
% 5.15/5.35 thf(fact_1108_diff__diff__eq2,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.15/5.35 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq2
% 5.15/5.35 thf(fact_1109_diff__diff__eq2,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.15/5.35 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq2
% 5.15/5.35 thf(fact_1110_diff__add__eq,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_eq
% 5.15/5.35 thf(fact_1111_diff__add__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_eq
% 5.15/5.35 thf(fact_1112_diff__add__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_eq
% 5.15/5.35 thf(fact_1113_diff__add__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_eq
% 5.15/5.35 thf(fact_1114_diff__add__eq__diff__diff__swap,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.15/5.35 = ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_eq_diff_diff_swap
% 5.15/5.35 thf(fact_1115_diff__add__eq__diff__diff__swap,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.15/5.35 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_eq_diff_diff_swap
% 5.15/5.35 thf(fact_1116_diff__add__eq__diff__diff__swap,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.35 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_eq_diff_diff_swap
% 5.15/5.35 thf(fact_1117_diff__add__eq__diff__diff__swap,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.15/5.35 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add_eq_diff_diff_swap
% 5.15/5.35 thf(fact_1118_add__implies__diff,axiom,
% 5.15/5.35 ! [C: complex,B: complex,A: complex] :
% 5.15/5.35 ( ( ( plus_plus_complex @ C @ B )
% 5.15/5.35 = A )
% 5.15/5.35 => ( C
% 5.15/5.35 = ( minus_minus_complex @ A @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_implies_diff
% 5.15/5.35 thf(fact_1119_add__implies__diff,axiom,
% 5.15/5.35 ! [C: real,B: real,A: real] :
% 5.15/5.35 ( ( ( plus_plus_real @ C @ B )
% 5.15/5.35 = A )
% 5.15/5.35 => ( C
% 5.15/5.35 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_implies_diff
% 5.15/5.35 thf(fact_1120_add__implies__diff,axiom,
% 5.15/5.35 ! [C: rat,B: rat,A: rat] :
% 5.15/5.35 ( ( ( plus_plus_rat @ C @ B )
% 5.15/5.35 = A )
% 5.15/5.35 => ( C
% 5.15/5.35 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_implies_diff
% 5.15/5.35 thf(fact_1121_add__implies__diff,axiom,
% 5.15/5.35 ! [C: nat,B: nat,A: nat] :
% 5.15/5.35 ( ( ( plus_plus_nat @ C @ B )
% 5.15/5.35 = A )
% 5.15/5.35 => ( C
% 5.15/5.35 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_implies_diff
% 5.15/5.35 thf(fact_1122_add__implies__diff,axiom,
% 5.15/5.35 ! [C: int,B: int,A: int] :
% 5.15/5.35 ( ( ( plus_plus_int @ C @ B )
% 5.15/5.35 = A )
% 5.15/5.35 => ( C
% 5.15/5.35 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_implies_diff
% 5.15/5.35 thf(fact_1123_diff__diff__eq,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq
% 5.15/5.35 thf(fact_1124_diff__diff__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq
% 5.15/5.35 thf(fact_1125_diff__diff__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq
% 5.15/5.35 thf(fact_1126_diff__diff__eq,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq
% 5.15/5.35 thf(fact_1127_diff__diff__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_diff_eq
% 5.15/5.35 thf(fact_1128_add__mono__thms__linordered__field_I4_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( ord_less_eq_real @ I @ J )
% 5.15/5.35 & ( ord_less_real @ K @ L ) )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(4)
% 5.15/5.35 thf(fact_1129_add__mono__thms__linordered__field_I4_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( ord_less_eq_rat @ I @ J )
% 5.15/5.35 & ( ord_less_rat @ K @ L ) )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(4)
% 5.15/5.35 thf(fact_1130_add__mono__thms__linordered__field_I4_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.35 & ( ord_less_nat @ K @ L ) )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(4)
% 5.15/5.35 thf(fact_1131_add__mono__thms__linordered__field_I4_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( ord_less_eq_int @ I @ J )
% 5.15/5.35 & ( ord_less_int @ K @ L ) )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(4)
% 5.15/5.35 thf(fact_1132_add__mono__thms__linordered__field_I3_J,axiom,
% 5.15/5.35 ! [I: real,J: real,K: real,L: real] :
% 5.15/5.35 ( ( ( ord_less_real @ I @ J )
% 5.15/5.35 & ( ord_less_eq_real @ K @ L ) )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(3)
% 5.15/5.35 thf(fact_1133_add__mono__thms__linordered__field_I3_J,axiom,
% 5.15/5.35 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.15/5.35 ( ( ( ord_less_rat @ I @ J )
% 5.15/5.35 & ( ord_less_eq_rat @ K @ L ) )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(3)
% 5.15/5.35 thf(fact_1134_add__mono__thms__linordered__field_I3_J,axiom,
% 5.15/5.35 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.15/5.35 ( ( ( ord_less_nat @ I @ J )
% 5.15/5.35 & ( ord_less_eq_nat @ K @ L ) )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(3)
% 5.15/5.35 thf(fact_1135_add__mono__thms__linordered__field_I3_J,axiom,
% 5.15/5.35 ! [I: int,J: int,K: int,L: int] :
% 5.15/5.35 ( ( ( ord_less_int @ I @ J )
% 5.15/5.35 & ( ord_less_eq_int @ K @ L ) )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_mono_thms_linordered_field(3)
% 5.15/5.35 thf(fact_1136_add__le__less__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.35 => ( ( ord_less_real @ C @ D )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_less_mono
% 5.15/5.35 thf(fact_1137_add__le__less__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.35 => ( ( ord_less_rat @ C @ D )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_less_mono
% 5.15/5.35 thf(fact_1138_add__le__less__mono,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( ord_less_nat @ C @ D )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_less_mono
% 5.15/5.35 thf(fact_1139_add__le__less__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.35 => ( ( ord_less_int @ C @ D )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_le_less_mono
% 5.15/5.35 thf(fact_1140_add__less__le__mono,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.35 ( ( ord_less_real @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_real @ C @ D )
% 5.15/5.35 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_le_mono
% 5.15/5.35 thf(fact_1141_add__less__le__mono,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.35 ( ( ord_less_rat @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_rat @ C @ D )
% 5.15/5.35 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_le_mono
% 5.15/5.35 thf(fact_1142_add__less__le__mono,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.35 ( ( ord_less_nat @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_nat @ C @ D )
% 5.15/5.35 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_le_mono
% 5.15/5.35 thf(fact_1143_add__less__le__mono,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.35 ( ( ord_less_int @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_int @ C @ D )
% 5.15/5.35 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_less_le_mono
% 5.15/5.35 thf(fact_1144_diff__le__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.15/5.35 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_le_eq
% 5.15/5.35 thf(fact_1145_diff__le__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.15/5.35 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_le_eq
% 5.15/5.35 thf(fact_1146_diff__le__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.15/5.35 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_le_eq
% 5.15/5.35 thf(fact_1147_le__diff__eq,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.15/5.35 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % le_diff_eq
% 5.15/5.35 thf(fact_1148_le__diff__eq,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.15/5.35 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % le_diff_eq
% 5.15/5.35 thf(fact_1149_le__diff__eq,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.15/5.35 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % le_diff_eq
% 5.15/5.35 thf(fact_1150_diff__add,axiom,
% 5.15/5.35 ! [A: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.15/5.35 = B ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_add
% 5.15/5.35 thf(fact_1151_le__add__diff,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % le_add_diff
% 5.15/5.35 thf(fact_1152_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.15/5.35 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.15/5.35 thf(fact_1153_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.15/5.35 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.15/5.35 thf(fact_1154_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.15/5.35 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.15/5.35 thf(fact_1155_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.15/5.35 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.15/5.35 thf(fact_1156_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.15/5.35 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.15/5.35 thf(fact_1157_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.15/5.35 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.15/5.35 thf(fact_1158_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.15/5.35 ! [A: nat,B: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.15/5.35 = B ) ) ).
% 5.15/5.35
% 5.15/5.35 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.15/5.35 thf(fact_1159_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.15/5.35 ! [A: nat,B: nat,C: nat] :
% 5.15/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.35 => ( ( ( minus_minus_nat @ B @ A )
% 5.15/5.35 = C )
% 5.15/5.35 = ( B
% 5.15/5.35 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.15/5.35 thf(fact_1160_diff__less__eq,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.15/5.35 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_less_eq
% 5.15/5.35 thf(fact_1161_diff__less__eq,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.15/5.35 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_less_eq
% 5.15/5.35 thf(fact_1162_diff__less__eq,axiom,
% 5.15/5.35 ! [A: int,B: int,C: int] :
% 5.15/5.35 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.15/5.35 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_less_eq
% 5.15/5.35 thf(fact_1163_less__diff__eq,axiom,
% 5.15/5.35 ! [A: real,C: real,B: real] :
% 5.15/5.35 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.15/5.35 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % less_diff_eq
% 5.15/5.35 thf(fact_1164_less__diff__eq,axiom,
% 5.15/5.35 ! [A: rat,C: rat,B: rat] :
% 5.15/5.35 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.15/5.35 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % less_diff_eq
% 5.15/5.35 thf(fact_1165_less__diff__eq,axiom,
% 5.15/5.35 ! [A: int,C: int,B: int] :
% 5.15/5.35 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.15/5.35 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % less_diff_eq
% 5.15/5.35 thf(fact_1166_discrete,axiom,
% 5.15/5.35 ( ord_less_nat
% 5.15/5.35 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % discrete
% 5.15/5.35 thf(fact_1167_discrete,axiom,
% 5.15/5.35 ( ord_less_int
% 5.15/5.35 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % discrete
% 5.15/5.35 thf(fact_1168_divmod__step__eq,axiom,
% 5.15/5.35 ! [L: num,R2: nat,Q3: nat] :
% 5.15/5.35 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.15/5.35 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.15/5.35 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.15/5.35 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.15/5.35 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.15/5.35 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divmod_step_eq
% 5.15/5.35 thf(fact_1169_divmod__step__eq,axiom,
% 5.15/5.35 ! [L: num,R2: int,Q3: int] :
% 5.15/5.35 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.15/5.35 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.35 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.15/5.35 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.15/5.35 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.35 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divmod_step_eq
% 5.15/5.35 thf(fact_1170_divmod__step__eq,axiom,
% 5.15/5.35 ! [L: num,R2: code_integer,Q3: code_integer] :
% 5.15/5.35 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.15/5.35 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.15/5.35 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.15/5.35 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.15/5.35 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.15/5.35 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divmod_step_eq
% 5.15/5.35 thf(fact_1171_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.15/5.35 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.15/5.35 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X )
% 5.15/5.35 = ( ( X = Mi )
% 5.15/5.35 | ( X = Ma )
% 5.15/5.35 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.35 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.35 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % VEBT_internal.membermima.simps(4)
% 5.15/5.35 thf(fact_1172_times__divide__eq__left,axiom,
% 5.15/5.35 ! [B: complex,C: complex,A: complex] :
% 5.15/5.35 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.15/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_eq_left
% 5.15/5.35 thf(fact_1173_times__divide__eq__left,axiom,
% 5.15/5.35 ! [B: real,C: real,A: real] :
% 5.15/5.35 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.15/5.35 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_eq_left
% 5.15/5.35 thf(fact_1174_times__divide__eq__left,axiom,
% 5.15/5.35 ! [B: rat,C: rat,A: rat] :
% 5.15/5.35 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.15/5.35 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_eq_left
% 5.15/5.35 thf(fact_1175_divide__divide__eq__left,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.15/5.35 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_left
% 5.15/5.35 thf(fact_1176_divide__divide__eq__left,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.15/5.35 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_left
% 5.15/5.35 thf(fact_1177_divide__divide__eq__left,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.15/5.35 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_left
% 5.15/5.35 thf(fact_1178_divide__divide__eq__right,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_right
% 5.15/5.35 thf(fact_1179_divide__divide__eq__right,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.15/5.35 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_right
% 5.15/5.35 thf(fact_1180_divide__divide__eq__right,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.35 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_right
% 5.15/5.35 thf(fact_1181_times__divide__eq__right,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_eq_right
% 5.15/5.35 thf(fact_1182_times__divide__eq__right,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.15/5.35 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_eq_right
% 5.15/5.35 thf(fact_1183_times__divide__eq__right,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.35 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_eq_right
% 5.15/5.35 thf(fact_1184_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.15/5.35 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.15/5.35 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X )
% 5.15/5.35 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.35 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.35 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % VEBT_internal.naive_member.simps(3)
% 5.15/5.35 thf(fact_1185_nth__mem,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_complex] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.15/5.35 => ( member_complex @ ( nth_complex @ Xs2 @ N2 ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nth_mem
% 5.15/5.35 thf(fact_1186_nth__mem,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_real] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.15/5.35 => ( member_real @ ( nth_real @ Xs2 @ N2 ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nth_mem
% 5.15/5.35 thf(fact_1187_nth__mem,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_set_nat] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.15/5.35 => ( member_set_nat @ ( nth_set_nat @ Xs2 @ N2 ) @ ( set_set_nat2 @ Xs2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nth_mem
% 5.15/5.35 thf(fact_1188_nth__mem,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_nat] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.35 => ( member_nat @ ( nth_nat @ Xs2 @ N2 ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nth_mem
% 5.15/5.35 thf(fact_1189_nth__mem,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_VEBT_VEBT] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.35 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nth_mem
% 5.15/5.35 thf(fact_1190_nth__mem,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_o] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.35 => ( member_o @ ( nth_o @ Xs2 @ N2 ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nth_mem
% 5.15/5.35 thf(fact_1191_nth__mem,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_int] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.35 => ( member_int @ ( nth_int @ Xs2 @ N2 ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % nth_mem
% 5.15/5.35 thf(fact_1192_list__ball__nth,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_nat,P: nat > $o] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.35 => ( ! [X3: nat] :
% 5.15/5.35 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X3 ) )
% 5.15/5.35 => ( P @ ( nth_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % list_ball_nth
% 5.15/5.35 thf(fact_1193_list__ball__nth,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.35 => ( ! [X3: vEBT_VEBT] :
% 5.15/5.35 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X3 ) )
% 5.15/5.35 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % list_ball_nth
% 5.15/5.35 thf(fact_1194_list__ball__nth,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_o,P: $o > $o] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.35 => ( ! [X3: $o] :
% 5.15/5.35 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X3 ) )
% 5.15/5.35 => ( P @ ( nth_o @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % list_ball_nth
% 5.15/5.35 thf(fact_1195_list__ball__nth,axiom,
% 5.15/5.35 ! [N2: nat,Xs2: list_int,P: int > $o] :
% 5.15/5.35 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.35 => ( ! [X3: int] :
% 5.15/5.35 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X3 ) )
% 5.15/5.35 => ( P @ ( nth_int @ Xs2 @ N2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % list_ball_nth
% 5.15/5.35 thf(fact_1196_in__set__conv__nth,axiom,
% 5.15/5.35 ! [X: complex,Xs2: list_complex] :
% 5.15/5.35 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.15/5.35 = ( ? [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.15/5.35 & ( ( nth_complex @ Xs2 @ I3 )
% 5.15/5.35 = X ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % in_set_conv_nth
% 5.15/5.35 thf(fact_1197_in__set__conv__nth,axiom,
% 5.15/5.35 ! [X: real,Xs2: list_real] :
% 5.15/5.35 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.15/5.35 = ( ? [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 5.15/5.35 & ( ( nth_real @ Xs2 @ I3 )
% 5.15/5.35 = X ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % in_set_conv_nth
% 5.15/5.35 thf(fact_1198_in__set__conv__nth,axiom,
% 5.15/5.35 ! [X: set_nat,Xs2: list_set_nat] :
% 5.15/5.35 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.15/5.35 = ( ? [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.15/5.35 & ( ( nth_set_nat @ Xs2 @ I3 )
% 5.15/5.35 = X ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % in_set_conv_nth
% 5.15/5.35 thf(fact_1199_in__set__conv__nth,axiom,
% 5.15/5.35 ! [X: nat,Xs2: list_nat] :
% 5.15/5.35 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.15/5.35 = ( ? [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.35 & ( ( nth_nat @ Xs2 @ I3 )
% 5.15/5.35 = X ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % in_set_conv_nth
% 5.15/5.35 thf(fact_1200_in__set__conv__nth,axiom,
% 5.15/5.35 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.15/5.35 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.35 = ( ? [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.35 & ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 5.15/5.35 = X ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % in_set_conv_nth
% 5.15/5.35 thf(fact_1201_in__set__conv__nth,axiom,
% 5.15/5.35 ! [X: $o,Xs2: list_o] :
% 5.15/5.35 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.15/5.35 = ( ? [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.35 & ( ( nth_o @ Xs2 @ I3 )
% 5.15/5.35 = X ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % in_set_conv_nth
% 5.15/5.35 thf(fact_1202_in__set__conv__nth,axiom,
% 5.15/5.35 ! [X: int,Xs2: list_int] :
% 5.15/5.35 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.15/5.35 = ( ? [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.35 & ( ( nth_int @ Xs2 @ I3 )
% 5.15/5.35 = X ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % in_set_conv_nth
% 5.15/5.35 thf(fact_1203_all__nth__imp__all__set,axiom,
% 5.15/5.35 ! [Xs2: list_complex,P: complex > $o,X: complex] :
% 5.15/5.35 ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.15/5.35 => ( P @ ( nth_complex @ Xs2 @ I2 ) ) )
% 5.15/5.35 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % all_nth_imp_all_set
% 5.15/5.35 thf(fact_1204_all__nth__imp__all__set,axiom,
% 5.15/5.35 ! [Xs2: list_real,P: real > $o,X: real] :
% 5.15/5.35 ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs2 ) )
% 5.15/5.35 => ( P @ ( nth_real @ Xs2 @ I2 ) ) )
% 5.15/5.35 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % all_nth_imp_all_set
% 5.15/5.35 thf(fact_1205_all__nth__imp__all__set,axiom,
% 5.15/5.35 ! [Xs2: list_set_nat,P: set_nat > $o,X: set_nat] :
% 5.15/5.35 ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.15/5.35 => ( P @ ( nth_set_nat @ Xs2 @ I2 ) ) )
% 5.15/5.35 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % all_nth_imp_all_set
% 5.15/5.35 thf(fact_1206_all__nth__imp__all__set,axiom,
% 5.15/5.35 ! [Xs2: list_nat,P: nat > $o,X: nat] :
% 5.15/5.35 ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.35 => ( P @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.15/5.35 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % all_nth_imp_all_set
% 5.15/5.35 thf(fact_1207_all__nth__imp__all__set,axiom,
% 5.15/5.35 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.15/5.35 ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.35 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.15/5.35 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % all_nth_imp_all_set
% 5.15/5.35 thf(fact_1208_all__nth__imp__all__set,axiom,
% 5.15/5.35 ! [Xs2: list_o,P: $o > $o,X: $o] :
% 5.15/5.35 ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.35 => ( P @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.15/5.35 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % all_nth_imp_all_set
% 5.15/5.35 thf(fact_1209_all__nth__imp__all__set,axiom,
% 5.15/5.35 ! [Xs2: list_int,P: int > $o,X: int] :
% 5.15/5.35 ( ! [I2: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.35 => ( P @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.15/5.35 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.15/5.35 => ( P @ X ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % all_nth_imp_all_set
% 5.15/5.35 thf(fact_1210_both__member__options__def,axiom,
% 5.15/5.35 ( vEBT_V8194947554948674370ptions
% 5.15/5.35 = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 5.15/5.35 ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 5.15/5.35 | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % both_member_options_def
% 5.15/5.35 thf(fact_1211_member__valid__both__member__options,axiom,
% 5.15/5.35 ! [Tree: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.35 ( ( vEBT_invar_vebt @ Tree @ N2 )
% 5.15/5.35 => ( ( vEBT_vebt_member @ Tree @ X )
% 5.15/5.35 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 5.15/5.35 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % member_valid_both_member_options
% 5.15/5.35 thf(fact_1212_xor__num_Ocases,axiom,
% 5.15/5.35 ! [X: product_prod_num_num] :
% 5.15/5.35 ( ( X
% 5.15/5.35 != ( product_Pair_num_num @ one @ one ) )
% 5.15/5.35 => ( ! [N: num] :
% 5.15/5.35 ( X
% 5.15/5.35 != ( product_Pair_num_num @ one @ ( bit0 @ N ) ) )
% 5.15/5.35 => ( ! [N: num] :
% 5.15/5.35 ( X
% 5.15/5.35 != ( product_Pair_num_num @ one @ ( bit1 @ N ) ) )
% 5.15/5.35 => ( ! [M3: num] :
% 5.15/5.35 ( X
% 5.15/5.35 != ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) )
% 5.15/5.35 => ( ! [M3: num,N: num] :
% 5.15/5.35 ( X
% 5.15/5.35 != ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N ) ) )
% 5.15/5.35 => ( ! [M3: num,N: num] :
% 5.15/5.35 ( X
% 5.15/5.35 != ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N ) ) )
% 5.15/5.35 => ( ! [M3: num] :
% 5.15/5.35 ( X
% 5.15/5.35 != ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) )
% 5.15/5.35 => ( ! [M3: num,N: num] :
% 5.15/5.35 ( X
% 5.15/5.35 != ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N ) ) )
% 5.15/5.35 => ~ ! [M3: num,N: num] :
% 5.15/5.35 ( X
% 5.15/5.35 != ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % xor_num.cases
% 5.15/5.35 thf(fact_1213_linordered__field__no__ub,axiom,
% 5.15/5.35 ! [X5: real] :
% 5.15/5.35 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 5.15/5.35
% 5.15/5.35 % linordered_field_no_ub
% 5.15/5.35 thf(fact_1214_linordered__field__no__ub,axiom,
% 5.15/5.35 ! [X5: rat] :
% 5.15/5.35 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 5.15/5.35
% 5.15/5.35 % linordered_field_no_ub
% 5.15/5.35 thf(fact_1215_linordered__field__no__lb,axiom,
% 5.15/5.35 ! [X5: real] :
% 5.15/5.35 ? [Y3: real] : ( ord_less_real @ Y3 @ X5 ) ).
% 5.15/5.35
% 5.15/5.35 % linordered_field_no_lb
% 5.15/5.35 thf(fact_1216_linordered__field__no__lb,axiom,
% 5.15/5.35 ! [X5: rat] :
% 5.15/5.35 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X5 ) ).
% 5.15/5.35
% 5.15/5.35 % linordered_field_no_lb
% 5.15/5.35 thf(fact_1217_subset__code_I1_J,axiom,
% 5.15/5.35 ! [Xs2: list_complex,B3: set_complex] :
% 5.15/5.35 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B3 )
% 5.15/5.35 = ( ! [X2: complex] :
% 5.15/5.35 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.15/5.35 => ( member_complex @ X2 @ B3 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % subset_code(1)
% 5.15/5.35 thf(fact_1218_subset__code_I1_J,axiom,
% 5.15/5.35 ! [Xs2: list_real,B3: set_real] :
% 5.15/5.35 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B3 )
% 5.15/5.35 = ( ! [X2: real] :
% 5.15/5.35 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.15/5.35 => ( member_real @ X2 @ B3 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % subset_code(1)
% 5.15/5.35 thf(fact_1219_subset__code_I1_J,axiom,
% 5.15/5.35 ! [Xs2: list_set_nat,B3: set_set_nat] :
% 5.15/5.35 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ B3 )
% 5.15/5.35 = ( ! [X2: set_nat] :
% 5.15/5.35 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs2 ) )
% 5.15/5.35 => ( member_set_nat @ X2 @ B3 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % subset_code(1)
% 5.15/5.35 thf(fact_1220_subset__code_I1_J,axiom,
% 5.15/5.35 ! [Xs2: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.15/5.35 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B3 )
% 5.15/5.35 = ( ! [X2: vEBT_VEBT] :
% 5.15/5.35 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.35 => ( member_VEBT_VEBT @ X2 @ B3 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % subset_code(1)
% 5.15/5.35 thf(fact_1221_subset__code_I1_J,axiom,
% 5.15/5.35 ! [Xs2: list_int,B3: set_int] :
% 5.15/5.35 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B3 )
% 5.15/5.35 = ( ! [X2: int] :
% 5.15/5.35 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.15/5.35 => ( member_int @ X2 @ B3 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % subset_code(1)
% 5.15/5.35 thf(fact_1222_subset__code_I1_J,axiom,
% 5.15/5.35 ! [Xs2: list_nat,B3: set_nat] :
% 5.15/5.35 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B3 )
% 5.15/5.35 = ( ! [X2: nat] :
% 5.15/5.35 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.15/5.35 => ( member_nat @ X2 @ B3 ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % subset_code(1)
% 5.15/5.35 thf(fact_1223_neq__if__length__neq,axiom,
% 5.15/5.35 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.15/5.35 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.15/5.35 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.15/5.35 => ( Xs2 != Ys ) ) ).
% 5.15/5.35
% 5.15/5.35 % neq_if_length_neq
% 5.15/5.35 thf(fact_1224_neq__if__length__neq,axiom,
% 5.15/5.35 ! [Xs2: list_o,Ys: list_o] :
% 5.15/5.35 ( ( ( size_size_list_o @ Xs2 )
% 5.15/5.35 != ( size_size_list_o @ Ys ) )
% 5.15/5.35 => ( Xs2 != Ys ) ) ).
% 5.15/5.35
% 5.15/5.35 % neq_if_length_neq
% 5.15/5.35 thf(fact_1225_neq__if__length__neq,axiom,
% 5.15/5.35 ! [Xs2: list_int,Ys: list_int] :
% 5.15/5.35 ( ( ( size_size_list_int @ Xs2 )
% 5.15/5.35 != ( size_size_list_int @ Ys ) )
% 5.15/5.35 => ( Xs2 != Ys ) ) ).
% 5.15/5.35
% 5.15/5.35 % neq_if_length_neq
% 5.15/5.35 thf(fact_1226_Ex__list__of__length,axiom,
% 5.15/5.35 ! [N2: nat] :
% 5.15/5.35 ? [Xs3: list_VEBT_VEBT] :
% 5.15/5.35 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.15/5.35 = N2 ) ).
% 5.15/5.35
% 5.15/5.35 % Ex_list_of_length
% 5.15/5.35 thf(fact_1227_Ex__list__of__length,axiom,
% 5.15/5.35 ! [N2: nat] :
% 5.15/5.35 ? [Xs3: list_o] :
% 5.15/5.35 ( ( size_size_list_o @ Xs3 )
% 5.15/5.35 = N2 ) ).
% 5.15/5.35
% 5.15/5.35 % Ex_list_of_length
% 5.15/5.35 thf(fact_1228_Ex__list__of__length,axiom,
% 5.15/5.35 ! [N2: nat] :
% 5.15/5.35 ? [Xs3: list_int] :
% 5.15/5.35 ( ( size_size_list_int @ Xs3 )
% 5.15/5.35 = N2 ) ).
% 5.15/5.35
% 5.15/5.35 % Ex_list_of_length
% 5.15/5.35 thf(fact_1229_divide__divide__eq__left_H,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.15/5.35 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_left'
% 5.15/5.35 thf(fact_1230_divide__divide__eq__left_H,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.15/5.35 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_left'
% 5.15/5.35 thf(fact_1231_divide__divide__eq__left_H,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.15/5.35 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_eq_left'
% 5.15/5.35 thf(fact_1232_divide__divide__times__eq,axiom,
% 5.15/5.35 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 5.15/5.35 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.15/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_times_eq
% 5.15/5.35 thf(fact_1233_divide__divide__times__eq,axiom,
% 5.15/5.35 ! [X: real,Y: real,Z: real,W: real] :
% 5.15/5.35 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.15/5.35 = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_times_eq
% 5.15/5.35 thf(fact_1234_divide__divide__times__eq,axiom,
% 5.15/5.35 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 5.15/5.35 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 5.15/5.35 = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % divide_divide_times_eq
% 5.15/5.35 thf(fact_1235_times__divide__times__eq,axiom,
% 5.15/5.35 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 5.15/5.35 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.15/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_times_eq
% 5.15/5.35 thf(fact_1236_times__divide__times__eq,axiom,
% 5.15/5.35 ! [X: real,Y: real,Z: real,W: real] :
% 5.15/5.35 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.15/5.35 = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_times_eq
% 5.15/5.35 thf(fact_1237_times__divide__times__eq,axiom,
% 5.15/5.35 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 5.15/5.35 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 5.15/5.35 = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % times_divide_times_eq
% 5.15/5.35 thf(fact_1238_add__divide__distrib,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_divide_distrib
% 5.15/5.35 thf(fact_1239_add__divide__distrib,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_divide_distrib
% 5.15/5.35 thf(fact_1240_add__divide__distrib,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.15/5.35 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % add_divide_distrib
% 5.15/5.35 thf(fact_1241_diff__divide__distrib,axiom,
% 5.15/5.35 ! [A: complex,B: complex,C: complex] :
% 5.15/5.35 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_divide_distrib
% 5.15/5.35 thf(fact_1242_diff__divide__distrib,axiom,
% 5.15/5.35 ! [A: real,B: real,C: real] :
% 5.15/5.35 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_divide_distrib
% 5.15/5.35 thf(fact_1243_diff__divide__distrib,axiom,
% 5.15/5.35 ! [A: rat,B: rat,C: rat] :
% 5.15/5.35 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.15/5.35 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % diff_divide_distrib
% 5.15/5.35 thf(fact_1244_length__induct,axiom,
% 5.15/5.35 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.15/5.35 ( ! [Xs3: list_VEBT_VEBT] :
% 5.15/5.35 ( ! [Ys2: list_VEBT_VEBT] :
% 5.15/5.35 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.15/5.35 => ( P @ Ys2 ) )
% 5.15/5.35 => ( P @ Xs3 ) )
% 5.15/5.35 => ( P @ Xs2 ) ) ).
% 5.15/5.35
% 5.15/5.35 % length_induct
% 5.15/5.35 thf(fact_1245_length__induct,axiom,
% 5.15/5.35 ! [P: list_o > $o,Xs2: list_o] :
% 5.15/5.35 ( ! [Xs3: list_o] :
% 5.15/5.35 ( ! [Ys2: list_o] :
% 5.15/5.35 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.15/5.35 => ( P @ Ys2 ) )
% 5.15/5.35 => ( P @ Xs3 ) )
% 5.15/5.35 => ( P @ Xs2 ) ) ).
% 5.15/5.35
% 5.15/5.35 % length_induct
% 5.15/5.35 thf(fact_1246_length__induct,axiom,
% 5.15/5.35 ! [P: list_int > $o,Xs2: list_int] :
% 5.15/5.35 ( ! [Xs3: list_int] :
% 5.15/5.35 ( ! [Ys2: list_int] :
% 5.15/5.35 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.15/5.35 => ( P @ Ys2 ) )
% 5.15/5.35 => ( P @ Xs3 ) )
% 5.15/5.35 => ( P @ Xs2 ) ) ).
% 5.15/5.35
% 5.15/5.35 % length_induct
% 5.15/5.35 thf(fact_1247_list__eq__iff__nth__eq,axiom,
% 5.15/5.35 ( ( ^ [Y5: list_nat,Z5: list_nat] : ( Y5 = Z5 ) )
% 5.15/5.35 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.15/5.35 ( ( ( size_size_list_nat @ Xs )
% 5.15/5.35 = ( size_size_list_nat @ Ys3 ) )
% 5.15/5.35 & ! [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.15/5.35 => ( ( nth_nat @ Xs @ I3 )
% 5.15/5.35 = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % list_eq_iff_nth_eq
% 5.15/5.35 thf(fact_1248_list__eq__iff__nth__eq,axiom,
% 5.15/5.35 ( ( ^ [Y5: list_VEBT_VEBT,Z5: list_VEBT_VEBT] : ( Y5 = Z5 ) )
% 5.15/5.35 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.15/5.35 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.15/5.35 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.15/5.35 & ! [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.15/5.35 => ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 5.15/5.35 = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % list_eq_iff_nth_eq
% 5.15/5.35 thf(fact_1249_list__eq__iff__nth__eq,axiom,
% 5.15/5.35 ( ( ^ [Y5: list_o,Z5: list_o] : ( Y5 = Z5 ) )
% 5.15/5.35 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.15/5.35 ( ( ( size_size_list_o @ Xs )
% 5.15/5.35 = ( size_size_list_o @ Ys3 ) )
% 5.15/5.35 & ! [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.15/5.35 => ( ( nth_o @ Xs @ I3 )
% 5.15/5.35 = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % list_eq_iff_nth_eq
% 5.15/5.35 thf(fact_1250_list__eq__iff__nth__eq,axiom,
% 5.15/5.35 ( ( ^ [Y5: list_int,Z5: list_int] : ( Y5 = Z5 ) )
% 5.15/5.35 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.15/5.35 ( ( ( size_size_list_int @ Xs )
% 5.15/5.35 = ( size_size_list_int @ Ys3 ) )
% 5.15/5.35 & ! [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.15/5.35 => ( ( nth_int @ Xs @ I3 )
% 5.15/5.35 = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % list_eq_iff_nth_eq
% 5.15/5.35 thf(fact_1251_Skolem__list__nth,axiom,
% 5.15/5.35 ! [K: nat,P: nat > nat > $o] :
% 5.15/5.35 ( ( ! [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ K )
% 5.15/5.35 => ? [X4: nat] : ( P @ I3 @ X4 ) ) )
% 5.15/5.35 = ( ? [Xs: list_nat] :
% 5.15/5.35 ( ( ( size_size_list_nat @ Xs )
% 5.15/5.35 = K )
% 5.15/5.35 & ! [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ K )
% 5.15/5.35 => ( P @ I3 @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ) ).
% 5.15/5.35
% 5.15/5.35 % Skolem_list_nth
% 5.15/5.35 thf(fact_1252_Skolem__list__nth,axiom,
% 5.15/5.35 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.15/5.35 ( ( ! [I3: nat] :
% 5.15/5.35 ( ( ord_less_nat @ I3 @ K )
% 5.15/5.35 => ? [X4: vEBT_VEBT] : ( P @ I3 @ X4 ) ) )
% 5.15/5.35 = ( ? [Xs: list_VEBT_VEBT] :
% 5.15/5.35 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.15/5.36 = K )
% 5.15/5.36 & ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ K )
% 5.15/5.36 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % Skolem_list_nth
% 5.15/5.36 thf(fact_1253_Skolem__list__nth,axiom,
% 5.15/5.36 ! [K: nat,P: nat > $o > $o] :
% 5.15/5.36 ( ( ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ K )
% 5.15/5.36 => ? [X4: $o] : ( P @ I3 @ X4 ) ) )
% 5.15/5.36 = ( ? [Xs: list_o] :
% 5.15/5.36 ( ( ( size_size_list_o @ Xs )
% 5.15/5.36 = K )
% 5.15/5.36 & ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ K )
% 5.15/5.36 => ( P @ I3 @ ( nth_o @ Xs @ I3 ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % Skolem_list_nth
% 5.15/5.36 thf(fact_1254_Skolem__list__nth,axiom,
% 5.15/5.36 ! [K: nat,P: nat > int > $o] :
% 5.15/5.36 ( ( ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ K )
% 5.15/5.36 => ? [X4: int] : ( P @ I3 @ X4 ) ) )
% 5.15/5.36 = ( ? [Xs: list_int] :
% 5.15/5.36 ( ( ( size_size_list_int @ Xs )
% 5.15/5.36 = K )
% 5.15/5.36 & ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ K )
% 5.15/5.36 => ( P @ I3 @ ( nth_int @ Xs @ I3 ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % Skolem_list_nth
% 5.15/5.36 thf(fact_1255_nth__equalityI,axiom,
% 5.15/5.36 ! [Xs2: list_nat,Ys: list_nat] :
% 5.15/5.36 ( ( ( size_size_list_nat @ Xs2 )
% 5.15/5.36 = ( size_size_list_nat @ Ys ) )
% 5.15/5.36 => ( ! [I2: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.36 => ( ( nth_nat @ Xs2 @ I2 )
% 5.15/5.36 = ( nth_nat @ Ys @ I2 ) ) )
% 5.15/5.36 => ( Xs2 = Ys ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % nth_equalityI
% 5.15/5.36 thf(fact_1256_nth__equalityI,axiom,
% 5.15/5.36 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.15/5.36 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.15/5.36 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.15/5.36 => ( ! [I2: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.36 => ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.15/5.36 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 5.15/5.36 => ( Xs2 = Ys ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % nth_equalityI
% 5.15/5.36 thf(fact_1257_nth__equalityI,axiom,
% 5.15/5.36 ! [Xs2: list_o,Ys: list_o] :
% 5.15/5.36 ( ( ( size_size_list_o @ Xs2 )
% 5.15/5.36 = ( size_size_list_o @ Ys ) )
% 5.15/5.36 => ( ! [I2: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.36 => ( ( nth_o @ Xs2 @ I2 )
% 5.15/5.36 = ( nth_o @ Ys @ I2 ) ) )
% 5.15/5.36 => ( Xs2 = Ys ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % nth_equalityI
% 5.15/5.36 thf(fact_1258_nth__equalityI,axiom,
% 5.15/5.36 ! [Xs2: list_int,Ys: list_int] :
% 5.15/5.36 ( ( ( size_size_list_int @ Xs2 )
% 5.15/5.36 = ( size_size_list_int @ Ys ) )
% 5.15/5.36 => ( ! [I2: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.36 => ( ( nth_int @ Xs2 @ I2 )
% 5.15/5.36 = ( nth_int @ Ys @ I2 ) ) )
% 5.15/5.36 => ( Xs2 = Ys ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % nth_equalityI
% 5.15/5.36 thf(fact_1259_less__half__sum,axiom,
% 5.15/5.36 ! [A: real,B: real] :
% 5.15/5.36 ( ( ord_less_real @ A @ B )
% 5.15/5.36 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % less_half_sum
% 5.15/5.36 thf(fact_1260_less__half__sum,axiom,
% 5.15/5.36 ! [A: rat,B: rat] :
% 5.15/5.36 ( ( ord_less_rat @ A @ B )
% 5.15/5.36 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % less_half_sum
% 5.15/5.36 thf(fact_1261_gt__half__sum,axiom,
% 5.15/5.36 ! [A: real,B: real] :
% 5.15/5.36 ( ( ord_less_real @ A @ B )
% 5.15/5.36 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % gt_half_sum
% 5.15/5.36 thf(fact_1262_gt__half__sum,axiom,
% 5.15/5.36 ! [A: rat,B: rat] :
% 5.15/5.36 ( ( ord_less_rat @ A @ B )
% 5.15/5.36 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % gt_half_sum
% 5.15/5.36 thf(fact_1263_all__set__conv__all__nth,axiom,
% 5.15/5.36 ! [Xs2: list_nat,P: nat > $o] :
% 5.15/5.36 ( ( ! [X2: nat] :
% 5.15/5.36 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.15/5.36 => ( P @ X2 ) ) )
% 5.15/5.36 = ( ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.36 => ( P @ ( nth_nat @ Xs2 @ I3 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % all_set_conv_all_nth
% 5.15/5.36 thf(fact_1264_all__set__conv__all__nth,axiom,
% 5.15/5.36 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.15/5.36 ( ( ! [X2: vEBT_VEBT] :
% 5.15/5.36 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.36 => ( P @ X2 ) ) )
% 5.15/5.36 = ( ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.36 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % all_set_conv_all_nth
% 5.15/5.36 thf(fact_1265_all__set__conv__all__nth,axiom,
% 5.15/5.36 ! [Xs2: list_o,P: $o > $o] :
% 5.15/5.36 ( ( ! [X2: $o] :
% 5.15/5.36 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.15/5.36 => ( P @ X2 ) ) )
% 5.15/5.36 = ( ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.36 => ( P @ ( nth_o @ Xs2 @ I3 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % all_set_conv_all_nth
% 5.15/5.36 thf(fact_1266_all__set__conv__all__nth,axiom,
% 5.15/5.36 ! [Xs2: list_int,P: int > $o] :
% 5.15/5.36 ( ( ! [X2: int] :
% 5.15/5.36 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.15/5.36 => ( P @ X2 ) ) )
% 5.15/5.36 = ( ! [I3: nat] :
% 5.15/5.36 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.36 => ( P @ ( nth_int @ Xs2 @ I3 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % all_set_conv_all_nth
% 5.15/5.36 thf(fact_1267_nested__mint,axiom,
% 5.15/5.36 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,Va: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.15/5.36 => ( ( N2
% 5.15/5.36 = ( suc @ ( suc @ Va ) ) )
% 5.15/5.36 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.15/5.36 => ( ( Ma != Mi )
% 5.15/5.36 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % nested_mint
% 5.15/5.36 thf(fact_1268_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.15/5.36 ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 5.15/5.36 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X )
% 5.15/5.36 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.36 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % VEBT_internal.membermima.simps(5)
% 5.15/5.36 thf(fact_1269_low__def,axiom,
% 5.15/5.36 ( vEBT_VEBT_low
% 5.15/5.36 = ( ^ [X2: nat,N3: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % low_def
% 5.15/5.36 thf(fact_1270_is__succ__in__set__def,axiom,
% 5.15/5.36 ( vEBT_is_succ_in_set
% 5.15/5.36 = ( ^ [Xs: set_nat,X2: nat,Y2: nat] :
% 5.15/5.36 ( ( member_nat @ Y2 @ Xs )
% 5.15/5.36 & ( ord_less_nat @ X2 @ Y2 )
% 5.15/5.36 & ! [Z3: nat] :
% 5.15/5.36 ( ( member_nat @ Z3 @ Xs )
% 5.15/5.36 => ( ( ord_less_nat @ X2 @ Z3 )
% 5.15/5.36 => ( ord_less_eq_nat @ Y2 @ Z3 ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % is_succ_in_set_def
% 5.15/5.36 thf(fact_1271_is__pred__in__set__def,axiom,
% 5.15/5.36 ( vEBT_is_pred_in_set
% 5.15/5.36 = ( ^ [Xs: set_nat,X2: nat,Y2: nat] :
% 5.15/5.36 ( ( member_nat @ Y2 @ Xs )
% 5.15/5.36 & ( ord_less_nat @ Y2 @ X2 )
% 5.15/5.36 & ! [Z3: nat] :
% 5.15/5.36 ( ( member_nat @ Z3 @ Xs )
% 5.15/5.36 => ( ( ord_less_nat @ Z3 @ X2 )
% 5.15/5.36 => ( ord_less_eq_nat @ Z3 @ Y2 ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % is_pred_in_set_def
% 5.15/5.36 thf(fact_1272_buildup__nothing__in__leaf,axiom,
% 5.15/5.36 ! [N2: nat,X: nat] :
% 5.15/5.36 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X ) ).
% 5.15/5.36
% 5.15/5.36 % buildup_nothing_in_leaf
% 5.15/5.36 thf(fact_1273_obtain__set__succ,axiom,
% 5.15/5.36 ! [X: nat,Z: nat,A2: set_nat,B3: set_nat] :
% 5.15/5.36 ( ( ord_less_nat @ X @ Z )
% 5.15/5.36 => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 5.15/5.36 => ( ( finite_finite_nat @ B3 )
% 5.15/5.36 => ( ( A2 = B3 )
% 5.15/5.36 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_1 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % obtain_set_succ
% 5.15/5.36 thf(fact_1274_obtain__set__pred,axiom,
% 5.15/5.36 ! [Z: nat,X: nat,A2: set_nat] :
% 5.15/5.36 ( ( ord_less_nat @ Z @ X )
% 5.15/5.36 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 5.15/5.36 => ( ( finite_finite_nat @ A2 )
% 5.15/5.36 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % obtain_set_pred
% 5.15/5.36 thf(fact_1275_buildup__nothing__in__min__max,axiom,
% 5.15/5.36 ! [N2: nat,X: nat] :
% 5.15/5.36 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X ) ).
% 5.15/5.36
% 5.15/5.36 % buildup_nothing_in_min_max
% 5.15/5.36 thf(fact_1276_invar__vebt_Ointros_I3_J,axiom,
% 5.15/5.36 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.15/5.36 ( ! [X3: vEBT_VEBT] :
% 5.15/5.36 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.36 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.15/5.36 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.15/5.36 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.15/5.36 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.36 => ( ( M
% 5.15/5.36 = ( suc @ N2 ) )
% 5.15/5.36 => ( ( Deg
% 5.15/5.36 = ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.36 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.15/5.36 => ( ! [X3: vEBT_VEBT] :
% 5.15/5.36 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.36 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.15/5.36 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % invar_vebt.intros(3)
% 5.15/5.36 thf(fact_1277_set__vebt__finite,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % set_vebt_finite
% 5.15/5.36 thf(fact_1278_pred__none__empty,axiom,
% 5.15/5.36 ! [Xs2: set_nat,A: nat] :
% 5.15/5.36 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 5.15/5.36 => ( ( finite_finite_nat @ Xs2 )
% 5.15/5.36 => ~ ? [X5: nat] :
% 5.15/5.36 ( ( member_nat @ X5 @ Xs2 )
% 5.15/5.36 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pred_none_empty
% 5.15/5.36 thf(fact_1279_succ__none__empty,axiom,
% 5.15/5.36 ! [Xs2: set_nat,A: nat] :
% 5.15/5.36 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 5.15/5.36 => ( ( finite_finite_nat @ Xs2 )
% 5.15/5.36 => ~ ? [X5: nat] :
% 5.15/5.36 ( ( member_nat @ X5 @ Xs2 )
% 5.15/5.36 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % succ_none_empty
% 5.15/5.36 thf(fact_1280_mod__mod__trivial,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mod_trivial
% 5.15/5.36 thf(fact_1281_mod__mod__trivial,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mod_trivial
% 5.15/5.36 thf(fact_1282_mod__mod__trivial,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mod_trivial
% 5.15/5.36 thf(fact_1283_mod__add__self1,axiom,
% 5.15/5.36 ! [B: nat,A: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_self1
% 5.15/5.36 thf(fact_1284_mod__add__self1,axiom,
% 5.15/5.36 ! [B: int,A: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_self1
% 5.15/5.36 thf(fact_1285_mod__add__self1,axiom,
% 5.15/5.36 ! [B: code_integer,A: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_self1
% 5.15/5.36 thf(fact_1286_mod__add__self2,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_self2
% 5.15/5.36 thf(fact_1287_mod__add__self2,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_self2
% 5.15/5.36 thf(fact_1288_mod__add__self2,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_self2
% 5.15/5.36 thf(fact_1289_List_Ofinite__set,axiom,
% 5.15/5.36 ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % List.finite_set
% 5.15/5.36 thf(fact_1290_List_Ofinite__set,axiom,
% 5.15/5.36 ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % List.finite_set
% 5.15/5.36 thf(fact_1291_List_Ofinite__set,axiom,
% 5.15/5.36 ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % List.finite_set
% 5.15/5.36 thf(fact_1292_List_Ofinite__set,axiom,
% 5.15/5.36 ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % List.finite_set
% 5.15/5.36 thf(fact_1293_minus__mod__self2,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mod_self2
% 5.15/5.36 thf(fact_1294_minus__mod__self2,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mod_self2
% 5.15/5.36 thf(fact_1295_mod__less,axiom,
% 5.15/5.36 ! [M: nat,N2: nat] :
% 5.15/5.36 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.36 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.15/5.36 = M ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_less
% 5.15/5.36 thf(fact_1296_mod__mult__self4,axiom,
% 5.15/5.36 ! [B: nat,C: nat,A: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self4
% 5.15/5.36 thf(fact_1297_mod__mult__self4,axiom,
% 5.15/5.36 ! [B: int,C: int,A: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self4
% 5.15/5.36 thf(fact_1298_mod__mult__self4,axiom,
% 5.15/5.36 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self4
% 5.15/5.36 thf(fact_1299_mod__mult__self3,axiom,
% 5.15/5.36 ! [C: nat,B: nat,A: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self3
% 5.15/5.36 thf(fact_1300_mod__mult__self3,axiom,
% 5.15/5.36 ! [C: int,B: int,A: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self3
% 5.15/5.36 thf(fact_1301_mod__mult__self3,axiom,
% 5.15/5.36 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self3
% 5.15/5.36 thf(fact_1302_mod__mult__self2,axiom,
% 5.15/5.36 ! [A: nat,B: nat,C: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self2
% 5.15/5.36 thf(fact_1303_mod__mult__self2,axiom,
% 5.15/5.36 ! [A: int,B: int,C: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self2
% 5.15/5.36 thf(fact_1304_mod__mult__self2,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self2
% 5.15/5.36 thf(fact_1305_mod__mult__self1,axiom,
% 5.15/5.36 ! [A: nat,C: nat,B: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self1
% 5.15/5.36 thf(fact_1306_mod__mult__self1,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self1
% 5.15/5.36 thf(fact_1307_mod__mult__self1,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_self1
% 5.15/5.36 thf(fact_1308_Suc__mod__mult__self4,axiom,
% 5.15/5.36 ! [N2: nat,K: nat,M: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % Suc_mod_mult_self4
% 5.15/5.36 thf(fact_1309_Suc__mod__mult__self3,axiom,
% 5.15/5.36 ! [K: nat,N2: nat,M: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % Suc_mod_mult_self3
% 5.15/5.36 thf(fact_1310_Suc__mod__mult__self2,axiom,
% 5.15/5.36 ! [M: nat,N2: nat,K: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % Suc_mod_mult_self2
% 5.15/5.36 thf(fact_1311_Suc__mod__mult__self1,axiom,
% 5.15/5.36 ! [M: nat,K: nat,N2: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % Suc_mod_mult_self1
% 5.15/5.36 thf(fact_1312_one__mod__two__eq__one,axiom,
% 5.15/5.36 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.36 = one_one_nat ) ).
% 5.15/5.36
% 5.15/5.36 % one_mod_two_eq_one
% 5.15/5.36 thf(fact_1313_one__mod__two__eq__one,axiom,
% 5.15/5.36 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.36 = one_one_int ) ).
% 5.15/5.36
% 5.15/5.36 % one_mod_two_eq_one
% 5.15/5.36 thf(fact_1314_one__mod__two__eq__one,axiom,
% 5.15/5.36 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.36 = one_one_Code_integer ) ).
% 5.15/5.36
% 5.15/5.36 % one_mod_two_eq_one
% 5.15/5.36 thf(fact_1315_bits__one__mod__two__eq__one,axiom,
% 5.15/5.36 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.36 = one_one_nat ) ).
% 5.15/5.36
% 5.15/5.36 % bits_one_mod_two_eq_one
% 5.15/5.36 thf(fact_1316_bits__one__mod__two__eq__one,axiom,
% 5.15/5.36 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.36 = one_one_int ) ).
% 5.15/5.36
% 5.15/5.36 % bits_one_mod_two_eq_one
% 5.15/5.36 thf(fact_1317_bits__one__mod__two__eq__one,axiom,
% 5.15/5.36 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.36 = one_one_Code_integer ) ).
% 5.15/5.36
% 5.15/5.36 % bits_one_mod_two_eq_one
% 5.15/5.36 thf(fact_1318_mod2__Suc__Suc,axiom,
% 5.15/5.36 ! [M: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.36 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod2_Suc_Suc
% 5.15/5.36 thf(fact_1319_Suc__times__numeral__mod__eq,axiom,
% 5.15/5.36 ! [K: num,N2: nat] :
% 5.15/5.36 ( ( ( numeral_numeral_nat @ K )
% 5.15/5.36 != one_one_nat )
% 5.15/5.36 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 5.15/5.36 = one_one_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % Suc_times_numeral_mod_eq
% 5.15/5.36 thf(fact_1320_mod__Suc__eq__mod__add3,axiom,
% 5.15/5.36 ! [M: nat,N2: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.15/5.36 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_Suc_eq_mod_add3
% 5.15/5.36 thf(fact_1321_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.15/5.36 ! [M: nat,V: num] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.15/5.36 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % Suc_mod_eq_add3_mod_numeral
% 5.15/5.36 thf(fact_1322_mod__mult__eq,axiom,
% 5.15/5.36 ! [A: nat,C: nat,B: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_eq
% 5.15/5.36 thf(fact_1323_mod__mult__eq,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_eq
% 5.15/5.36 thf(fact_1324_mod__mult__eq,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_eq
% 5.15/5.36 thf(fact_1325_mod__mult__cong,axiom,
% 5.15/5.36 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.15/5.36 ( ( ( modulo_modulo_nat @ A @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.15/5.36 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.15/5.36 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_cong
% 5.15/5.36 thf(fact_1326_mod__mult__cong,axiom,
% 5.15/5.36 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.15/5.36 ( ( ( modulo_modulo_int @ A @ C )
% 5.15/5.36 = ( modulo_modulo_int @ A4 @ C ) )
% 5.15/5.36 => ( ( ( modulo_modulo_int @ B @ C )
% 5.15/5.36 = ( modulo_modulo_int @ B4 @ C ) )
% 5.15/5.36 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_cong
% 5.15/5.36 thf(fact_1327_mod__mult__cong,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.15/5.36 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.15/5.36 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.15/5.36 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_cong
% 5.15/5.36 thf(fact_1328_mod__mult__mult2,axiom,
% 5.15/5.36 ! [A: nat,C: nat,B: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.15/5.36 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_mult2
% 5.15/5.36 thf(fact_1329_mod__mult__mult2,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.15/5.36 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_mult2
% 5.15/5.36 thf(fact_1330_mod__mult__mult2,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.15/5.36 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_mult2
% 5.15/5.36 thf(fact_1331_mult__mod__right,axiom,
% 5.15/5.36 ! [C: nat,A: nat,B: nat] :
% 5.15/5.36 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.15/5.36 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_mod_right
% 5.15/5.36 thf(fact_1332_mult__mod__right,axiom,
% 5.15/5.36 ! [C: int,A: int,B: int] :
% 5.15/5.36 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.15/5.36 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_mod_right
% 5.15/5.36 thf(fact_1333_mult__mod__right,axiom,
% 5.15/5.36 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_mod_right
% 5.15/5.36 thf(fact_1334_mod__mult__left__eq,axiom,
% 5.15/5.36 ! [A: nat,C: nat,B: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_left_eq
% 5.15/5.36 thf(fact_1335_mod__mult__left__eq,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_left_eq
% 5.15/5.36 thf(fact_1336_mod__mult__left__eq,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_left_eq
% 5.15/5.36 thf(fact_1337_mod__mult__right__eq,axiom,
% 5.15/5.36 ! [A: nat,B: nat,C: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_right_eq
% 5.15/5.36 thf(fact_1338_mod__mult__right__eq,axiom,
% 5.15/5.36 ! [A: int,B: int,C: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_right_eq
% 5.15/5.36 thf(fact_1339_mod__mult__right__eq,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_right_eq
% 5.15/5.36 thf(fact_1340_mod__add__eq,axiom,
% 5.15/5.36 ! [A: nat,C: nat,B: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_eq
% 5.15/5.36 thf(fact_1341_mod__add__eq,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_eq
% 5.15/5.36 thf(fact_1342_mod__add__eq,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_eq
% 5.15/5.36 thf(fact_1343_mod__add__cong,axiom,
% 5.15/5.36 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.15/5.36 ( ( ( modulo_modulo_nat @ A @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.15/5.36 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.15/5.36 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_cong
% 5.15/5.36 thf(fact_1344_mod__add__cong,axiom,
% 5.15/5.36 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.15/5.36 ( ( ( modulo_modulo_int @ A @ C )
% 5.15/5.36 = ( modulo_modulo_int @ A4 @ C ) )
% 5.15/5.36 => ( ( ( modulo_modulo_int @ B @ C )
% 5.15/5.36 = ( modulo_modulo_int @ B4 @ C ) )
% 5.15/5.36 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_cong
% 5.15/5.36 thf(fact_1345_mod__add__cong,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.15/5.36 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.15/5.36 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.15/5.36 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_cong
% 5.15/5.36 thf(fact_1346_mod__add__left__eq,axiom,
% 5.15/5.36 ! [A: nat,C: nat,B: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_left_eq
% 5.15/5.36 thf(fact_1347_mod__add__left__eq,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_left_eq
% 5.15/5.36 thf(fact_1348_mod__add__left__eq,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_left_eq
% 5.15/5.36 thf(fact_1349_mod__add__right__eq,axiom,
% 5.15/5.36 ! [A: nat,B: nat,C: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_right_eq
% 5.15/5.36 thf(fact_1350_mod__add__right__eq,axiom,
% 5.15/5.36 ! [A: int,B: int,C: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_right_eq
% 5.15/5.36 thf(fact_1351_mod__add__right__eq,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_add_right_eq
% 5.15/5.36 thf(fact_1352_mod__diff__right__eq,axiom,
% 5.15/5.36 ! [A: int,B: int,C: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_diff_right_eq
% 5.15/5.36 thf(fact_1353_mod__diff__right__eq,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_diff_right_eq
% 5.15/5.36 thf(fact_1354_mod__diff__left__eq,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_diff_left_eq
% 5.15/5.36 thf(fact_1355_mod__diff__left__eq,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_diff_left_eq
% 5.15/5.36 thf(fact_1356_mod__diff__cong,axiom,
% 5.15/5.36 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.15/5.36 ( ( ( modulo_modulo_int @ A @ C )
% 5.15/5.36 = ( modulo_modulo_int @ A4 @ C ) )
% 5.15/5.36 => ( ( ( modulo_modulo_int @ B @ C )
% 5.15/5.36 = ( modulo_modulo_int @ B4 @ C ) )
% 5.15/5.36 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_diff_cong
% 5.15/5.36 thf(fact_1357_mod__diff__cong,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.15/5.36 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.15/5.36 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.15/5.36 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_diff_cong
% 5.15/5.36 thf(fact_1358_mod__diff__eq,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_diff_eq
% 5.15/5.36 thf(fact_1359_mod__diff__eq,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_diff_eq
% 5.15/5.36 thf(fact_1360_power__mod,axiom,
% 5.15/5.36 ! [A: nat,B: nat,N2: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
% 5.15/5.36 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % power_mod
% 5.15/5.36 thf(fact_1361_power__mod,axiom,
% 5.15/5.36 ! [A: int,B: int,N2: nat] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N2 ) @ B )
% 5.15/5.36 = ( modulo_modulo_int @ ( power_power_int @ A @ N2 ) @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % power_mod
% 5.15/5.36 thf(fact_1362_power__mod,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N2 ) @ B )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % power_mod
% 5.15/5.36 thf(fact_1363_mod__Suc__Suc__eq,axiom,
% 5.15/5.36 ! [M: nat,N2: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_Suc_Suc_eq
% 5.15/5.36 thf(fact_1364_mod__Suc__eq,axiom,
% 5.15/5.36 ! [M: nat,N2: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_Suc_eq
% 5.15/5.36 thf(fact_1365_mod__less__eq__dividend,axiom,
% 5.15/5.36 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 5.15/5.36
% 5.15/5.36 % mod_less_eq_dividend
% 5.15/5.36 thf(fact_1366_finite__list,axiom,
% 5.15/5.36 ! [A2: set_VEBT_VEBT] :
% 5.15/5.36 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.36 => ? [Xs3: list_VEBT_VEBT] :
% 5.15/5.36 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.15/5.36 = A2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_list
% 5.15/5.36 thf(fact_1367_finite__list,axiom,
% 5.15/5.36 ! [A2: set_nat] :
% 5.15/5.36 ( ( finite_finite_nat @ A2 )
% 5.15/5.36 => ? [Xs3: list_nat] :
% 5.15/5.36 ( ( set_nat2 @ Xs3 )
% 5.15/5.36 = A2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_list
% 5.15/5.36 thf(fact_1368_finite__list,axiom,
% 5.15/5.36 ! [A2: set_complex] :
% 5.15/5.36 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.36 => ? [Xs3: list_complex] :
% 5.15/5.36 ( ( set_complex2 @ Xs3 )
% 5.15/5.36 = A2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_list
% 5.15/5.36 thf(fact_1369_finite__list,axiom,
% 5.15/5.36 ! [A2: set_int] :
% 5.15/5.36 ( ( finite_finite_int @ A2 )
% 5.15/5.36 => ? [Xs3: list_int] :
% 5.15/5.36 ( ( set_int2 @ Xs3 )
% 5.15/5.36 = A2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_list
% 5.15/5.36 thf(fact_1370_finite__lists__length__eq,axiom,
% 5.15/5.36 ! [A2: set_complex,N2: nat] :
% 5.15/5.36 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.36 => ( finite8712137658972009173omplex
% 5.15/5.36 @ ( collect_list_complex
% 5.15/5.36 @ ^ [Xs: list_complex] :
% 5.15/5.36 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.15/5.36 = N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_eq
% 5.15/5.36 thf(fact_1371_finite__lists__length__eq,axiom,
% 5.15/5.36 ! [A2: set_VEBT_VEBT,N2: nat] :
% 5.15/5.36 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.36 => ( finite3004134309566078307T_VEBT
% 5.15/5.36 @ ( collec5608196760682091941T_VEBT
% 5.15/5.36 @ ^ [Xs: list_VEBT_VEBT] :
% 5.15/5.36 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.15/5.36 = N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_eq
% 5.15/5.36 thf(fact_1372_finite__lists__length__eq,axiom,
% 5.15/5.36 ! [A2: set_o,N2: nat] :
% 5.15/5.36 ( ( finite_finite_o @ A2 )
% 5.15/5.36 => ( finite_finite_list_o
% 5.15/5.36 @ ( collect_list_o
% 5.15/5.36 @ ^ [Xs: list_o] :
% 5.15/5.36 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ( size_size_list_o @ Xs )
% 5.15/5.36 = N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_eq
% 5.15/5.36 thf(fact_1373_finite__lists__length__eq,axiom,
% 5.15/5.36 ! [A2: set_int,N2: nat] :
% 5.15/5.36 ( ( finite_finite_int @ A2 )
% 5.15/5.36 => ( finite3922522038869484883st_int
% 5.15/5.36 @ ( collect_list_int
% 5.15/5.36 @ ^ [Xs: list_int] :
% 5.15/5.36 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ( size_size_list_int @ Xs )
% 5.15/5.36 = N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_eq
% 5.15/5.36 thf(fact_1374_finite__lists__length__eq,axiom,
% 5.15/5.36 ! [A2: set_nat,N2: nat] :
% 5.15/5.36 ( ( finite_finite_nat @ A2 )
% 5.15/5.36 => ( finite8100373058378681591st_nat
% 5.15/5.36 @ ( collect_list_nat
% 5.15/5.36 @ ^ [Xs: list_nat] :
% 5.15/5.36 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ( size_size_list_nat @ Xs )
% 5.15/5.36 = N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_eq
% 5.15/5.36 thf(fact_1375_finite__lists__length__le,axiom,
% 5.15/5.36 ! [A2: set_complex,N2: nat] :
% 5.15/5.36 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.36 => ( finite8712137658972009173omplex
% 5.15/5.36 @ ( collect_list_complex
% 5.15/5.36 @ ^ [Xs: list_complex] :
% 5.15/5.36 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_le
% 5.15/5.36 thf(fact_1376_finite__lists__length__le,axiom,
% 5.15/5.36 ! [A2: set_VEBT_VEBT,N2: nat] :
% 5.15/5.36 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.36 => ( finite3004134309566078307T_VEBT
% 5.15/5.36 @ ( collec5608196760682091941T_VEBT
% 5.15/5.36 @ ^ [Xs: list_VEBT_VEBT] :
% 5.15/5.36 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_le
% 5.15/5.36 thf(fact_1377_finite__lists__length__le,axiom,
% 5.15/5.36 ! [A2: set_o,N2: nat] :
% 5.15/5.36 ( ( finite_finite_o @ A2 )
% 5.15/5.36 => ( finite_finite_list_o
% 5.15/5.36 @ ( collect_list_o
% 5.15/5.36 @ ^ [Xs: list_o] :
% 5.15/5.36 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_le
% 5.15/5.36 thf(fact_1378_finite__lists__length__le,axiom,
% 5.15/5.36 ! [A2: set_int,N2: nat] :
% 5.15/5.36 ( ( finite_finite_int @ A2 )
% 5.15/5.36 => ( finite3922522038869484883st_int
% 5.15/5.36 @ ( collect_list_int
% 5.15/5.36 @ ^ [Xs: list_int] :
% 5.15/5.36 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_le
% 5.15/5.36 thf(fact_1379_finite__lists__length__le,axiom,
% 5.15/5.36 ! [A2: set_nat,N2: nat] :
% 5.15/5.36 ( ( finite_finite_nat @ A2 )
% 5.15/5.36 => ( finite8100373058378681591st_nat
% 5.15/5.36 @ ( collect_list_nat
% 5.15/5.36 @ ^ [Xs: list_nat] :
% 5.15/5.36 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.15/5.36 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_lists_length_le
% 5.15/5.36 thf(fact_1380_cong__exp__iff__simps_I9_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.36 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.15/5.36 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(9)
% 5.15/5.36 thf(fact_1381_cong__exp__iff__simps_I9_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.36 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.15/5.36 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(9)
% 5.15/5.36 thf(fact_1382_cong__exp__iff__simps_I9_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.36 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(9)
% 5.15/5.36 thf(fact_1383_cong__exp__iff__simps_I4_J,axiom,
% 5.15/5.36 ! [M: num,N2: num] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.15/5.36 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(4)
% 5.15/5.36 thf(fact_1384_cong__exp__iff__simps_I4_J,axiom,
% 5.15/5.36 ! [M: num,N2: num] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.15/5.36 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(4)
% 5.15/5.36 thf(fact_1385_cong__exp__iff__simps_I4_J,axiom,
% 5.15/5.36 ! [M: num,N2: num] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(4)
% 5.15/5.36 thf(fact_1386_mod__eqE,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( ( modulo_modulo_int @ A @ C )
% 5.15/5.36 = ( modulo_modulo_int @ B @ C ) )
% 5.15/5.36 => ~ ! [D3: int] :
% 5.15/5.36 ( B
% 5.15/5.36 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_eqE
% 5.15/5.36 thf(fact_1387_mod__eqE,axiom,
% 5.15/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.36 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.15/5.36 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.15/5.36 => ~ ! [D3: code_integer] :
% 5.15/5.36 ( B
% 5.15/5.36 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_eqE
% 5.15/5.36 thf(fact_1388_div__add1__eq,axiom,
% 5.15/5.36 ! [A: nat,B: nat,C: nat] :
% 5.15/5.36 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.36 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_add1_eq
% 5.15/5.36 thf(fact_1389_div__add1__eq,axiom,
% 5.15/5.36 ! [A: int,B: int,C: int] :
% 5.15/5.36 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.36 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_add1_eq
% 5.15/5.36 thf(fact_1390_div__add1__eq,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.36 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.15/5.36 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_add1_eq
% 5.15/5.36 thf(fact_1391_mod__induct,axiom,
% 5.15/5.36 ! [P: nat > $o,N2: nat,P2: nat,M: nat] :
% 5.15/5.36 ( ( P @ N2 )
% 5.15/5.36 => ( ( ord_less_nat @ N2 @ P2 )
% 5.15/5.36 => ( ( ord_less_nat @ M @ P2 )
% 5.15/5.36 => ( ! [N: nat] :
% 5.15/5.36 ( ( ord_less_nat @ N @ P2 )
% 5.15/5.36 => ( ( P @ N )
% 5.15/5.36 => ( P @ ( modulo_modulo_nat @ ( suc @ N ) @ P2 ) ) ) )
% 5.15/5.36 => ( P @ M ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_induct
% 5.15/5.36 thf(fact_1392_mod__Suc__le__divisor,axiom,
% 5.15/5.36 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 5.15/5.36
% 5.15/5.36 % mod_Suc_le_divisor
% 5.15/5.36 thf(fact_1393_mod__geq,axiom,
% 5.15/5.36 ! [M: nat,N2: nat] :
% 5.15/5.36 ( ~ ( ord_less_nat @ M @ N2 )
% 5.15/5.36 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_geq
% 5.15/5.36 thf(fact_1394_mod__if,axiom,
% 5.15/5.36 ( modulo_modulo_nat
% 5.15/5.36 = ( ^ [M5: nat,N3: nat] : ( if_nat @ ( ord_less_nat @ M5 @ N3 ) @ M5 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M5 @ N3 ) @ N3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_if
% 5.15/5.36 thf(fact_1395_le__mod__geq,axiom,
% 5.15/5.36 ! [N2: nat,M: nat] :
% 5.15/5.36 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.36 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % le_mod_geq
% 5.15/5.36 thf(fact_1396_nat__mod__eq__iff,axiom,
% 5.15/5.36 ! [X: nat,N2: nat,Y: nat] :
% 5.15/5.36 ( ( ( modulo_modulo_nat @ X @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.15/5.36 = ( ? [Q1: nat,Q22: nat] :
% 5.15/5.36 ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
% 5.15/5.36 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % nat_mod_eq_iff
% 5.15/5.36 thf(fact_1397_vebt__member_Osimps_I2_J,axiom,
% 5.15/5.36 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.15/5.36 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 5.15/5.36
% 5.15/5.36 % vebt_member.simps(2)
% 5.15/5.36 thf(fact_1398_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.15/5.36 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.15/5.36
% 5.15/5.36 % VEBT_internal.minNull.simps(4)
% 5.15/5.36 thf(fact_1399_cong__exp__iff__simps_I8_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(8)
% 5.15/5.36 thf(fact_1400_cong__exp__iff__simps_I8_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(8)
% 5.15/5.36 thf(fact_1401_cong__exp__iff__simps_I8_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(8)
% 5.15/5.36 thf(fact_1402_cong__exp__iff__simps_I6_J,axiom,
% 5.15/5.36 ! [Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(6)
% 5.15/5.36 thf(fact_1403_cong__exp__iff__simps_I6_J,axiom,
% 5.15/5.36 ! [Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(6)
% 5.15/5.36 thf(fact_1404_cong__exp__iff__simps_I6_J,axiom,
% 5.15/5.36 ! [Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(6)
% 5.15/5.36 thf(fact_1405_cancel__div__mod__rules_I2_J,axiom,
% 5.15/5.36 ! [B: nat,A: nat,C: nat] :
% 5.15/5.36 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.15/5.36 = ( plus_plus_nat @ A @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % cancel_div_mod_rules(2)
% 5.15/5.36 thf(fact_1406_cancel__div__mod__rules_I2_J,axiom,
% 5.15/5.36 ! [B: int,A: int,C: int] :
% 5.15/5.36 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.15/5.36 = ( plus_plus_int @ A @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % cancel_div_mod_rules(2)
% 5.15/5.36 thf(fact_1407_cancel__div__mod__rules_I2_J,axiom,
% 5.15/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.36 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.15/5.36 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % cancel_div_mod_rules(2)
% 5.15/5.36 thf(fact_1408_cancel__div__mod__rules_I1_J,axiom,
% 5.15/5.36 ! [A: nat,B: nat,C: nat] :
% 5.15/5.36 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.15/5.36 = ( plus_plus_nat @ A @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % cancel_div_mod_rules(1)
% 5.15/5.36 thf(fact_1409_cancel__div__mod__rules_I1_J,axiom,
% 5.15/5.36 ! [A: int,B: int,C: int] :
% 5.15/5.36 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.15/5.36 = ( plus_plus_int @ A @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % cancel_div_mod_rules(1)
% 5.15/5.36 thf(fact_1410_cancel__div__mod__rules_I1_J,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.36 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.15/5.36 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.15/5.36
% 5.15/5.36 % cancel_div_mod_rules(1)
% 5.15/5.36 thf(fact_1411_mod__div__decomp,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( A
% 5.15/5.36 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_div_decomp
% 5.15/5.36 thf(fact_1412_mod__div__decomp,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( A
% 5.15/5.36 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_div_decomp
% 5.15/5.36 thf(fact_1413_mod__div__decomp,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( A
% 5.15/5.36 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_div_decomp
% 5.15/5.36 thf(fact_1414_div__mult__mod__eq,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % div_mult_mod_eq
% 5.15/5.36 thf(fact_1415_div__mult__mod__eq,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % div_mult_mod_eq
% 5.15/5.36 thf(fact_1416_div__mult__mod__eq,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % div_mult_mod_eq
% 5.15/5.36 thf(fact_1417_mod__div__mult__eq,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mod_div_mult_eq
% 5.15/5.36 thf(fact_1418_mod__div__mult__eq,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mod_div_mult_eq
% 5.15/5.36 thf(fact_1419_mod__div__mult__eq,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mod_div_mult_eq
% 5.15/5.36 thf(fact_1420_mod__mult__div__eq,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_div_eq
% 5.15/5.36 thf(fact_1421_mod__mult__div__eq,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_div_eq
% 5.15/5.36 thf(fact_1422_mod__mult__div__eq,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult_div_eq
% 5.15/5.36 thf(fact_1423_mult__div__mod__eq,axiom,
% 5.15/5.36 ! [B: nat,A: nat] :
% 5.15/5.36 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mult_div_mod_eq
% 5.15/5.36 thf(fact_1424_mult__div__mod__eq,axiom,
% 5.15/5.36 ! [B: int,A: int] :
% 5.15/5.36 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mult_div_mod_eq
% 5.15/5.36 thf(fact_1425_mult__div__mod__eq,axiom,
% 5.15/5.36 ! [B: code_integer,A: code_integer] :
% 5.15/5.36 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % mult_div_mod_eq
% 5.15/5.36 thf(fact_1426_div__mult1__eq,axiom,
% 5.15/5.36 ! [A: nat,B: nat,C: nat] :
% 5.15/5.36 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.15/5.36 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_mult1_eq
% 5.15/5.36 thf(fact_1427_div__mult1__eq,axiom,
% 5.15/5.36 ! [A: int,B: int,C: int] :
% 5.15/5.36 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.15/5.36 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_mult1_eq
% 5.15/5.36 thf(fact_1428_div__mult1__eq,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.36 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.15/5.36 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_mult1_eq
% 5.15/5.36 thf(fact_1429_minus__mult__div__eq__mod,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mult_div_eq_mod
% 5.15/5.36 thf(fact_1430_minus__mult__div__eq__mod,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mult_div_eq_mod
% 5.15/5.36 thf(fact_1431_minus__mult__div__eq__mod,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mult_div_eq_mod
% 5.15/5.36 thf(fact_1432_minus__mod__eq__mult__div,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.15/5.36 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mod_eq_mult_div
% 5.15/5.36 thf(fact_1433_minus__mod__eq__mult__div,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.15/5.36 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mod_eq_mult_div
% 5.15/5.36 thf(fact_1434_minus__mod__eq__mult__div,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.15/5.36 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mod_eq_mult_div
% 5.15/5.36 thf(fact_1435_minus__mod__eq__div__mult,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.15/5.36 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mod_eq_div_mult
% 5.15/5.36 thf(fact_1436_minus__mod__eq__div__mult,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.15/5.36 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mod_eq_div_mult
% 5.15/5.36 thf(fact_1437_minus__mod__eq__div__mult,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.15/5.36 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_mod_eq_div_mult
% 5.15/5.36 thf(fact_1438_minus__div__mult__eq__mod,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.15/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_div_mult_eq_mod
% 5.15/5.36 thf(fact_1439_minus__div__mult__eq__mod,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.15/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_div_mult_eq_mod
% 5.15/5.36 thf(fact_1440_minus__div__mult__eq__mod,axiom,
% 5.15/5.36 ! [A: code_integer,B: code_integer] :
% 5.15/5.36 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.15/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.15/5.36
% 5.15/5.36 % minus_div_mult_eq_mod
% 5.15/5.36 thf(fact_1441_cong__exp__iff__simps_I13_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.36 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.15/5.36 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(13)
% 5.15/5.36 thf(fact_1442_cong__exp__iff__simps_I13_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.36 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.15/5.36 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(13)
% 5.15/5.36 thf(fact_1443_cong__exp__iff__simps_I13_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.36 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.15/5.36 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(13)
% 5.15/5.36 thf(fact_1444_cong__exp__iff__simps_I12_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(12)
% 5.15/5.36 thf(fact_1445_cong__exp__iff__simps_I12_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(12)
% 5.15/5.36 thf(fact_1446_cong__exp__iff__simps_I12_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(12)
% 5.15/5.36 thf(fact_1447_cong__exp__iff__simps_I10_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(10)
% 5.15/5.36 thf(fact_1448_cong__exp__iff__simps_I10_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(10)
% 5.15/5.36 thf(fact_1449_cong__exp__iff__simps_I10_J,axiom,
% 5.15/5.36 ! [M: num,Q3: num,N2: num] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.36 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % cong_exp_iff_simps(10)
% 5.15/5.36 thf(fact_1450_nat__mod__eq__lemma,axiom,
% 5.15/5.36 ! [X: nat,N2: nat,Y: nat] :
% 5.15/5.36 ( ( ( modulo_modulo_nat @ X @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.15/5.36 => ( ( ord_less_eq_nat @ Y @ X )
% 5.15/5.36 => ? [Q2: nat] :
% 5.15/5.36 ( X
% 5.15/5.36 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % nat_mod_eq_lemma
% 5.15/5.36 thf(fact_1451_mod__eq__nat2E,axiom,
% 5.15/5.36 ! [M: nat,Q3: nat,N2: nat] :
% 5.15/5.36 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.15/5.36 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 5.15/5.36 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.36 => ~ ! [S2: nat] :
% 5.15/5.36 ( N2
% 5.15/5.36 != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_eq_nat2E
% 5.15/5.36 thf(fact_1452_mod__eq__nat1E,axiom,
% 5.15/5.36 ! [M: nat,Q3: nat,N2: nat] :
% 5.15/5.36 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.15/5.36 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 5.15/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.36 => ~ ! [S2: nat] :
% 5.15/5.36 ( M
% 5.15/5.36 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q3 @ S2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_eq_nat1E
% 5.15/5.36 thf(fact_1453_mod__mult2__eq,axiom,
% 5.15/5.36 ! [M: nat,N2: nat,Q3: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q3 ) )
% 5.15/5.36 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q3 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mod_mult2_eq
% 5.15/5.36 thf(fact_1454_modulo__nat__def,axiom,
% 5.15/5.36 ( modulo_modulo_nat
% 5.15/5.36 = ( ^ [M5: nat,N3: nat] : ( minus_minus_nat @ M5 @ ( times_times_nat @ ( divide_divide_nat @ M5 @ N3 ) @ N3 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % modulo_nat_def
% 5.15/5.36 thf(fact_1455_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J,axiom,
% 5.15/5.36 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.15/5.36 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 5.15/5.36 = one_one_nat ) ).
% 5.15/5.36
% 5.15/5.36 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(4)
% 5.15/5.36 thf(fact_1456_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J,axiom,
% 5.15/5.36 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.36 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.36 = one_one_nat ) ).
% 5.15/5.36
% 5.15/5.36 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(4)
% 5.15/5.36 thf(fact_1457_Suc__mod__eq__add3__mod,axiom,
% 5.15/5.36 ! [M: nat,N2: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.15/5.36 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % Suc_mod_eq_add3_mod
% 5.15/5.36 thf(fact_1458_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 5.15/5.36 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.15/5.36 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X )
% 5.15/5.36 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 5.15/5.36 thf(fact_1459_div__exp__mod__exp__eq,axiom,
% 5.15/5.36 ! [A: nat,N2: nat,M: nat] :
% 5.15/5.36 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.36 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_exp_mod_exp_eq
% 5.15/5.36 thf(fact_1460_div__exp__mod__exp__eq,axiom,
% 5.15/5.36 ! [A: int,N2: nat,M: nat] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.36 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_exp_mod_exp_eq
% 5.15/5.36 thf(fact_1461_div__exp__mod__exp__eq,axiom,
% 5.15/5.36 ! [A: code_integer,N2: nat,M: nat] :
% 5.15/5.36 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.36 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % div_exp_mod_exp_eq
% 5.15/5.36 thf(fact_1462_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 5.15/5.36 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.36 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.36 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(4)
% 5.15/5.36 thf(fact_1463_mult__exp__mod__exp__eq,axiom,
% 5.15/5.36 ! [M: nat,N2: nat,A: nat] :
% 5.15/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.36 => ( ( 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 ) )
% 5.15/5.36 = ( 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 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_exp_mod_exp_eq
% 5.15/5.36 thf(fact_1464_mult__exp__mod__exp__eq,axiom,
% 5.15/5.36 ! [M: nat,N2: nat,A: int] :
% 5.15/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.36 => ( ( 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 ) )
% 5.15/5.36 = ( 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 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_exp_mod_exp_eq
% 5.15/5.36 thf(fact_1465_mult__exp__mod__exp__eq,axiom,
% 5.15/5.36 ! [M: nat,N2: nat,A: code_integer] :
% 5.15/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.36 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.36 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_exp_mod_exp_eq
% 5.15/5.36 thf(fact_1466_invar__vebt_Ointros_I2_J,axiom,
% 5.15/5.36 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.15/5.36 ( ! [X3: vEBT_VEBT] :
% 5.15/5.36 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.36 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.15/5.36 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.15/5.36 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.15/5.36 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.36 => ( ( M = N2 )
% 5.15/5.36 => ( ( Deg
% 5.15/5.36 = ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.36 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.15/5.36 => ( ! [X3: vEBT_VEBT] :
% 5.15/5.36 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.36 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.15/5.36 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % invar_vebt.intros(2)
% 5.15/5.36 thf(fact_1467_summaxma,axiom,
% 5.15/5.36 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.15/5.36 => ( ( Mi != Ma )
% 5.15/5.36 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.15/5.36 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % summaxma
% 5.15/5.36 thf(fact_1468_mintlistlength,axiom,
% 5.15/5.36 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.15/5.36 => ( ( Mi != Ma )
% 5.15/5.36 => ( ( ord_less_nat @ Mi @ Ma )
% 5.15/5.36 & ? [M3: nat] :
% 5.15/5.36 ( ( ( some_nat @ M3 )
% 5.15/5.36 = ( vEBT_vebt_mint @ Summary ) )
% 5.15/5.36 & ( ord_less_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mintlistlength
% 5.15/5.36 thf(fact_1469_option_Ocollapse,axiom,
% 5.15/5.36 ! [Option: option4927543243414619207at_nat] :
% 5.15/5.36 ( ( Option != none_P5556105721700978146at_nat )
% 5.15/5.36 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.15/5.36 = Option ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.collapse
% 5.15/5.36 thf(fact_1470_option_Ocollapse,axiom,
% 5.15/5.36 ! [Option: option_nat] :
% 5.15/5.36 ( ( Option != none_nat )
% 5.15/5.36 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.15/5.36 = Option ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.collapse
% 5.15/5.36 thf(fact_1471_option_Ocollapse,axiom,
% 5.15/5.36 ! [Option: option_num] :
% 5.15/5.36 ( ( Option != none_num )
% 5.15/5.36 => ( ( some_num @ ( the_num @ Option ) )
% 5.15/5.36 = Option ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.collapse
% 5.15/5.36 thf(fact_1472_vebt__insert_Osimps_I4_J,axiom,
% 5.15/5.36 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.36 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.36 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 5.15/5.36
% 5.15/5.36 % vebt_insert.simps(4)
% 5.15/5.36 thf(fact_1473_finite__Collect__le__nat,axiom,
% 5.15/5.36 ! [K: nat] :
% 5.15/5.36 ( finite_finite_nat
% 5.15/5.36 @ ( collect_nat
% 5.15/5.36 @ ^ [N3: nat] : ( ord_less_eq_nat @ N3 @ K ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_le_nat
% 5.15/5.36 thf(fact_1474_finite__Collect__less__nat,axiom,
% 5.15/5.36 ! [K: nat] :
% 5.15/5.36 ( finite_finite_nat
% 5.15/5.36 @ ( collect_nat
% 5.15/5.36 @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_less_nat
% 5.15/5.36 thf(fact_1475_finite__Collect__subsets,axiom,
% 5.15/5.36 ! [A2: set_complex] :
% 5.15/5.36 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.36 => ( finite6551019134538273531omplex
% 5.15/5.36 @ ( collect_set_complex
% 5.15/5.36 @ ^ [B5: set_complex] : ( ord_le211207098394363844omplex @ B5 @ A2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_subsets
% 5.15/5.36 thf(fact_1476_finite__Collect__subsets,axiom,
% 5.15/5.36 ! [A2: set_int] :
% 5.15/5.36 ( ( finite_finite_int @ A2 )
% 5.15/5.36 => ( finite6197958912794628473et_int
% 5.15/5.36 @ ( collect_set_int
% 5.15/5.36 @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_subsets
% 5.15/5.36 thf(fact_1477_finite__Collect__subsets,axiom,
% 5.15/5.36 ! [A2: set_nat] :
% 5.15/5.36 ( ( finite_finite_nat @ A2 )
% 5.15/5.36 => ( finite1152437895449049373et_nat
% 5.15/5.36 @ ( collect_set_nat
% 5.15/5.36 @ ^ [B5: set_nat] : ( ord_less_eq_set_nat @ B5 @ A2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_subsets
% 5.15/5.36 thf(fact_1478_finite__roots__unity,axiom,
% 5.15/5.36 ! [N2: nat] :
% 5.15/5.36 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.15/5.36 => ( finite_finite_real
% 5.15/5.36 @ ( collect_real
% 5.15/5.36 @ ^ [Z3: real] :
% 5.15/5.36 ( ( power_power_real @ Z3 @ N2 )
% 5.15/5.36 = one_one_real ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_roots_unity
% 5.15/5.36 thf(fact_1479_finite__roots__unity,axiom,
% 5.15/5.36 ! [N2: nat] :
% 5.15/5.36 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.15/5.36 => ( finite3207457112153483333omplex
% 5.15/5.36 @ ( collect_complex
% 5.15/5.36 @ ^ [Z3: complex] :
% 5.15/5.36 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.36 = one_one_complex ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_roots_unity
% 5.15/5.36 thf(fact_1480_not__None__eq,axiom,
% 5.15/5.36 ! [X: option4927543243414619207at_nat] :
% 5.15/5.36 ( ( X != none_P5556105721700978146at_nat )
% 5.15/5.36 = ( ? [Y2: product_prod_nat_nat] :
% 5.15/5.36 ( X
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ Y2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_None_eq
% 5.15/5.36 thf(fact_1481_not__None__eq,axiom,
% 5.15/5.36 ! [X: option_nat] :
% 5.15/5.36 ( ( X != none_nat )
% 5.15/5.36 = ( ? [Y2: nat] :
% 5.15/5.36 ( X
% 5.15/5.36 = ( some_nat @ Y2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_None_eq
% 5.15/5.36 thf(fact_1482_not__None__eq,axiom,
% 5.15/5.36 ! [X: option_num] :
% 5.15/5.36 ( ( X != none_num )
% 5.15/5.36 = ( ? [Y2: num] :
% 5.15/5.36 ( X
% 5.15/5.36 = ( some_num @ Y2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_None_eq
% 5.15/5.36 thf(fact_1483_not__Some__eq,axiom,
% 5.15/5.36 ! [X: option4927543243414619207at_nat] :
% 5.15/5.36 ( ( ! [Y2: product_prod_nat_nat] :
% 5.15/5.36 ( X
% 5.15/5.36 != ( some_P7363390416028606310at_nat @ Y2 ) ) )
% 5.15/5.36 = ( X = none_P5556105721700978146at_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_Some_eq
% 5.15/5.36 thf(fact_1484_not__Some__eq,axiom,
% 5.15/5.36 ! [X: option_nat] :
% 5.15/5.36 ( ( ! [Y2: nat] :
% 5.15/5.36 ( X
% 5.15/5.36 != ( some_nat @ Y2 ) ) )
% 5.15/5.36 = ( X = none_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_Some_eq
% 5.15/5.36 thf(fact_1485_not__Some__eq,axiom,
% 5.15/5.36 ! [X: option_num] :
% 5.15/5.36 ( ( ! [Y2: num] :
% 5.15/5.36 ( X
% 5.15/5.36 != ( some_num @ Y2 ) ) )
% 5.15/5.36 = ( X = none_num ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_Some_eq
% 5.15/5.36 thf(fact_1486_minminNull,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT] :
% 5.15/5.36 ( ( ( vEBT_vebt_mint @ T )
% 5.15/5.36 = none_nat )
% 5.15/5.36 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.15/5.36
% 5.15/5.36 % minminNull
% 5.15/5.36 thf(fact_1487_minNullmin,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT] :
% 5.15/5.36 ( ( vEBT_VEBT_minNull @ T )
% 5.15/5.36 => ( ( vEBT_vebt_mint @ T )
% 5.15/5.36 = none_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % minNullmin
% 5.15/5.36 thf(fact_1488_maxbmo,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,X: nat] :
% 5.15/5.36 ( ( ( vEBT_vebt_maxt @ T )
% 5.15/5.36 = ( some_nat @ X ) )
% 5.15/5.36 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 5.15/5.36
% 5.15/5.36 % maxbmo
% 5.15/5.36 thf(fact_1489_power__shift,axiom,
% 5.15/5.36 ! [X: nat,Y: nat,Z: nat] :
% 5.15/5.36 ( ( ( power_power_nat @ X @ Y )
% 5.15/5.36 = Z )
% 5.15/5.36 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.15/5.36 = ( some_nat @ Z ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % power_shift
% 5.15/5.36 thf(fact_1490_mint__member,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,Maxi: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_mint @ T )
% 5.15/5.36 = ( some_nat @ Maxi ) )
% 5.15/5.36 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mint_member
% 5.15/5.36 thf(fact_1491_maxt__member,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,Maxi: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_maxt @ T )
% 5.15/5.36 = ( some_nat @ Maxi ) )
% 5.15/5.36 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % maxt_member
% 5.15/5.36 thf(fact_1492_option_Oinject,axiom,
% 5.15/5.36 ! [X22: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 5.15/5.36 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ Y22 ) )
% 5.15/5.36 = ( X22 = Y22 ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.inject
% 5.15/5.36 thf(fact_1493_option_Oinject,axiom,
% 5.15/5.36 ! [X22: nat,Y22: nat] :
% 5.15/5.36 ( ( ( some_nat @ X22 )
% 5.15/5.36 = ( some_nat @ Y22 ) )
% 5.15/5.36 = ( X22 = Y22 ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.inject
% 5.15/5.36 thf(fact_1494_option_Oinject,axiom,
% 5.15/5.36 ! [X22: num,Y22: num] :
% 5.15/5.36 ( ( ( some_num @ X22 )
% 5.15/5.36 = ( some_num @ Y22 ) )
% 5.15/5.36 = ( X22 = Y22 ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.inject
% 5.15/5.36 thf(fact_1495_mint__corr__help,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,Mini: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_mint @ T )
% 5.15/5.36 = ( some_nat @ Mini ) )
% 5.15/5.36 => ( ( vEBT_vebt_member @ T @ X )
% 5.15/5.36 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mint_corr_help
% 5.15/5.36 thf(fact_1496_maxt__corr__help,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,Maxi: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_maxt @ T )
% 5.15/5.36 = ( some_nat @ Maxi ) )
% 5.15/5.36 => ( ( vEBT_vebt_member @ T @ X )
% 5.15/5.36 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % maxt_corr_help
% 5.15/5.36 thf(fact_1497_finite__Collect__disjI,axiom,
% 5.15/5.36 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.15/5.36 ( ( finite2998713641127702882nt_int
% 5.15/5.36 @ ( collec213857154873943460nt_int
% 5.15/5.36 @ ^ [X2: product_prod_int_int] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 | ( Q @ X2 ) ) ) )
% 5.15/5.36 = ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.15/5.36 & ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ Q ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_disjI
% 5.15/5.36 thf(fact_1498_finite__Collect__disjI,axiom,
% 5.15/5.36 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.15/5.36 ( ( finite1152437895449049373et_nat
% 5.15/5.36 @ ( collect_set_nat
% 5.15/5.36 @ ^ [X2: set_nat] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 | ( Q @ X2 ) ) ) )
% 5.15/5.36 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.15/5.36 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_disjI
% 5.15/5.36 thf(fact_1499_finite__Collect__disjI,axiom,
% 5.15/5.36 ! [P: nat > $o,Q: nat > $o] :
% 5.15/5.36 ( ( finite_finite_nat
% 5.15/5.36 @ ( collect_nat
% 5.15/5.36 @ ^ [X2: nat] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 | ( Q @ X2 ) ) ) )
% 5.15/5.36 = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.36 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_disjI
% 5.15/5.36 thf(fact_1500_finite__Collect__disjI,axiom,
% 5.15/5.36 ! [P: complex > $o,Q: complex > $o] :
% 5.15/5.36 ( ( finite3207457112153483333omplex
% 5.15/5.36 @ ( collect_complex
% 5.15/5.36 @ ^ [X2: complex] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 | ( Q @ X2 ) ) ) )
% 5.15/5.36 = ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.15/5.36 & ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_disjI
% 5.15/5.36 thf(fact_1501_finite__Collect__disjI,axiom,
% 5.15/5.36 ! [P: int > $o,Q: int > $o] :
% 5.15/5.36 ( ( finite_finite_int
% 5.15/5.36 @ ( collect_int
% 5.15/5.36 @ ^ [X2: int] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 | ( Q @ X2 ) ) ) )
% 5.15/5.36 = ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.15/5.36 & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_disjI
% 5.15/5.36 thf(fact_1502_finite__Collect__conjI,axiom,
% 5.15/5.36 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.15/5.36 ( ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.15/5.36 | ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ Q ) ) )
% 5.15/5.36 => ( finite2998713641127702882nt_int
% 5.15/5.36 @ ( collec213857154873943460nt_int
% 5.15/5.36 @ ^ [X2: product_prod_int_int] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 & ( Q @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_conjI
% 5.15/5.36 thf(fact_1503_finite__Collect__conjI,axiom,
% 5.15/5.36 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.15/5.36 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.15/5.36 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) )
% 5.15/5.36 => ( finite1152437895449049373et_nat
% 5.15/5.36 @ ( collect_set_nat
% 5.15/5.36 @ ^ [X2: set_nat] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 & ( Q @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_conjI
% 5.15/5.36 thf(fact_1504_finite__Collect__conjI,axiom,
% 5.15/5.36 ! [P: nat > $o,Q: nat > $o] :
% 5.15/5.36 ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.36 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 5.15/5.36 => ( finite_finite_nat
% 5.15/5.36 @ ( collect_nat
% 5.15/5.36 @ ^ [X2: nat] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 & ( Q @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_conjI
% 5.15/5.36 thf(fact_1505_finite__Collect__conjI,axiom,
% 5.15/5.36 ! [P: complex > $o,Q: complex > $o] :
% 5.15/5.36 ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.15/5.36 | ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) )
% 5.15/5.36 => ( finite3207457112153483333omplex
% 5.15/5.36 @ ( collect_complex
% 5.15/5.36 @ ^ [X2: complex] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 & ( Q @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_conjI
% 5.15/5.36 thf(fact_1506_finite__Collect__conjI,axiom,
% 5.15/5.36 ! [P: int > $o,Q: int > $o] :
% 5.15/5.36 ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.15/5.36 | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 5.15/5.36 => ( finite_finite_int
% 5.15/5.36 @ ( collect_int
% 5.15/5.36 @ ^ [X2: int] :
% 5.15/5.36 ( ( P @ X2 )
% 5.15/5.36 & ( Q @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_Collect_conjI
% 5.15/5.36 thf(fact_1507_mint__corr,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_mint @ T )
% 5.15/5.36 = ( some_nat @ X ) )
% 5.15/5.36 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mint_corr
% 5.15/5.36 thf(fact_1508_mint__sound,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.15/5.36 => ( ( vEBT_vebt_mint @ T )
% 5.15/5.36 = ( some_nat @ X ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mint_sound
% 5.15/5.36 thf(fact_1509_maxt__corr,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_maxt @ T )
% 5.15/5.36 = ( some_nat @ X ) )
% 5.15/5.36 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % maxt_corr
% 5.15/5.36 thf(fact_1510_maxt__sound,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.15/5.36 => ( ( vEBT_vebt_maxt @ T )
% 5.15/5.36 = ( some_nat @ X ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % maxt_sound
% 5.15/5.36 thf(fact_1511_misiz,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,M: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( some_nat @ M )
% 5.15/5.36 = ( vEBT_vebt_mint @ T ) )
% 5.15/5.36 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % misiz
% 5.15/5.36 thf(fact_1512_zmod__numeral__Bit0,axiom,
% 5.15/5.36 ! [V: num,W: num] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.15/5.36 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % zmod_numeral_Bit0
% 5.15/5.36 thf(fact_1513_zmod__numeral__Bit1,axiom,
% 5.15/5.36 ! [V: num,W: num] :
% 5.15/5.36 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.15/5.36 = ( 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 ) ) ).
% 5.15/5.36
% 5.15/5.36 % zmod_numeral_Bit1
% 5.15/5.36 thf(fact_1514_lesseq__shift,axiom,
% 5.15/5.36 ( ord_less_eq_nat
% 5.15/5.36 = ( ^ [X2: nat,Y2: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % lesseq_shift
% 5.15/5.36 thf(fact_1515_finite__maxlen,axiom,
% 5.15/5.36 ! [M7: set_list_VEBT_VEBT] :
% 5.15/5.36 ( ( finite3004134309566078307T_VEBT @ M7 )
% 5.15/5.36 => ? [N: nat] :
% 5.15/5.36 ! [X5: list_VEBT_VEBT] :
% 5.15/5.36 ( ( member2936631157270082147T_VEBT @ X5 @ M7 )
% 5.15/5.36 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_maxlen
% 5.15/5.36 thf(fact_1516_finite__maxlen,axiom,
% 5.15/5.36 ! [M7: set_list_o] :
% 5.15/5.36 ( ( finite_finite_list_o @ M7 )
% 5.15/5.36 => ? [N: nat] :
% 5.15/5.36 ! [X5: list_o] :
% 5.15/5.36 ( ( member_list_o @ X5 @ M7 )
% 5.15/5.36 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_maxlen
% 5.15/5.36 thf(fact_1517_finite__maxlen,axiom,
% 5.15/5.36 ! [M7: set_list_int] :
% 5.15/5.36 ( ( finite3922522038869484883st_int @ M7 )
% 5.15/5.36 => ? [N: nat] :
% 5.15/5.36 ! [X5: list_int] :
% 5.15/5.36 ( ( member_list_int @ X5 @ M7 )
% 5.15/5.36 => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_maxlen
% 5.15/5.36 thf(fact_1518_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_real,B3: set_nat,R: real > nat > $o] :
% 5.15/5.36 ( ~ ( finite_finite_real @ A2 )
% 5.15/5.36 => ( ( finite_finite_nat @ B3 )
% 5.15/5.36 => ( ! [X3: real] :
% 5.15/5.36 ( ( member_real @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: nat] :
% 5.15/5.36 ( ( member_nat @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite_finite_real
% 5.15/5.36 @ ( collect_real
% 5.15/5.36 @ ^ [A3: real] :
% 5.15/5.36 ( ( member_real @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1519_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_real,B3: set_complex,R: real > complex > $o] :
% 5.15/5.36 ( ~ ( finite_finite_real @ A2 )
% 5.15/5.36 => ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.36 => ( ! [X3: real] :
% 5.15/5.36 ( ( member_real @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: complex] :
% 5.15/5.36 ( ( member_complex @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: complex] :
% 5.15/5.36 ( ( member_complex @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite_finite_real
% 5.15/5.36 @ ( collect_real
% 5.15/5.36 @ ^ [A3: real] :
% 5.15/5.36 ( ( member_real @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1520_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_real,B3: set_int,R: real > int > $o] :
% 5.15/5.36 ( ~ ( finite_finite_real @ A2 )
% 5.15/5.36 => ( ( finite_finite_int @ B3 )
% 5.15/5.36 => ( ! [X3: real] :
% 5.15/5.36 ( ( member_real @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: int] :
% 5.15/5.36 ( ( member_int @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: int] :
% 5.15/5.36 ( ( member_int @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite_finite_real
% 5.15/5.36 @ ( collect_real
% 5.15/5.36 @ ^ [A3: real] :
% 5.15/5.36 ( ( member_real @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1521_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_nat,B3: set_nat,R: nat > nat > $o] :
% 5.15/5.36 ( ~ ( finite_finite_nat @ A2 )
% 5.15/5.36 => ( ( finite_finite_nat @ B3 )
% 5.15/5.36 => ( ! [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: nat] :
% 5.15/5.36 ( ( member_nat @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite_finite_nat
% 5.15/5.36 @ ( collect_nat
% 5.15/5.36 @ ^ [A3: nat] :
% 5.15/5.36 ( ( member_nat @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1522_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_nat,B3: set_complex,R: nat > complex > $o] :
% 5.15/5.36 ( ~ ( finite_finite_nat @ A2 )
% 5.15/5.36 => ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.36 => ( ! [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: complex] :
% 5.15/5.36 ( ( member_complex @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: complex] :
% 5.15/5.36 ( ( member_complex @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite_finite_nat
% 5.15/5.36 @ ( collect_nat
% 5.15/5.36 @ ^ [A3: nat] :
% 5.15/5.36 ( ( member_nat @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1523_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_nat,B3: set_int,R: nat > int > $o] :
% 5.15/5.36 ( ~ ( finite_finite_nat @ A2 )
% 5.15/5.36 => ( ( finite_finite_int @ B3 )
% 5.15/5.36 => ( ! [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: int] :
% 5.15/5.36 ( ( member_int @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: int] :
% 5.15/5.36 ( ( member_int @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite_finite_nat
% 5.15/5.36 @ ( collect_nat
% 5.15/5.36 @ ^ [A3: nat] :
% 5.15/5.36 ( ( member_nat @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1524_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_complex,B3: set_nat,R: complex > nat > $o] :
% 5.15/5.36 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.15/5.36 => ( ( finite_finite_nat @ B3 )
% 5.15/5.36 => ( ! [X3: complex] :
% 5.15/5.36 ( ( member_complex @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: nat] :
% 5.15/5.36 ( ( member_nat @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite3207457112153483333omplex
% 5.15/5.36 @ ( collect_complex
% 5.15/5.36 @ ^ [A3: complex] :
% 5.15/5.36 ( ( member_complex @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1525_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_complex,B3: set_complex,R: complex > complex > $o] :
% 5.15/5.36 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.15/5.36 => ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.36 => ( ! [X3: complex] :
% 5.15/5.36 ( ( member_complex @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: complex] :
% 5.15/5.36 ( ( member_complex @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: complex] :
% 5.15/5.36 ( ( member_complex @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite3207457112153483333omplex
% 5.15/5.36 @ ( collect_complex
% 5.15/5.36 @ ^ [A3: complex] :
% 5.15/5.36 ( ( member_complex @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1526_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_complex,B3: set_int,R: complex > int > $o] :
% 5.15/5.36 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.15/5.36 => ( ( finite_finite_int @ B3 )
% 5.15/5.36 => ( ! [X3: complex] :
% 5.15/5.36 ( ( member_complex @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: int] :
% 5.15/5.36 ( ( member_int @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: int] :
% 5.15/5.36 ( ( member_int @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite3207457112153483333omplex
% 5.15/5.36 @ ( collect_complex
% 5.15/5.36 @ ^ [A3: complex] :
% 5.15/5.36 ( ( member_complex @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1527_pigeonhole__infinite__rel,axiom,
% 5.15/5.36 ! [A2: set_int,B3: set_nat,R: int > nat > $o] :
% 5.15/5.36 ( ~ ( finite_finite_int @ A2 )
% 5.15/5.36 => ( ( finite_finite_nat @ B3 )
% 5.15/5.36 => ( ! [X3: int] :
% 5.15/5.36 ( ( member_int @ X3 @ A2 )
% 5.15/5.36 => ? [Xa: nat] :
% 5.15/5.36 ( ( member_nat @ Xa @ B3 )
% 5.15/5.36 & ( R @ X3 @ Xa ) ) )
% 5.15/5.36 => ? [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ B3 )
% 5.15/5.36 & ~ ( finite_finite_int
% 5.15/5.36 @ ( collect_int
% 5.15/5.36 @ ^ [A3: int] :
% 5.15/5.36 ( ( member_int @ A3 @ A2 )
% 5.15/5.36 & ( R @ A3 @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pigeonhole_infinite_rel
% 5.15/5.36 thf(fact_1528_not__finite__existsD,axiom,
% 5.15/5.36 ! [P: product_prod_int_int > $o] :
% 5.15/5.36 ( ~ ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.15/5.36 => ? [X_1: product_prod_int_int] : ( P @ X_1 ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_finite_existsD
% 5.15/5.36 thf(fact_1529_not__finite__existsD,axiom,
% 5.15/5.36 ! [P: set_nat > $o] :
% 5.15/5.36 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.15/5.36 => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_finite_existsD
% 5.15/5.36 thf(fact_1530_not__finite__existsD,axiom,
% 5.15/5.36 ! [P: nat > $o] :
% 5.15/5.36 ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.36 => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_finite_existsD
% 5.15/5.36 thf(fact_1531_not__finite__existsD,axiom,
% 5.15/5.36 ! [P: complex > $o] :
% 5.15/5.36 ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.15/5.36 => ? [X_1: complex] : ( P @ X_1 ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_finite_existsD
% 5.15/5.36 thf(fact_1532_not__finite__existsD,axiom,
% 5.15/5.36 ! [P: int > $o] :
% 5.15/5.36 ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 5.15/5.36 => ? [X_1: int] : ( P @ X_1 ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_finite_existsD
% 5.15/5.36 thf(fact_1533_finite__has__maximal2,axiom,
% 5.15/5.36 ! [A2: set_real,A: real] :
% 5.15/5.36 ( ( finite_finite_real @ A2 )
% 5.15/5.36 => ( ( member_real @ A @ A2 )
% 5.15/5.36 => ? [X3: real] :
% 5.15/5.36 ( ( member_real @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_real @ A @ X3 )
% 5.15/5.36 & ! [Xa: real] :
% 5.15/5.36 ( ( member_real @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_maximal2
% 5.15/5.36 thf(fact_1534_finite__has__maximal2,axiom,
% 5.15/5.36 ! [A2: set_set_nat,A: set_nat] :
% 5.15/5.36 ( ( finite1152437895449049373et_nat @ A2 )
% 5.15/5.36 => ( ( member_set_nat @ A @ A2 )
% 5.15/5.36 => ? [X3: set_nat] :
% 5.15/5.36 ( ( member_set_nat @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_set_nat @ A @ X3 )
% 5.15/5.36 & ! [Xa: set_nat] :
% 5.15/5.36 ( ( member_set_nat @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_maximal2
% 5.15/5.36 thf(fact_1535_finite__has__maximal2,axiom,
% 5.15/5.36 ! [A2: set_rat,A: rat] :
% 5.15/5.36 ( ( finite_finite_rat @ A2 )
% 5.15/5.36 => ( ( member_rat @ A @ A2 )
% 5.15/5.36 => ? [X3: rat] :
% 5.15/5.36 ( ( member_rat @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_rat @ A @ X3 )
% 5.15/5.36 & ! [Xa: rat] :
% 5.15/5.36 ( ( member_rat @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_maximal2
% 5.15/5.36 thf(fact_1536_finite__has__maximal2,axiom,
% 5.15/5.36 ! [A2: set_num,A: num] :
% 5.15/5.36 ( ( finite_finite_num @ A2 )
% 5.15/5.36 => ( ( member_num @ A @ A2 )
% 5.15/5.36 => ? [X3: num] :
% 5.15/5.36 ( ( member_num @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_num @ A @ X3 )
% 5.15/5.36 & ! [Xa: num] :
% 5.15/5.36 ( ( member_num @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_maximal2
% 5.15/5.36 thf(fact_1537_finite__has__maximal2,axiom,
% 5.15/5.36 ! [A2: set_nat,A: nat] :
% 5.15/5.36 ( ( finite_finite_nat @ A2 )
% 5.15/5.36 => ( ( member_nat @ A @ A2 )
% 5.15/5.36 => ? [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_nat @ A @ X3 )
% 5.15/5.36 & ! [Xa: nat] :
% 5.15/5.36 ( ( member_nat @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_maximal2
% 5.15/5.36 thf(fact_1538_finite__has__maximal2,axiom,
% 5.15/5.36 ! [A2: set_int,A: int] :
% 5.15/5.36 ( ( finite_finite_int @ A2 )
% 5.15/5.36 => ( ( member_int @ A @ A2 )
% 5.15/5.36 => ? [X3: int] :
% 5.15/5.36 ( ( member_int @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_int @ A @ X3 )
% 5.15/5.36 & ! [Xa: int] :
% 5.15/5.36 ( ( member_int @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_maximal2
% 5.15/5.36 thf(fact_1539_finite__has__minimal2,axiom,
% 5.15/5.36 ! [A2: set_real,A: real] :
% 5.15/5.36 ( ( finite_finite_real @ A2 )
% 5.15/5.36 => ( ( member_real @ A @ A2 )
% 5.15/5.36 => ? [X3: real] :
% 5.15/5.36 ( ( member_real @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_real @ X3 @ A )
% 5.15/5.36 & ! [Xa: real] :
% 5.15/5.36 ( ( member_real @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_minimal2
% 5.15/5.36 thf(fact_1540_finite__has__minimal2,axiom,
% 5.15/5.36 ! [A2: set_set_nat,A: set_nat] :
% 5.15/5.36 ( ( finite1152437895449049373et_nat @ A2 )
% 5.15/5.36 => ( ( member_set_nat @ A @ A2 )
% 5.15/5.36 => ? [X3: set_nat] :
% 5.15/5.36 ( ( member_set_nat @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_set_nat @ X3 @ A )
% 5.15/5.36 & ! [Xa: set_nat] :
% 5.15/5.36 ( ( member_set_nat @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_minimal2
% 5.15/5.36 thf(fact_1541_finite__has__minimal2,axiom,
% 5.15/5.36 ! [A2: set_rat,A: rat] :
% 5.15/5.36 ( ( finite_finite_rat @ A2 )
% 5.15/5.36 => ( ( member_rat @ A @ A2 )
% 5.15/5.36 => ? [X3: rat] :
% 5.15/5.36 ( ( member_rat @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_rat @ X3 @ A )
% 5.15/5.36 & ! [Xa: rat] :
% 5.15/5.36 ( ( member_rat @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_minimal2
% 5.15/5.36 thf(fact_1542_finite__has__minimal2,axiom,
% 5.15/5.36 ! [A2: set_num,A: num] :
% 5.15/5.36 ( ( finite_finite_num @ A2 )
% 5.15/5.36 => ( ( member_num @ A @ A2 )
% 5.15/5.36 => ? [X3: num] :
% 5.15/5.36 ( ( member_num @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_num @ X3 @ A )
% 5.15/5.36 & ! [Xa: num] :
% 5.15/5.36 ( ( member_num @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_minimal2
% 5.15/5.36 thf(fact_1543_finite__has__minimal2,axiom,
% 5.15/5.36 ! [A2: set_nat,A: nat] :
% 5.15/5.36 ( ( finite_finite_nat @ A2 )
% 5.15/5.36 => ( ( member_nat @ A @ A2 )
% 5.15/5.36 => ? [X3: nat] :
% 5.15/5.36 ( ( member_nat @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_nat @ X3 @ A )
% 5.15/5.36 & ! [Xa: nat] :
% 5.15/5.36 ( ( member_nat @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_minimal2
% 5.15/5.36 thf(fact_1544_finite__has__minimal2,axiom,
% 5.15/5.36 ! [A2: set_int,A: int] :
% 5.15/5.36 ( ( finite_finite_int @ A2 )
% 5.15/5.36 => ( ( member_int @ A @ A2 )
% 5.15/5.36 => ? [X3: int] :
% 5.15/5.36 ( ( member_int @ X3 @ A2 )
% 5.15/5.36 & ( ord_less_eq_int @ X3 @ A )
% 5.15/5.36 & ! [Xa: int] :
% 5.15/5.36 ( ( member_int @ Xa @ A2 )
% 5.15/5.36 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.15/5.36 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % finite_has_minimal2
% 5.15/5.36 thf(fact_1545_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.15/5.36 ( ( ( X = none_P5556105721700978146at_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: product_prod_nat_nat,B6: product_prod_nat_nat] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1546_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 5.15/5.36 ( ( ( X = none_P5556105721700978146at_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: product_prod_nat_nat,B6: nat] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_nat @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1547_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 5.15/5.36 ( ( ( X = none_P5556105721700978146at_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_num )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: product_prod_nat_nat,B6: num] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_num @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1548_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.15/5.36 ( ( ( X = none_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: nat,B6: product_prod_nat_nat] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_nat @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1549_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option_nat,P: option_nat > option_nat > $o,Y: option_nat] :
% 5.15/5.36 ( ( ( X = none_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: nat,B6: nat] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_nat @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_nat @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1550_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option_nat,P: option_nat > option_num > $o,Y: option_num] :
% 5.15/5.36 ( ( ( X = none_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_num )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: nat,B6: num] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_nat @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_num @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1551_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.15/5.36 ( ( ( X = none_num )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: num,B6: product_prod_nat_nat] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_num @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1552_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option_num,P: option_num > option_nat > $o,Y: option_nat] :
% 5.15/5.36 ( ( ( X = none_num )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_nat )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: num,B6: nat] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_num @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_nat @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1553_combine__options__cases,axiom,
% 5.15/5.36 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 5.15/5.36 ( ( ( X = none_num )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ( ( Y = none_num )
% 5.15/5.36 => ( P @ X @ Y ) )
% 5.15/5.36 => ( ! [A5: num,B6: num] :
% 5.15/5.36 ( ( X
% 5.15/5.36 = ( some_num @ A5 ) )
% 5.15/5.36 => ( ( Y
% 5.15/5.36 = ( some_num @ B6 ) )
% 5.15/5.36 => ( P @ X @ Y ) ) )
% 5.15/5.36 => ( P @ X @ Y ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % combine_options_cases
% 5.15/5.36 thf(fact_1554_split__option__all,axiom,
% 5.15/5.36 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.15/5.36 ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.15/5.36 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.15/5.36 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.15/5.36 & ! [X2: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % split_option_all
% 5.15/5.36 thf(fact_1555_split__option__all,axiom,
% 5.15/5.36 ( ( ^ [P3: option_nat > $o] :
% 5.15/5.36 ! [X6: option_nat] : ( P3 @ X6 ) )
% 5.15/5.36 = ( ^ [P4: option_nat > $o] :
% 5.15/5.36 ( ( P4 @ none_nat )
% 5.15/5.36 & ! [X2: nat] : ( P4 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % split_option_all
% 5.15/5.36 thf(fact_1556_split__option__all,axiom,
% 5.15/5.36 ( ( ^ [P3: option_num > $o] :
% 5.15/5.36 ! [X6: option_num] : ( P3 @ X6 ) )
% 5.15/5.36 = ( ^ [P4: option_num > $o] :
% 5.15/5.36 ( ( P4 @ none_num )
% 5.15/5.36 & ! [X2: num] : ( P4 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % split_option_all
% 5.15/5.36 thf(fact_1557_split__option__ex,axiom,
% 5.15/5.36 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.15/5.36 ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.15/5.36 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.15/5.36 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.15/5.36 | ? [X2: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % split_option_ex
% 5.15/5.36 thf(fact_1558_split__option__ex,axiom,
% 5.15/5.36 ( ( ^ [P3: option_nat > $o] :
% 5.15/5.36 ? [X6: option_nat] : ( P3 @ X6 ) )
% 5.15/5.36 = ( ^ [P4: option_nat > $o] :
% 5.15/5.36 ( ( P4 @ none_nat )
% 5.15/5.36 | ? [X2: nat] : ( P4 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % split_option_ex
% 5.15/5.36 thf(fact_1559_split__option__ex,axiom,
% 5.15/5.36 ( ( ^ [P3: option_num > $o] :
% 5.15/5.36 ? [X6: option_num] : ( P3 @ X6 ) )
% 5.15/5.36 = ( ^ [P4: option_num > $o] :
% 5.15/5.36 ( ( P4 @ none_num )
% 5.15/5.36 | ? [X2: num] : ( P4 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % split_option_ex
% 5.15/5.36 thf(fact_1560_option_Oexhaust,axiom,
% 5.15/5.36 ! [Y: option4927543243414619207at_nat] :
% 5.15/5.36 ( ( Y != none_P5556105721700978146at_nat )
% 5.15/5.36 => ~ ! [X23: product_prod_nat_nat] :
% 5.15/5.36 ( Y
% 5.15/5.36 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.exhaust
% 5.15/5.36 thf(fact_1561_option_Oexhaust,axiom,
% 5.15/5.36 ! [Y: option_nat] :
% 5.15/5.36 ( ( Y != none_nat )
% 5.15/5.36 => ~ ! [X23: nat] :
% 5.15/5.36 ( Y
% 5.15/5.36 != ( some_nat @ X23 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.exhaust
% 5.15/5.36 thf(fact_1562_option_Oexhaust,axiom,
% 5.15/5.36 ! [Y: option_num] :
% 5.15/5.36 ( ( Y != none_num )
% 5.15/5.36 => ~ ! [X23: num] :
% 5.15/5.36 ( Y
% 5.15/5.36 != ( some_num @ X23 ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.exhaust
% 5.15/5.36 thf(fact_1563_option_OdiscI,axiom,
% 5.15/5.36 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.15/5.36 ( ( Option
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.15/5.36 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.discI
% 5.15/5.36 thf(fact_1564_option_OdiscI,axiom,
% 5.15/5.36 ! [Option: option_nat,X22: nat] :
% 5.15/5.36 ( ( Option
% 5.15/5.36 = ( some_nat @ X22 ) )
% 5.15/5.36 => ( Option != none_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.discI
% 5.15/5.36 thf(fact_1565_option_OdiscI,axiom,
% 5.15/5.36 ! [Option: option_num,X22: num] :
% 5.15/5.36 ( ( Option
% 5.15/5.36 = ( some_num @ X22 ) )
% 5.15/5.36 => ( Option != none_num ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.discI
% 5.15/5.36 thf(fact_1566_option_Odistinct_I1_J,axiom,
% 5.15/5.36 ! [X22: product_prod_nat_nat] :
% 5.15/5.36 ( none_P5556105721700978146at_nat
% 5.15/5.36 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.distinct(1)
% 5.15/5.36 thf(fact_1567_option_Odistinct_I1_J,axiom,
% 5.15/5.36 ! [X22: nat] :
% 5.15/5.36 ( none_nat
% 5.15/5.36 != ( some_nat @ X22 ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.distinct(1)
% 5.15/5.36 thf(fact_1568_option_Odistinct_I1_J,axiom,
% 5.15/5.36 ! [X22: num] :
% 5.15/5.36 ( none_num
% 5.15/5.36 != ( some_num @ X22 ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.distinct(1)
% 5.15/5.36 thf(fact_1569_option_Osel,axiom,
% 5.15/5.36 ! [X22: product_prod_nat_nat] :
% 5.15/5.36 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.15/5.36 = X22 ) ).
% 5.15/5.36
% 5.15/5.36 % option.sel
% 5.15/5.36 thf(fact_1570_option_Osel,axiom,
% 5.15/5.36 ! [X22: nat] :
% 5.15/5.36 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.15/5.36 = X22 ) ).
% 5.15/5.36
% 5.15/5.36 % option.sel
% 5.15/5.36 thf(fact_1571_option_Osel,axiom,
% 5.15/5.36 ! [X22: num] :
% 5.15/5.36 ( ( the_num @ ( some_num @ X22 ) )
% 5.15/5.36 = X22 ) ).
% 5.15/5.36
% 5.15/5.36 % option.sel
% 5.15/5.36 thf(fact_1572_option_Oexhaust__sel,axiom,
% 5.15/5.36 ! [Option: option4927543243414619207at_nat] :
% 5.15/5.36 ( ( Option != none_P5556105721700978146at_nat )
% 5.15/5.36 => ( Option
% 5.15/5.36 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.exhaust_sel
% 5.15/5.36 thf(fact_1573_option_Oexhaust__sel,axiom,
% 5.15/5.36 ! [Option: option_nat] :
% 5.15/5.36 ( ( Option != none_nat )
% 5.15/5.36 => ( Option
% 5.15/5.36 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.exhaust_sel
% 5.15/5.36 thf(fact_1574_option_Oexhaust__sel,axiom,
% 5.15/5.36 ! [Option: option_num] :
% 5.15/5.36 ( ( Option != none_num )
% 5.15/5.36 => ( Option
% 5.15/5.36 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % option.exhaust_sel
% 5.15/5.36 thf(fact_1575_succ__list__to__short,axiom,
% 5.15/5.36 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.36 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.15/5.36 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.36 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = none_nat ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % succ_list_to_short
% 5.15/5.36 thf(fact_1576_pred__list__to__short,axiom,
% 5.15/5.36 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.36 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.15/5.36 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.36 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = none_nat ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pred_list_to_short
% 5.15/5.36 thf(fact_1577_succ__min,axiom,
% 5.15/5.36 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.36 => ( ( ord_less_nat @ X @ Mi )
% 5.15/5.36 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = ( some_nat @ Mi ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % succ_min
% 5.15/5.36 thf(fact_1578_pred__max,axiom,
% 5.15/5.36 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.36 => ( ( ord_less_nat @ Ma @ X )
% 5.15/5.36 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = ( some_nat @ Ma ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pred_max
% 5.15/5.36 thf(fact_1579_less__shift,axiom,
% 5.15/5.36 ( ord_less_nat
% 5.15/5.36 = ( ^ [X2: nat,Y2: nat] : ( vEBT_VEBT_less @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % less_shift
% 5.15/5.36 thf(fact_1580_greater__shift,axiom,
% 5.15/5.36 ( ord_less_nat
% 5.15/5.36 = ( ^ [Y2: nat,X2: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % greater_shift
% 5.15/5.36 thf(fact_1581_helpypredd,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.15/5.36 = ( some_nat @ Y ) )
% 5.15/5.36 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % helpypredd
% 5.15/5.36 thf(fact_1582_helpyd,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.15/5.36 = ( some_nat @ Y ) )
% 5.15/5.36 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % helpyd
% 5.15/5.36 thf(fact_1583_pred__correct,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.15/5.36 = ( some_nat @ Sx ) )
% 5.15/5.36 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pred_correct
% 5.15/5.36 thf(fact_1584_succ__correct,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.15/5.36 = ( some_nat @ Sx ) )
% 5.15/5.36 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % succ_correct
% 5.15/5.36 thf(fact_1585_succ__corr,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.15/5.36 = ( some_nat @ Sx ) )
% 5.15/5.36 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % succ_corr
% 5.15/5.36 thf(fact_1586_pred__corr,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat,Px: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.15/5.36 = ( some_nat @ Px ) )
% 5.15/5.36 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pred_corr
% 5.15/5.36 thf(fact_1587_geqmaxNone,axiom,
% 5.15/5.36 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.15/5.36 => ( ( ord_less_eq_nat @ Ma @ X )
% 5.15/5.36 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = none_nat ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % geqmaxNone
% 5.15/5.36 thf(fact_1588_local_Opower__def,axiom,
% 5.15/5.36 ( vEBT_VEBT_power
% 5.15/5.36 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % local.power_def
% 5.15/5.36 thf(fact_1589_vebt__succ_Osimps_I3_J,axiom,
% 5.15/5.36 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.15/5.36 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.15/5.36 = none_nat ) ).
% 5.15/5.36
% 5.15/5.36 % vebt_succ.simps(3)
% 5.15/5.36 thf(fact_1590_vebt__pred_Osimps_I4_J,axiom,
% 5.15/5.36 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.15/5.36 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.15/5.36 = none_nat ) ).
% 5.15/5.36
% 5.15/5.36 % vebt_pred.simps(4)
% 5.15/5.36 thf(fact_1591_pred__less__length__list,axiom,
% 5.15/5.36 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.36 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.15/5.36 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.36 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = ( if_option_nat
% 5.15/5.36 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 != none_nat )
% 5.15/5.36 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.36 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 @ ( if_option_nat
% 5.15/5.36 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.36 = none_nat )
% 5.15/5.36 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.15/5.36 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pred_less_length_list
% 5.15/5.36 thf(fact_1592_pred__lesseq__max,axiom,
% 5.15/5.36 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.36 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.15/5.36 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.36 @ ( if_option_nat
% 5.15/5.36 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 != none_nat )
% 5.15/5.36 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.36 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 @ ( if_option_nat
% 5.15/5.36 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.36 = none_nat )
% 5.15/5.36 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.15/5.36 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.36 @ none_nat ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pred_lesseq_max
% 5.15/5.36 thf(fact_1593_succ__greatereq__min,axiom,
% 5.15/5.36 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.36 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.15/5.36 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.36 @ ( if_option_nat
% 5.15/5.36 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 != none_nat )
% 5.15/5.36 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.36 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 @ ( if_option_nat
% 5.15/5.36 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.36 = none_nat )
% 5.15/5.36 @ none_nat
% 5.15/5.36 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.36 @ none_nat ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % succ_greatereq_min
% 5.15/5.36 thf(fact_1594_succ__less__length__list,axiom,
% 5.15/5.36 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.15/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.36 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.15/5.36 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.36 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.36 = ( if_option_nat
% 5.15/5.36 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 != none_nat )
% 5.15/5.36 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.36 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 @ ( if_option_nat
% 5.15/5.36 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.36 = none_nat )
% 5.15/5.36 @ none_nat
% 5.15/5.36 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % succ_less_length_list
% 5.15/5.36 thf(fact_1595_vebt__maxt_Osimps_I3_J,axiom,
% 5.15/5.36 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.15/5.36 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.15/5.36 = ( some_nat @ Ma ) ) ).
% 5.15/5.36
% 5.15/5.36 % vebt_maxt.simps(3)
% 5.15/5.36 thf(fact_1596_vebt__mint_Osimps_I3_J,axiom,
% 5.15/5.36 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.15/5.36 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.15/5.36 = ( some_nat @ Mi ) ) ).
% 5.15/5.36
% 5.15/5.36 % vebt_mint.simps(3)
% 5.15/5.36 thf(fact_1597_pred__empty,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.15/5.36 = none_nat )
% 5.15/5.36 = ( ( collect_nat
% 5.15/5.36 @ ^ [Y2: nat] :
% 5.15/5.36 ( ( vEBT_vebt_member @ T @ Y2 )
% 5.15/5.36 & ( ord_less_nat @ Y2 @ X ) ) )
% 5.15/5.36 = bot_bot_set_nat ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % pred_empty
% 5.15/5.36 thf(fact_1598_succ__empty,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.15/5.36 = none_nat )
% 5.15/5.36 = ( ( collect_nat
% 5.15/5.36 @ ^ [Y2: nat] :
% 5.15/5.36 ( ( vEBT_vebt_member @ T @ Y2 )
% 5.15/5.36 & ( ord_less_nat @ X @ Y2 ) ) )
% 5.15/5.36 = bot_bot_set_nat ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % succ_empty
% 5.15/5.36 thf(fact_1599_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.15/5.36 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.36 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.15/5.36 => ( ! [Mi2: nat,Ma2: nat] :
% 5.15/5.36 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.15/5.36 ( X
% 5.15/5.36 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.15/5.36 => ~ ( ( Xa2 = Mi2 )
% 5.15/5.36 | ( Xa2 = Ma2 ) ) )
% 5.15/5.36 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.36 ( ? [Vc2: vEBT_VEBT] :
% 5.15/5.36 ( X
% 5.15/5.36 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.15/5.36 => ~ ( ( Xa2 = Mi2 )
% 5.15/5.36 | ( Xa2 = Ma2 )
% 5.15/5.36 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.36 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.15/5.36 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.36 ( ? [Vd2: vEBT_VEBT] :
% 5.15/5.36 ( X
% 5.15/5.36 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.15/5.36 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.36 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.36 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % VEBT_internal.membermima.elims(2)
% 5.15/5.36 thf(fact_1600_mul__shift,axiom,
% 5.15/5.36 ! [X: nat,Y: nat,Z: nat] :
% 5.15/5.36 ( ( ( times_times_nat @ X @ Y )
% 5.15/5.36 = Z )
% 5.15/5.36 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.15/5.36 = ( some_nat @ Z ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mul_shift
% 5.15/5.36 thf(fact_1601_valid__0__not,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT] :
% 5.15/5.36 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.15/5.36
% 5.15/5.36 % valid_0_not
% 5.15/5.36 thf(fact_1602_valid__tree__deg__neq__0,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT] :
% 5.15/5.36 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.15/5.36
% 5.15/5.36 % valid_tree_deg_neq_0
% 5.15/5.36 thf(fact_1603_deg__not__0,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % deg_not_0
% 5.15/5.36 thf(fact_1604_add__shift,axiom,
% 5.15/5.36 ! [X: nat,Y: nat,Z: nat] :
% 5.15/5.36 ( ( ( plus_plus_nat @ X @ Y )
% 5.15/5.36 = Z )
% 5.15/5.36 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.15/5.36 = ( some_nat @ Z ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % add_shift
% 5.15/5.36 thf(fact_1605_buildup__gives__empty,axiom,
% 5.15/5.36 ! [N2: nat] :
% 5.15/5.36 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N2 ) )
% 5.15/5.36 = bot_bot_set_nat ) ).
% 5.15/5.36
% 5.15/5.36 % buildup_gives_empty
% 5.15/5.36 thf(fact_1606_add__def,axiom,
% 5.15/5.36 ( vEBT_VEBT_add
% 5.15/5.36 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % add_def
% 5.15/5.36 thf(fact_1607_mul__def,axiom,
% 5.15/5.36 ( vEBT_VEBT_mul
% 5.15/5.36 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % mul_def
% 5.15/5.36 thf(fact_1608_buildup__gives__valid,axiom,
% 5.15/5.36 ! [N2: nat] :
% 5.15/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.36 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 5.15/5.36
% 5.15/5.36 % buildup_gives_valid
% 5.15/5.36 thf(fact_1609_mint__corr__help__empty,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_mint @ T )
% 5.15/5.36 = none_nat )
% 5.15/5.36 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.15/5.36 = bot_bot_set_nat ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mint_corr_help_empty
% 5.15/5.36 thf(fact_1610_maxt__corr__help__empty,axiom,
% 5.15/5.36 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.36 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.36 => ( ( ( vEBT_vebt_maxt @ T )
% 5.15/5.36 = none_nat )
% 5.15/5.36 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.15/5.36 = bot_bot_set_nat ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % maxt_corr_help_empty
% 5.15/5.36 thf(fact_1611_le__zero__eq,axiom,
% 5.15/5.36 ! [N2: nat] :
% 5.15/5.36 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.15/5.36 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % le_zero_eq
% 5.15/5.36 thf(fact_1612_not__gr__zero,axiom,
% 5.15/5.36 ! [N2: nat] :
% 5.15/5.36 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.36 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.36
% 5.15/5.36 % not_gr_zero
% 5.15/5.36 thf(fact_1613_mult__cancel__right,axiom,
% 5.15/5.36 ! [A: complex,C: complex,B: complex] :
% 5.15/5.36 ( ( ( times_times_complex @ A @ C )
% 5.15/5.36 = ( times_times_complex @ B @ C ) )
% 5.15/5.36 = ( ( C = zero_zero_complex )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_right
% 5.15/5.36 thf(fact_1614_mult__cancel__right,axiom,
% 5.15/5.36 ! [A: real,C: real,B: real] :
% 5.15/5.36 ( ( ( times_times_real @ A @ C )
% 5.15/5.36 = ( times_times_real @ B @ C ) )
% 5.15/5.36 = ( ( C = zero_zero_real )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_right
% 5.15/5.36 thf(fact_1615_mult__cancel__right,axiom,
% 5.15/5.36 ! [A: rat,C: rat,B: rat] :
% 5.15/5.36 ( ( ( times_times_rat @ A @ C )
% 5.15/5.36 = ( times_times_rat @ B @ C ) )
% 5.15/5.36 = ( ( C = zero_zero_rat )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_right
% 5.15/5.36 thf(fact_1616_mult__cancel__right,axiom,
% 5.15/5.36 ! [A: nat,C: nat,B: nat] :
% 5.15/5.36 ( ( ( times_times_nat @ A @ C )
% 5.15/5.36 = ( times_times_nat @ B @ C ) )
% 5.15/5.36 = ( ( C = zero_zero_nat )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_right
% 5.15/5.36 thf(fact_1617_mult__cancel__right,axiom,
% 5.15/5.36 ! [A: int,C: int,B: int] :
% 5.15/5.36 ( ( ( times_times_int @ A @ C )
% 5.15/5.36 = ( times_times_int @ B @ C ) )
% 5.15/5.36 = ( ( C = zero_zero_int )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_right
% 5.15/5.36 thf(fact_1618_mult__cancel__left,axiom,
% 5.15/5.36 ! [C: complex,A: complex,B: complex] :
% 5.15/5.36 ( ( ( times_times_complex @ C @ A )
% 5.15/5.36 = ( times_times_complex @ C @ B ) )
% 5.15/5.36 = ( ( C = zero_zero_complex )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_left
% 5.15/5.36 thf(fact_1619_mult__cancel__left,axiom,
% 5.15/5.36 ! [C: real,A: real,B: real] :
% 5.15/5.36 ( ( ( times_times_real @ C @ A )
% 5.15/5.36 = ( times_times_real @ C @ B ) )
% 5.15/5.36 = ( ( C = zero_zero_real )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_left
% 5.15/5.36 thf(fact_1620_mult__cancel__left,axiom,
% 5.15/5.36 ! [C: rat,A: rat,B: rat] :
% 5.15/5.36 ( ( ( times_times_rat @ C @ A )
% 5.15/5.36 = ( times_times_rat @ C @ B ) )
% 5.15/5.36 = ( ( C = zero_zero_rat )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_left
% 5.15/5.36 thf(fact_1621_mult__cancel__left,axiom,
% 5.15/5.36 ! [C: nat,A: nat,B: nat] :
% 5.15/5.36 ( ( ( times_times_nat @ C @ A )
% 5.15/5.36 = ( times_times_nat @ C @ B ) )
% 5.15/5.36 = ( ( C = zero_zero_nat )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_left
% 5.15/5.36 thf(fact_1622_mult__cancel__left,axiom,
% 5.15/5.36 ! [C: int,A: int,B: int] :
% 5.15/5.36 ( ( ( times_times_int @ C @ A )
% 5.15/5.36 = ( times_times_int @ C @ B ) )
% 5.15/5.36 = ( ( C = zero_zero_int )
% 5.15/5.36 | ( A = B ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_cancel_left
% 5.15/5.36 thf(fact_1623_mult__eq__0__iff,axiom,
% 5.15/5.36 ! [A: complex,B: complex] :
% 5.15/5.36 ( ( ( times_times_complex @ A @ B )
% 5.15/5.36 = zero_zero_complex )
% 5.15/5.36 = ( ( A = zero_zero_complex )
% 5.15/5.36 | ( B = zero_zero_complex ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_eq_0_iff
% 5.15/5.36 thf(fact_1624_mult__eq__0__iff,axiom,
% 5.15/5.36 ! [A: real,B: real] :
% 5.15/5.36 ( ( ( times_times_real @ A @ B )
% 5.15/5.36 = zero_zero_real )
% 5.15/5.36 = ( ( A = zero_zero_real )
% 5.15/5.36 | ( B = zero_zero_real ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_eq_0_iff
% 5.15/5.36 thf(fact_1625_mult__eq__0__iff,axiom,
% 5.15/5.36 ! [A: rat,B: rat] :
% 5.15/5.36 ( ( ( times_times_rat @ A @ B )
% 5.15/5.36 = zero_zero_rat )
% 5.15/5.36 = ( ( A = zero_zero_rat )
% 5.15/5.36 | ( B = zero_zero_rat ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_eq_0_iff
% 5.15/5.36 thf(fact_1626_mult__eq__0__iff,axiom,
% 5.15/5.36 ! [A: nat,B: nat] :
% 5.15/5.36 ( ( ( times_times_nat @ A @ B )
% 5.15/5.36 = zero_zero_nat )
% 5.15/5.36 = ( ( A = zero_zero_nat )
% 5.15/5.36 | ( B = zero_zero_nat ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_eq_0_iff
% 5.15/5.36 thf(fact_1627_mult__eq__0__iff,axiom,
% 5.15/5.36 ! [A: int,B: int] :
% 5.15/5.36 ( ( ( times_times_int @ A @ B )
% 5.15/5.36 = zero_zero_int )
% 5.15/5.36 = ( ( A = zero_zero_int )
% 5.15/5.36 | ( B = zero_zero_int ) ) ) ).
% 5.15/5.36
% 5.15/5.36 % mult_eq_0_iff
% 5.15/5.36 thf(fact_1628_mult__zero__right,axiom,
% 5.15/5.36 ! [A: complex] :
% 5.15/5.36 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.15/5.36 = zero_zero_complex ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_right
% 5.15/5.36 thf(fact_1629_mult__zero__right,axiom,
% 5.15/5.36 ! [A: real] :
% 5.15/5.36 ( ( times_times_real @ A @ zero_zero_real )
% 5.15/5.36 = zero_zero_real ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_right
% 5.15/5.36 thf(fact_1630_mult__zero__right,axiom,
% 5.15/5.36 ! [A: rat] :
% 5.15/5.36 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.15/5.36 = zero_zero_rat ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_right
% 5.15/5.36 thf(fact_1631_mult__zero__right,axiom,
% 5.15/5.36 ! [A: nat] :
% 5.15/5.36 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.15/5.36 = zero_zero_nat ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_right
% 5.15/5.36 thf(fact_1632_mult__zero__right,axiom,
% 5.15/5.36 ! [A: int] :
% 5.15/5.36 ( ( times_times_int @ A @ zero_zero_int )
% 5.15/5.36 = zero_zero_int ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_right
% 5.15/5.36 thf(fact_1633_mult__zero__left,axiom,
% 5.15/5.36 ! [A: complex] :
% 5.15/5.36 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.15/5.36 = zero_zero_complex ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_left
% 5.15/5.36 thf(fact_1634_mult__zero__left,axiom,
% 5.15/5.36 ! [A: real] :
% 5.15/5.36 ( ( times_times_real @ zero_zero_real @ A )
% 5.15/5.36 = zero_zero_real ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_left
% 5.15/5.36 thf(fact_1635_mult__zero__left,axiom,
% 5.15/5.36 ! [A: rat] :
% 5.15/5.36 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.15/5.36 = zero_zero_rat ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_left
% 5.15/5.36 thf(fact_1636_mult__zero__left,axiom,
% 5.15/5.36 ! [A: nat] :
% 5.15/5.36 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.15/5.36 = zero_zero_nat ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_left
% 5.15/5.36 thf(fact_1637_mult__zero__left,axiom,
% 5.15/5.36 ! [A: int] :
% 5.15/5.36 ( ( times_times_int @ zero_zero_int @ A )
% 5.15/5.36 = zero_zero_int ) ).
% 5.15/5.36
% 5.15/5.36 % mult_zero_left
% 5.15/5.36 thf(fact_1638_add__0,axiom,
% 5.15/5.36 ! [A: complex] :
% 5.15/5.36 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.15/5.36 = A ) ).
% 5.15/5.36
% 5.15/5.36 % add_0
% 5.15/5.36 thf(fact_1639_add__0,axiom,
% 5.15/5.36 ! [A: real] :
% 5.15/5.37 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add_0
% 5.15/5.37 thf(fact_1640_add__0,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add_0
% 5.15/5.37 thf(fact_1641_add__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add_0
% 5.15/5.37 thf(fact_1642_add__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add_0
% 5.15/5.37 thf(fact_1643_zero__eq__add__iff__both__eq__0,axiom,
% 5.15/5.37 ! [X: nat,Y: nat] :
% 5.15/5.37 ( ( zero_zero_nat
% 5.15/5.37 = ( plus_plus_nat @ X @ Y ) )
% 5.15/5.37 = ( ( X = zero_zero_nat )
% 5.15/5.37 & ( Y = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_eq_add_iff_both_eq_0
% 5.15/5.37 thf(fact_1644_add__eq__0__iff__both__eq__0,axiom,
% 5.15/5.37 ! [X: nat,Y: nat] :
% 5.15/5.37 ( ( ( plus_plus_nat @ X @ Y )
% 5.15/5.37 = zero_zero_nat )
% 5.15/5.37 = ( ( X = zero_zero_nat )
% 5.15/5.37 & ( Y = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_eq_0_iff_both_eq_0
% 5.15/5.37 thf(fact_1645_add__cancel__right__right,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_complex @ A @ B ) )
% 5.15/5.37 = ( B = zero_zero_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_right
% 5.15/5.37 thf(fact_1646_add__cancel__right__right,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_real @ A @ B ) )
% 5.15/5.37 = ( B = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_right
% 5.15/5.37 thf(fact_1647_add__cancel__right__right,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_rat @ A @ B ) )
% 5.15/5.37 = ( B = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_right
% 5.15/5.37 thf(fact_1648_add__cancel__right__right,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_nat @ A @ B ) )
% 5.15/5.37 = ( B = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_right
% 5.15/5.37 thf(fact_1649_add__cancel__right__right,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_int @ A @ B ) )
% 5.15/5.37 = ( B = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_right
% 5.15/5.37 thf(fact_1650_add__cancel__right__left,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_complex @ B @ A ) )
% 5.15/5.37 = ( B = zero_zero_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_left
% 5.15/5.37 thf(fact_1651_add__cancel__right__left,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_real @ B @ A ) )
% 5.15/5.37 = ( B = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_left
% 5.15/5.37 thf(fact_1652_add__cancel__right__left,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_rat @ B @ A ) )
% 5.15/5.37 = ( B = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_left
% 5.15/5.37 thf(fact_1653_add__cancel__right__left,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_nat @ B @ A ) )
% 5.15/5.37 = ( B = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_left
% 5.15/5.37 thf(fact_1654_add__cancel__right__left,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( plus_plus_int @ B @ A ) )
% 5.15/5.37 = ( B = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_right_left
% 5.15/5.37 thf(fact_1655_add__cancel__left__right,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( ( plus_plus_complex @ A @ B )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_right
% 5.15/5.37 thf(fact_1656_add__cancel__left__right,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ( plus_plus_real @ A @ B )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_right
% 5.15/5.37 thf(fact_1657_add__cancel__left__right,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ( plus_plus_rat @ A @ B )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_right
% 5.15/5.37 thf(fact_1658_add__cancel__left__right,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ( plus_plus_nat @ A @ B )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_right
% 5.15/5.37 thf(fact_1659_add__cancel__left__right,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ( plus_plus_int @ A @ B )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_right
% 5.15/5.37 thf(fact_1660_add__cancel__left__left,axiom,
% 5.15/5.37 ! [B: complex,A: complex] :
% 5.15/5.37 ( ( ( plus_plus_complex @ B @ A )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_left
% 5.15/5.37 thf(fact_1661_add__cancel__left__left,axiom,
% 5.15/5.37 ! [B: real,A: real] :
% 5.15/5.37 ( ( ( plus_plus_real @ B @ A )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_left
% 5.15/5.37 thf(fact_1662_add__cancel__left__left,axiom,
% 5.15/5.37 ! [B: rat,A: rat] :
% 5.15/5.37 ( ( ( plus_plus_rat @ B @ A )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_left
% 5.15/5.37 thf(fact_1663_add__cancel__left__left,axiom,
% 5.15/5.37 ! [B: nat,A: nat] :
% 5.15/5.37 ( ( ( plus_plus_nat @ B @ A )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_left
% 5.15/5.37 thf(fact_1664_add__cancel__left__left,axiom,
% 5.15/5.37 ! [B: int,A: int] :
% 5.15/5.37 ( ( ( plus_plus_int @ B @ A )
% 5.15/5.37 = A )
% 5.15/5.37 = ( B = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_cancel_left_left
% 5.15/5.37 thf(fact_1665_double__zero__sym,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( zero_zero_real
% 5.15/5.37 = ( plus_plus_real @ A @ A ) )
% 5.15/5.37 = ( A = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_zero_sym
% 5.15/5.37 thf(fact_1666_double__zero__sym,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( zero_zero_rat
% 5.15/5.37 = ( plus_plus_rat @ A @ A ) )
% 5.15/5.37 = ( A = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_zero_sym
% 5.15/5.37 thf(fact_1667_double__zero__sym,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( zero_zero_int
% 5.15/5.37 = ( plus_plus_int @ A @ A ) )
% 5.15/5.37 = ( A = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_zero_sym
% 5.15/5.37 thf(fact_1668_add_Oright__neutral,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.right_neutral
% 5.15/5.37 thf(fact_1669_add_Oright__neutral,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.right_neutral
% 5.15/5.37 thf(fact_1670_add_Oright__neutral,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.right_neutral
% 5.15/5.37 thf(fact_1671_add_Oright__neutral,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.right_neutral
% 5.15/5.37 thf(fact_1672_add_Oright__neutral,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.right_neutral
% 5.15/5.37 thf(fact_1673_diff__self,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( minus_minus_complex @ A @ A )
% 5.15/5.37 = zero_zero_complex ) ).
% 5.15/5.37
% 5.15/5.37 % diff_self
% 5.15/5.37 thf(fact_1674_diff__self,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( minus_minus_real @ A @ A )
% 5.15/5.37 = zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % diff_self
% 5.15/5.37 thf(fact_1675_diff__self,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( minus_minus_rat @ A @ A )
% 5.15/5.37 = zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % diff_self
% 5.15/5.37 thf(fact_1676_diff__self,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( minus_minus_int @ A @ A )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % diff_self
% 5.15/5.37 thf(fact_1677_diff__0__right,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_0_right
% 5.15/5.37 thf(fact_1678_diff__0__right,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_0_right
% 5.15/5.37 thf(fact_1679_diff__0__right,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_0_right
% 5.15/5.37 thf(fact_1680_diff__0__right,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_0_right
% 5.15/5.37 thf(fact_1681_zero__diff,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % zero_diff
% 5.15/5.37 thf(fact_1682_diff__zero,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_zero
% 5.15/5.37 thf(fact_1683_diff__zero,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_zero
% 5.15/5.37 thf(fact_1684_diff__zero,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_zero
% 5.15/5.37 thf(fact_1685_diff__zero,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_zero
% 5.15/5.37 thf(fact_1686_diff__zero,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % diff_zero
% 5.15/5.37 thf(fact_1687_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( minus_minus_complex @ A @ A )
% 5.15/5.37 = zero_zero_complex ) ).
% 5.15/5.37
% 5.15/5.37 % cancel_comm_monoid_add_class.diff_cancel
% 5.15/5.37 thf(fact_1688_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( minus_minus_real @ A @ A )
% 5.15/5.37 = zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % cancel_comm_monoid_add_class.diff_cancel
% 5.15/5.37 thf(fact_1689_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( minus_minus_rat @ A @ A )
% 5.15/5.37 = zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % cancel_comm_monoid_add_class.diff_cancel
% 5.15/5.37 thf(fact_1690_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( minus_minus_nat @ A @ A )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % cancel_comm_monoid_add_class.diff_cancel
% 5.15/5.37 thf(fact_1691_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( minus_minus_int @ A @ A )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % cancel_comm_monoid_add_class.diff_cancel
% 5.15/5.37 thf(fact_1692_division__ring__divide__zero,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.15/5.37 = zero_zero_complex ) ).
% 5.15/5.37
% 5.15/5.37 % division_ring_divide_zero
% 5.15/5.37 thf(fact_1693_division__ring__divide__zero,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.15/5.37 = zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % division_ring_divide_zero
% 5.15/5.37 thf(fact_1694_division__ring__divide__zero,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.15/5.37 = zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % division_ring_divide_zero
% 5.15/5.37 thf(fact_1695_divide__cancel__right,axiom,
% 5.15/5.37 ! [A: complex,C: complex,B: complex] :
% 5.15/5.37 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.15/5.37 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.37 = ( ( C = zero_zero_complex )
% 5.15/5.37 | ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_cancel_right
% 5.15/5.37 thf(fact_1696_divide__cancel__right,axiom,
% 5.15/5.37 ! [A: real,C: real,B: real] :
% 5.15/5.37 ( ( ( divide_divide_real @ A @ C )
% 5.15/5.37 = ( divide_divide_real @ B @ C ) )
% 5.15/5.37 = ( ( C = zero_zero_real )
% 5.15/5.37 | ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_cancel_right
% 5.15/5.37 thf(fact_1697_divide__cancel__right,axiom,
% 5.15/5.37 ! [A: rat,C: rat,B: rat] :
% 5.15/5.37 ( ( ( divide_divide_rat @ A @ C )
% 5.15/5.37 = ( divide_divide_rat @ B @ C ) )
% 5.15/5.37 = ( ( C = zero_zero_rat )
% 5.15/5.37 | ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_cancel_right
% 5.15/5.37 thf(fact_1698_divide__cancel__left,axiom,
% 5.15/5.37 ! [C: complex,A: complex,B: complex] :
% 5.15/5.37 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.15/5.37 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.15/5.37 = ( ( C = zero_zero_complex )
% 5.15/5.37 | ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_cancel_left
% 5.15/5.37 thf(fact_1699_divide__cancel__left,axiom,
% 5.15/5.37 ! [C: real,A: real,B: real] :
% 5.15/5.37 ( ( ( divide_divide_real @ C @ A )
% 5.15/5.37 = ( divide_divide_real @ C @ B ) )
% 5.15/5.37 = ( ( C = zero_zero_real )
% 5.15/5.37 | ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_cancel_left
% 5.15/5.37 thf(fact_1700_divide__cancel__left,axiom,
% 5.15/5.37 ! [C: rat,A: rat,B: rat] :
% 5.15/5.37 ( ( ( divide_divide_rat @ C @ A )
% 5.15/5.37 = ( divide_divide_rat @ C @ B ) )
% 5.15/5.37 = ( ( C = zero_zero_rat )
% 5.15/5.37 | ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_cancel_left
% 5.15/5.37 thf(fact_1701_divide__eq__0__iff,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.15/5.37 = zero_zero_complex )
% 5.15/5.37 = ( ( A = zero_zero_complex )
% 5.15/5.37 | ( B = zero_zero_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_0_iff
% 5.15/5.37 thf(fact_1702_divide__eq__0__iff,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ( divide_divide_real @ A @ B )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 = ( ( A = zero_zero_real )
% 5.15/5.37 | ( B = zero_zero_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_0_iff
% 5.15/5.37 thf(fact_1703_divide__eq__0__iff,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ( divide_divide_rat @ A @ B )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 = ( ( A = zero_zero_rat )
% 5.15/5.37 | ( B = zero_zero_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_0_iff
% 5.15/5.37 thf(fact_1704_bits__div__by__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % bits_div_by_0
% 5.15/5.37 thf(fact_1705_bits__div__by__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % bits_div_by_0
% 5.15/5.37 thf(fact_1706_bits__div__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % bits_div_0
% 5.15/5.37 thf(fact_1707_bits__div__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % bits_div_0
% 5.15/5.37 thf(fact_1708_div__by__0,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.15/5.37 = zero_zero_complex ) ).
% 5.15/5.37
% 5.15/5.37 % div_by_0
% 5.15/5.37 thf(fact_1709_div__by__0,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.15/5.37 = zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % div_by_0
% 5.15/5.37 thf(fact_1710_div__by__0,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.15/5.37 = zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % div_by_0
% 5.15/5.37 thf(fact_1711_div__by__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % div_by_0
% 5.15/5.37 thf(fact_1712_div__by__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % div_by_0
% 5.15/5.37 thf(fact_1713_div__0,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.15/5.37 = zero_zero_complex ) ).
% 5.15/5.37
% 5.15/5.37 % div_0
% 5.15/5.37 thf(fact_1714_div__0,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.15/5.37 = zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % div_0
% 5.15/5.37 thf(fact_1715_div__0,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.15/5.37 = zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % div_0
% 5.15/5.37 thf(fact_1716_div__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % div_0
% 5.15/5.37 thf(fact_1717_div__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % div_0
% 5.15/5.37 thf(fact_1718_mod__self,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ A @ A )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % mod_self
% 5.15/5.37 thf(fact_1719_mod__self,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( modulo_modulo_int @ A @ A )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % mod_self
% 5.15/5.37 thf(fact_1720_mod__self,axiom,
% 5.15/5.37 ! [A: code_integer] :
% 5.15/5.37 ( ( modulo364778990260209775nteger @ A @ A )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % mod_self
% 5.15/5.37 thf(fact_1721_mod__by__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % mod_by_0
% 5.15/5.37 thf(fact_1722_mod__by__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % mod_by_0
% 5.15/5.37 thf(fact_1723_mod__by__0,axiom,
% 5.15/5.37 ! [A: code_integer] :
% 5.15/5.37 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % mod_by_0
% 5.15/5.37 thf(fact_1724_mod__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % mod_0
% 5.15/5.37 thf(fact_1725_mod__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % mod_0
% 5.15/5.37 thf(fact_1726_mod__0,axiom,
% 5.15/5.37 ! [A: code_integer] :
% 5.15/5.37 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % mod_0
% 5.15/5.37 thf(fact_1727_bits__mod__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_0
% 5.15/5.37 thf(fact_1728_bits__mod__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_0
% 5.15/5.37 thf(fact_1729_bits__mod__0,axiom,
% 5.15/5.37 ! [A: code_integer] :
% 5.15/5.37 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_0
% 5.15/5.37 thf(fact_1730_less__nat__zero__code,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % less_nat_zero_code
% 5.15/5.37 thf(fact_1731_neq0__conv,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( N2 != zero_zero_nat )
% 5.15/5.37 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % neq0_conv
% 5.15/5.37 thf(fact_1732_bot__nat__0_Onot__eq__extremum,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( A != zero_zero_nat )
% 5.15/5.37 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % bot_nat_0.not_eq_extremum
% 5.15/5.37 thf(fact_1733_bot__nat__0_Oextremum,axiom,
% 5.15/5.37 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.15/5.37
% 5.15/5.37 % bot_nat_0.extremum
% 5.15/5.37 thf(fact_1734_le0,axiom,
% 5.15/5.37 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.15/5.37
% 5.15/5.37 % le0
% 5.15/5.37 thf(fact_1735_Nat_Oadd__0__right,axiom,
% 5.15/5.37 ! [M: nat] :
% 5.15/5.37 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.15/5.37 = M ) ).
% 5.15/5.37
% 5.15/5.37 % Nat.add_0_right
% 5.15/5.37 thf(fact_1736_add__is__0,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ( plus_plus_nat @ M @ N2 )
% 5.15/5.37 = zero_zero_nat )
% 5.15/5.37 = ( ( M = zero_zero_nat )
% 5.15/5.37 & ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_is_0
% 5.15/5.37 thf(fact_1737_diff__0__eq__0,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % diff_0_eq_0
% 5.15/5.37 thf(fact_1738_diff__self__eq__0,axiom,
% 5.15/5.37 ! [M: nat] :
% 5.15/5.37 ( ( minus_minus_nat @ M @ M )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % diff_self_eq_0
% 5.15/5.37 thf(fact_1739_mult__cancel2,axiom,
% 5.15/5.37 ! [M: nat,K: nat,N2: nat] :
% 5.15/5.37 ( ( ( times_times_nat @ M @ K )
% 5.15/5.37 = ( times_times_nat @ N2 @ K ) )
% 5.15/5.37 = ( ( M = N2 )
% 5.15/5.37 | ( K = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel2
% 5.15/5.37 thf(fact_1740_mult__cancel1,axiom,
% 5.15/5.37 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.37 ( ( ( times_times_nat @ K @ M )
% 5.15/5.37 = ( times_times_nat @ K @ N2 ) )
% 5.15/5.37 = ( ( M = N2 )
% 5.15/5.37 | ( K = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel1
% 5.15/5.37 thf(fact_1741_mult__0__right,axiom,
% 5.15/5.37 ! [M: nat] :
% 5.15/5.37 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % mult_0_right
% 5.15/5.37 thf(fact_1742_mult__is__0,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ( times_times_nat @ M @ N2 )
% 5.15/5.37 = zero_zero_nat )
% 5.15/5.37 = ( ( M = zero_zero_nat )
% 5.15/5.37 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_is_0
% 5.15/5.37 thf(fact_1743_add__le__same__cancel1,axiom,
% 5.15/5.37 ! [B: real,A: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.15/5.37 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_le_same_cancel1
% 5.15/5.37 thf(fact_1744_add__le__same__cancel1,axiom,
% 5.15/5.37 ! [B: rat,A: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.15/5.37 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_le_same_cancel1
% 5.15/5.37 thf(fact_1745_add__le__same__cancel1,axiom,
% 5.15/5.37 ! [B: nat,A: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.15/5.37 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_le_same_cancel1
% 5.15/5.37 thf(fact_1746_add__le__same__cancel1,axiom,
% 5.15/5.37 ! [B: int,A: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.15/5.37 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_le_same_cancel1
% 5.15/5.37 thf(fact_1747_add__le__same__cancel2,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.15/5.37 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_le_same_cancel2
% 5.15/5.37 thf(fact_1748_add__le__same__cancel2,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.15/5.37 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_le_same_cancel2
% 5.15/5.37 thf(fact_1749_add__le__same__cancel2,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.15/5.37 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_le_same_cancel2
% 5.15/5.37 thf(fact_1750_add__le__same__cancel2,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.15/5.37 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_le_same_cancel2
% 5.15/5.37 thf(fact_1751_le__add__same__cancel1,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.15/5.37 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_add_same_cancel1
% 5.15/5.37 thf(fact_1752_le__add__same__cancel1,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.15/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_add_same_cancel1
% 5.15/5.37 thf(fact_1753_le__add__same__cancel1,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.15/5.37 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_add_same_cancel1
% 5.15/5.37 thf(fact_1754_le__add__same__cancel1,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.15/5.37 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_add_same_cancel1
% 5.15/5.37 thf(fact_1755_le__add__same__cancel2,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.15/5.37 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_add_same_cancel2
% 5.15/5.37 thf(fact_1756_le__add__same__cancel2,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.15/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_add_same_cancel2
% 5.15/5.37 thf(fact_1757_le__add__same__cancel2,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.15/5.37 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_add_same_cancel2
% 5.15/5.37 thf(fact_1758_le__add__same__cancel2,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.15/5.37 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_add_same_cancel2
% 5.15/5.37 thf(fact_1759_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.15/5.37 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_add_le_zero_iff_single_add_le_zero
% 5.15/5.37 thf(fact_1760_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.15/5.37 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_add_le_zero_iff_single_add_le_zero
% 5.15/5.37 thf(fact_1761_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.15/5.37 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_add_le_zero_iff_single_add_le_zero
% 5.15/5.37 thf(fact_1762_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.15/5.37 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_le_double_add_iff_zero_le_single_add
% 5.15/5.37 thf(fact_1763_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.15/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_le_double_add_iff_zero_le_single_add
% 5.15/5.37 thf(fact_1764_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.15/5.37 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_le_double_add_iff_zero_le_single_add
% 5.15/5.37 thf(fact_1765_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.15/5.37 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_double_add_iff_zero_less_single_add
% 5.15/5.37 thf(fact_1766_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.15/5.37 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_double_add_iff_zero_less_single_add
% 5.15/5.37 thf(fact_1767_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.15/5.37 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_double_add_iff_zero_less_single_add
% 5.15/5.37 thf(fact_1768_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.15/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_add_less_zero_iff_single_add_less_zero
% 5.15/5.37 thf(fact_1769_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.15/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_add_less_zero_iff_single_add_less_zero
% 5.15/5.37 thf(fact_1770_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.15/5.37 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % double_add_less_zero_iff_single_add_less_zero
% 5.15/5.37 thf(fact_1771_less__add__same__cancel2,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.15/5.37 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_add_same_cancel2
% 5.15/5.37 thf(fact_1772_less__add__same__cancel2,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.15/5.37 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_add_same_cancel2
% 5.15/5.37 thf(fact_1773_less__add__same__cancel2,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.15/5.37 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_add_same_cancel2
% 5.15/5.37 thf(fact_1774_less__add__same__cancel2,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.15/5.37 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_add_same_cancel2
% 5.15/5.37 thf(fact_1775_less__add__same__cancel1,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.15/5.37 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_add_same_cancel1
% 5.15/5.37 thf(fact_1776_less__add__same__cancel1,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.15/5.37 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_add_same_cancel1
% 5.15/5.37 thf(fact_1777_less__add__same__cancel1,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.15/5.37 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_add_same_cancel1
% 5.15/5.37 thf(fact_1778_less__add__same__cancel1,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.15/5.37 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_add_same_cancel1
% 5.15/5.37 thf(fact_1779_add__less__same__cancel2,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.15/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_less_same_cancel2
% 5.15/5.37 thf(fact_1780_add__less__same__cancel2,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.15/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_less_same_cancel2
% 5.15/5.37 thf(fact_1781_add__less__same__cancel2,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.15/5.37 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_less_same_cancel2
% 5.15/5.37 thf(fact_1782_add__less__same__cancel2,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.15/5.37 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_less_same_cancel2
% 5.15/5.37 thf(fact_1783_add__less__same__cancel1,axiom,
% 5.15/5.37 ! [B: real,A: real] :
% 5.15/5.37 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.15/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_less_same_cancel1
% 5.15/5.37 thf(fact_1784_add__less__same__cancel1,axiom,
% 5.15/5.37 ! [B: rat,A: rat] :
% 5.15/5.37 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.15/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_less_same_cancel1
% 5.15/5.37 thf(fact_1785_add__less__same__cancel1,axiom,
% 5.15/5.37 ! [B: nat,A: nat] :
% 5.15/5.37 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.15/5.37 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_less_same_cancel1
% 5.15/5.37 thf(fact_1786_add__less__same__cancel1,axiom,
% 5.15/5.37 ! [B: int,A: int] :
% 5.15/5.37 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.15/5.37 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_less_same_cancel1
% 5.15/5.37 thf(fact_1787_diff__ge__0__iff__ge,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.15/5.37 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % diff_ge_0_iff_ge
% 5.15/5.37 thf(fact_1788_diff__ge__0__iff__ge,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.15/5.37 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % diff_ge_0_iff_ge
% 5.15/5.37 thf(fact_1789_diff__ge__0__iff__ge,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.15/5.37 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % diff_ge_0_iff_ge
% 5.15/5.37 thf(fact_1790_diff__gt__0__iff__gt,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.15/5.37 = ( ord_less_real @ B @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % diff_gt_0_iff_gt
% 5.15/5.37 thf(fact_1791_diff__gt__0__iff__gt,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.15/5.37 = ( ord_less_rat @ B @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % diff_gt_0_iff_gt
% 5.15/5.37 thf(fact_1792_diff__gt__0__iff__gt,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.15/5.37 = ( ord_less_int @ B @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % diff_gt_0_iff_gt
% 5.15/5.37 thf(fact_1793_mult__cancel__right2,axiom,
% 5.15/5.37 ! [A: complex,C: complex] :
% 5.15/5.37 ( ( ( times_times_complex @ A @ C )
% 5.15/5.37 = C )
% 5.15/5.37 = ( ( C = zero_zero_complex )
% 5.15/5.37 | ( A = one_one_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_right2
% 5.15/5.37 thf(fact_1794_mult__cancel__right2,axiom,
% 5.15/5.37 ! [A: real,C: real] :
% 5.15/5.37 ( ( ( times_times_real @ A @ C )
% 5.15/5.37 = C )
% 5.15/5.37 = ( ( C = zero_zero_real )
% 5.15/5.37 | ( A = one_one_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_right2
% 5.15/5.37 thf(fact_1795_mult__cancel__right2,axiom,
% 5.15/5.37 ! [A: rat,C: rat] :
% 5.15/5.37 ( ( ( times_times_rat @ A @ C )
% 5.15/5.37 = C )
% 5.15/5.37 = ( ( C = zero_zero_rat )
% 5.15/5.37 | ( A = one_one_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_right2
% 5.15/5.37 thf(fact_1796_mult__cancel__right2,axiom,
% 5.15/5.37 ! [A: int,C: int] :
% 5.15/5.37 ( ( ( times_times_int @ A @ C )
% 5.15/5.37 = C )
% 5.15/5.37 = ( ( C = zero_zero_int )
% 5.15/5.37 | ( A = one_one_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_right2
% 5.15/5.37 thf(fact_1797_mult__cancel__right1,axiom,
% 5.15/5.37 ! [C: complex,B: complex] :
% 5.15/5.37 ( ( C
% 5.15/5.37 = ( times_times_complex @ B @ C ) )
% 5.15/5.37 = ( ( C = zero_zero_complex )
% 5.15/5.37 | ( B = one_one_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_right1
% 5.15/5.37 thf(fact_1798_mult__cancel__right1,axiom,
% 5.15/5.37 ! [C: real,B: real] :
% 5.15/5.37 ( ( C
% 5.15/5.37 = ( times_times_real @ B @ C ) )
% 5.15/5.37 = ( ( C = zero_zero_real )
% 5.15/5.37 | ( B = one_one_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_right1
% 5.15/5.37 thf(fact_1799_mult__cancel__right1,axiom,
% 5.15/5.37 ! [C: rat,B: rat] :
% 5.15/5.37 ( ( C
% 5.15/5.37 = ( times_times_rat @ B @ C ) )
% 5.15/5.37 = ( ( C = zero_zero_rat )
% 5.15/5.37 | ( B = one_one_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_right1
% 5.15/5.37 thf(fact_1800_mult__cancel__right1,axiom,
% 5.15/5.37 ! [C: int,B: int] :
% 5.15/5.37 ( ( C
% 5.15/5.37 = ( times_times_int @ B @ C ) )
% 5.15/5.37 = ( ( C = zero_zero_int )
% 5.15/5.37 | ( B = one_one_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_right1
% 5.15/5.37 thf(fact_1801_mult__cancel__left2,axiom,
% 5.15/5.37 ! [C: complex,A: complex] :
% 5.15/5.37 ( ( ( times_times_complex @ C @ A )
% 5.15/5.37 = C )
% 5.15/5.37 = ( ( C = zero_zero_complex )
% 5.15/5.37 | ( A = one_one_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_left2
% 5.15/5.37 thf(fact_1802_mult__cancel__left2,axiom,
% 5.15/5.37 ! [C: real,A: real] :
% 5.15/5.37 ( ( ( times_times_real @ C @ A )
% 5.15/5.37 = C )
% 5.15/5.37 = ( ( C = zero_zero_real )
% 5.15/5.37 | ( A = one_one_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_left2
% 5.15/5.37 thf(fact_1803_mult__cancel__left2,axiom,
% 5.15/5.37 ! [C: rat,A: rat] :
% 5.15/5.37 ( ( ( times_times_rat @ C @ A )
% 5.15/5.37 = C )
% 5.15/5.37 = ( ( C = zero_zero_rat )
% 5.15/5.37 | ( A = one_one_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_left2
% 5.15/5.37 thf(fact_1804_mult__cancel__left2,axiom,
% 5.15/5.37 ! [C: int,A: int] :
% 5.15/5.37 ( ( ( times_times_int @ C @ A )
% 5.15/5.37 = C )
% 5.15/5.37 = ( ( C = zero_zero_int )
% 5.15/5.37 | ( A = one_one_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_left2
% 5.15/5.37 thf(fact_1805_mult__cancel__left1,axiom,
% 5.15/5.37 ! [C: complex,B: complex] :
% 5.15/5.37 ( ( C
% 5.15/5.37 = ( times_times_complex @ C @ B ) )
% 5.15/5.37 = ( ( C = zero_zero_complex )
% 5.15/5.37 | ( B = one_one_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_left1
% 5.15/5.37 thf(fact_1806_mult__cancel__left1,axiom,
% 5.15/5.37 ! [C: real,B: real] :
% 5.15/5.37 ( ( C
% 5.15/5.37 = ( times_times_real @ C @ B ) )
% 5.15/5.37 = ( ( C = zero_zero_real )
% 5.15/5.37 | ( B = one_one_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_left1
% 5.15/5.37 thf(fact_1807_mult__cancel__left1,axiom,
% 5.15/5.37 ! [C: rat,B: rat] :
% 5.15/5.37 ( ( C
% 5.15/5.37 = ( times_times_rat @ C @ B ) )
% 5.15/5.37 = ( ( C = zero_zero_rat )
% 5.15/5.37 | ( B = one_one_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_left1
% 5.15/5.37 thf(fact_1808_mult__cancel__left1,axiom,
% 5.15/5.37 ! [C: int,B: int] :
% 5.15/5.37 ( ( C
% 5.15/5.37 = ( times_times_int @ C @ B ) )
% 5.15/5.37 = ( ( C = zero_zero_int )
% 5.15/5.37 | ( B = one_one_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_cancel_left1
% 5.15/5.37 thf(fact_1809_sum__squares__eq__zero__iff,axiom,
% 5.15/5.37 ! [X: real,Y: real] :
% 5.15/5.37 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 = ( ( X = zero_zero_real )
% 5.15/5.37 & ( Y = zero_zero_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % sum_squares_eq_zero_iff
% 5.15/5.37 thf(fact_1810_sum__squares__eq__zero__iff,axiom,
% 5.15/5.37 ! [X: rat,Y: rat] :
% 5.15/5.37 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 = ( ( X = zero_zero_rat )
% 5.15/5.37 & ( Y = zero_zero_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % sum_squares_eq_zero_iff
% 5.15/5.37 thf(fact_1811_sum__squares__eq__zero__iff,axiom,
% 5.15/5.37 ! [X: int,Y: int] :
% 5.15/5.37 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.15/5.37 = zero_zero_int )
% 5.15/5.37 = ( ( X = zero_zero_int )
% 5.15/5.37 & ( Y = zero_zero_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % sum_squares_eq_zero_iff
% 5.15/5.37 thf(fact_1812_diff__numeral__special_I9_J,axiom,
% 5.15/5.37 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.15/5.37 = zero_zero_complex ) ).
% 5.15/5.37
% 5.15/5.37 % diff_numeral_special(9)
% 5.15/5.37 thf(fact_1813_diff__numeral__special_I9_J,axiom,
% 5.15/5.37 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.15/5.37 = zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % diff_numeral_special(9)
% 5.15/5.37 thf(fact_1814_diff__numeral__special_I9_J,axiom,
% 5.15/5.37 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.15/5.37 = zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % diff_numeral_special(9)
% 5.15/5.37 thf(fact_1815_diff__numeral__special_I9_J,axiom,
% 5.15/5.37 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % diff_numeral_special(9)
% 5.15/5.37 thf(fact_1816_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.15/5.37 ! [C: complex,A: complex,B: complex] :
% 5.15/5.37 ( ( C != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.15/5.37 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_right2
% 5.15/5.37 thf(fact_1817_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.15/5.37 ! [C: real,A: real,B: real] :
% 5.15/5.37 ( ( C != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.15/5.37 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_right2
% 5.15/5.37 thf(fact_1818_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.15/5.37 ! [C: rat,A: rat,B: rat] :
% 5.15/5.37 ( ( C != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.37 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_right2
% 5.15/5.37 thf(fact_1819_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.15/5.37 ! [C: complex,A: complex,B: complex] :
% 5.15/5.37 ( ( C != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.15/5.37 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_right
% 5.15/5.37 thf(fact_1820_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.15/5.37 ! [C: real,A: real,B: real] :
% 5.15/5.37 ( ( C != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.15/5.37 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_right
% 5.15/5.37 thf(fact_1821_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.15/5.37 ! [C: rat,A: rat,B: rat] :
% 5.15/5.37 ( ( C != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.15/5.37 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_right
% 5.15/5.37 thf(fact_1822_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.15/5.37 ! [C: complex,A: complex,B: complex] :
% 5.15/5.37 ( ( C != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.15/5.37 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_left2
% 5.15/5.37 thf(fact_1823_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.15/5.37 ! [C: real,A: real,B: real] :
% 5.15/5.37 ( ( C != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.15/5.37 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_left2
% 5.15/5.37 thf(fact_1824_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.15/5.37 ! [C: rat,A: rat,B: rat] :
% 5.15/5.37 ( ( C != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.15/5.37 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_left2
% 5.15/5.37 thf(fact_1825_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.15/5.37 ! [C: complex,A: complex,B: complex] :
% 5.15/5.37 ( ( C != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.15/5.37 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_left
% 5.15/5.37 thf(fact_1826_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.15/5.37 ! [C: real,A: real,B: real] :
% 5.15/5.37 ( ( C != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.37 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_left
% 5.15/5.37 thf(fact_1827_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.15/5.37 ! [C: rat,A: rat,B: rat] :
% 5.15/5.37 ( ( C != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.37 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_divide_mult_cancel_left
% 5.15/5.37 thf(fact_1828_mult__divide__mult__cancel__left__if,axiom,
% 5.15/5.37 ! [C: complex,A: complex,B: complex] :
% 5.15/5.37 ( ( ( C = zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.15/5.37 = zero_zero_complex ) )
% 5.15/5.37 & ( ( C != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.15/5.37 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_divide_mult_cancel_left_if
% 5.15/5.37 thf(fact_1829_mult__divide__mult__cancel__left__if,axiom,
% 5.15/5.37 ! [C: real,A: real,B: real] :
% 5.15/5.37 ( ( ( C = zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.37 = zero_zero_real ) )
% 5.15/5.37 & ( ( C != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.37 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_divide_mult_cancel_left_if
% 5.15/5.37 thf(fact_1830_mult__divide__mult__cancel__left__if,axiom,
% 5.15/5.37 ! [C: rat,A: rat,B: rat] :
% 5.15/5.37 ( ( ( C = zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.37 = zero_zero_rat ) )
% 5.15/5.37 & ( ( C != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.37 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_divide_mult_cancel_left_if
% 5.15/5.37 thf(fact_1831_div__mult__mult1,axiom,
% 5.15/5.37 ! [C: nat,A: nat,B: nat] :
% 5.15/5.37 ( ( C != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.15/5.37 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_mult1
% 5.15/5.37 thf(fact_1832_div__mult__mult1,axiom,
% 5.15/5.37 ! [C: int,A: int,B: int] :
% 5.15/5.37 ( ( C != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.37 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_mult1
% 5.15/5.37 thf(fact_1833_div__mult__mult2,axiom,
% 5.15/5.37 ! [C: nat,A: nat,B: nat] :
% 5.15/5.37 ( ( C != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.15/5.37 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_mult2
% 5.15/5.37 thf(fact_1834_div__mult__mult2,axiom,
% 5.15/5.37 ! [C: int,A: int,B: int] :
% 5.15/5.37 ( ( C != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.15/5.37 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_mult2
% 5.15/5.37 thf(fact_1835_div__mult__mult1__if,axiom,
% 5.15/5.37 ! [C: nat,A: nat,B: nat] :
% 5.15/5.37 ( ( ( C = zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.15/5.37 = zero_zero_nat ) )
% 5.15/5.37 & ( ( C != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.15/5.37 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_mult1_if
% 5.15/5.37 thf(fact_1836_div__mult__mult1__if,axiom,
% 5.15/5.37 ! [C: int,A: int,B: int] :
% 5.15/5.37 ( ( ( C = zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.37 = zero_zero_int ) )
% 5.15/5.37 & ( ( C != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.37 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_mult1_if
% 5.15/5.37 thf(fact_1837_nonzero__mult__div__cancel__right,axiom,
% 5.15/5.37 ! [B: complex,A: complex] :
% 5.15/5.37 ( ( B != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.15/5.37 = A ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_right
% 5.15/5.37 thf(fact_1838_nonzero__mult__div__cancel__right,axiom,
% 5.15/5.37 ! [B: real,A: real] :
% 5.15/5.37 ( ( B != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.15/5.37 = A ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_right
% 5.15/5.37 thf(fact_1839_nonzero__mult__div__cancel__right,axiom,
% 5.15/5.37 ! [B: rat,A: rat] :
% 5.15/5.37 ( ( B != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.15/5.37 = A ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_right
% 5.15/5.37 thf(fact_1840_nonzero__mult__div__cancel__right,axiom,
% 5.15/5.37 ! [B: nat,A: nat] :
% 5.15/5.37 ( ( B != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.15/5.37 = A ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_right
% 5.15/5.37 thf(fact_1841_nonzero__mult__div__cancel__right,axiom,
% 5.15/5.37 ! [B: int,A: int] :
% 5.15/5.37 ( ( B != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.15/5.37 = A ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_right
% 5.15/5.37 thf(fact_1842_nonzero__mult__div__cancel__left,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( A != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.15/5.37 = B ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_left
% 5.15/5.37 thf(fact_1843_nonzero__mult__div__cancel__left,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( A != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.15/5.37 = B ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_left
% 5.15/5.37 thf(fact_1844_nonzero__mult__div__cancel__left,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( A != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.15/5.37 = B ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_left
% 5.15/5.37 thf(fact_1845_nonzero__mult__div__cancel__left,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( A != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.15/5.37 = B ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_left
% 5.15/5.37 thf(fact_1846_nonzero__mult__div__cancel__left,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( A != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.15/5.37 = B ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_mult_div_cancel_left
% 5.15/5.37 thf(fact_1847_diff__add__zero,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % diff_add_zero
% 5.15/5.37 thf(fact_1848_zero__eq__1__divide__iff,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( zero_zero_real
% 5.15/5.37 = ( divide_divide_real @ one_one_real @ A ) )
% 5.15/5.37 = ( A = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_eq_1_divide_iff
% 5.15/5.37 thf(fact_1849_zero__eq__1__divide__iff,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( zero_zero_rat
% 5.15/5.37 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.15/5.37 = ( A = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_eq_1_divide_iff
% 5.15/5.37 thf(fact_1850_one__divide__eq__0__iff,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 = ( A = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % one_divide_eq_0_iff
% 5.15/5.37 thf(fact_1851_one__divide__eq__0__iff,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 = ( A = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % one_divide_eq_0_iff
% 5.15/5.37 thf(fact_1852_eq__divide__eq__1,axiom,
% 5.15/5.37 ! [B: real,A: real] :
% 5.15/5.37 ( ( one_one_real
% 5.15/5.37 = ( divide_divide_real @ B @ A ) )
% 5.15/5.37 = ( ( A != zero_zero_real )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % eq_divide_eq_1
% 5.15/5.37 thf(fact_1853_eq__divide__eq__1,axiom,
% 5.15/5.37 ! [B: rat,A: rat] :
% 5.15/5.37 ( ( one_one_rat
% 5.15/5.37 = ( divide_divide_rat @ B @ A ) )
% 5.15/5.37 = ( ( A != zero_zero_rat )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % eq_divide_eq_1
% 5.15/5.37 thf(fact_1854_divide__eq__eq__1,axiom,
% 5.15/5.37 ! [B: real,A: real] :
% 5.15/5.37 ( ( ( divide_divide_real @ B @ A )
% 5.15/5.37 = one_one_real )
% 5.15/5.37 = ( ( A != zero_zero_real )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_eq_1
% 5.15/5.37 thf(fact_1855_divide__eq__eq__1,axiom,
% 5.15/5.37 ! [B: rat,A: rat] :
% 5.15/5.37 ( ( ( divide_divide_rat @ B @ A )
% 5.15/5.37 = one_one_rat )
% 5.15/5.37 = ( ( A != zero_zero_rat )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_eq_1
% 5.15/5.37 thf(fact_1856_divide__self__if,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( ( A = zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.15/5.37 = zero_zero_complex ) )
% 5.15/5.37 & ( ( A != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.15/5.37 = one_one_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_self_if
% 5.15/5.37 thf(fact_1857_divide__self__if,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ( A = zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ A @ A )
% 5.15/5.37 = zero_zero_real ) )
% 5.15/5.37 & ( ( A != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ A @ A )
% 5.15/5.37 = one_one_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_self_if
% 5.15/5.37 thf(fact_1858_divide__self__if,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ( A = zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ A @ A )
% 5.15/5.37 = zero_zero_rat ) )
% 5.15/5.37 & ( ( A != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ A @ A )
% 5.15/5.37 = one_one_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_self_if
% 5.15/5.37 thf(fact_1859_divide__self,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( A != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.15/5.37 = one_one_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_self
% 5.15/5.37 thf(fact_1860_divide__self,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( A != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ A @ A )
% 5.15/5.37 = one_one_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_self
% 5.15/5.37 thf(fact_1861_divide__self,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( A != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ A @ A )
% 5.15/5.37 = one_one_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_self
% 5.15/5.37 thf(fact_1862_one__eq__divide__iff,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( one_one_complex
% 5.15/5.37 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.37 = ( ( B != zero_zero_complex )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % one_eq_divide_iff
% 5.15/5.37 thf(fact_1863_one__eq__divide__iff,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( one_one_real
% 5.15/5.37 = ( divide_divide_real @ A @ B ) )
% 5.15/5.37 = ( ( B != zero_zero_real )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % one_eq_divide_iff
% 5.15/5.37 thf(fact_1864_one__eq__divide__iff,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( one_one_rat
% 5.15/5.37 = ( divide_divide_rat @ A @ B ) )
% 5.15/5.37 = ( ( B != zero_zero_rat )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % one_eq_divide_iff
% 5.15/5.37 thf(fact_1865_divide__eq__1__iff,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.15/5.37 = one_one_complex )
% 5.15/5.37 = ( ( B != zero_zero_complex )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_1_iff
% 5.15/5.37 thf(fact_1866_divide__eq__1__iff,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ( divide_divide_real @ A @ B )
% 5.15/5.37 = one_one_real )
% 5.15/5.37 = ( ( B != zero_zero_real )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_1_iff
% 5.15/5.37 thf(fact_1867_divide__eq__1__iff,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ( divide_divide_rat @ A @ B )
% 5.15/5.37 = one_one_rat )
% 5.15/5.37 = ( ( B != zero_zero_rat )
% 5.15/5.37 & ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_1_iff
% 5.15/5.37 thf(fact_1868_div__self,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( A != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.15/5.37 = one_one_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_self
% 5.15/5.37 thf(fact_1869_div__self,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( A != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ A @ A )
% 5.15/5.37 = one_one_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_self
% 5.15/5.37 thf(fact_1870_div__self,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( A != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ A @ A )
% 5.15/5.37 = one_one_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_self
% 5.15/5.37 thf(fact_1871_div__self,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( A != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ A @ A )
% 5.15/5.37 = one_one_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_self
% 5.15/5.37 thf(fact_1872_div__self,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( A != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ A @ A )
% 5.15/5.37 = one_one_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_self
% 5.15/5.37 thf(fact_1873_power__0__Suc,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N2 ) )
% 5.15/5.37 = zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_Suc
% 5.15/5.37 thf(fact_1874_power__0__Suc,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_Suc
% 5.15/5.37 thf(fact_1875_power__0__Suc,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 5.15/5.37 = zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_Suc
% 5.15/5.37 thf(fact_1876_power__0__Suc,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 5.15/5.37 = zero_zero_complex ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_Suc
% 5.15/5.37 thf(fact_1877_power__0__Suc,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_Suc
% 5.15/5.37 thf(fact_1878_power__zero__numeral,axiom,
% 5.15/5.37 ! [K: num] :
% 5.15/5.37 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.15/5.37 = zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % power_zero_numeral
% 5.15/5.37 thf(fact_1879_power__zero__numeral,axiom,
% 5.15/5.37 ! [K: num] :
% 5.15/5.37 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % power_zero_numeral
% 5.15/5.37 thf(fact_1880_power__zero__numeral,axiom,
% 5.15/5.37 ! [K: num] :
% 5.15/5.37 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.15/5.37 = zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % power_zero_numeral
% 5.15/5.37 thf(fact_1881_power__zero__numeral,axiom,
% 5.15/5.37 ! [K: num] :
% 5.15/5.37 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.15/5.37 = zero_zero_complex ) ).
% 5.15/5.37
% 5.15/5.37 % power_zero_numeral
% 5.15/5.37 thf(fact_1882_power__zero__numeral,axiom,
% 5.15/5.37 ! [K: num] :
% 5.15/5.37 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % power_zero_numeral
% 5.15/5.37 thf(fact_1883_mod__mult__self2__is__0,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % mod_mult_self2_is_0
% 5.15/5.37 thf(fact_1884_mod__mult__self2__is__0,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % mod_mult_self2_is_0
% 5.15/5.37 thf(fact_1885_mod__mult__self2__is__0,axiom,
% 5.15/5.37 ! [A: code_integer,B: code_integer] :
% 5.15/5.37 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % mod_mult_self2_is_0
% 5.15/5.37 thf(fact_1886_mod__mult__self1__is__0,axiom,
% 5.15/5.37 ! [B: nat,A: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % mod_mult_self1_is_0
% 5.15/5.37 thf(fact_1887_mod__mult__self1__is__0,axiom,
% 5.15/5.37 ! [B: int,A: int] :
% 5.15/5.37 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % mod_mult_self1_is_0
% 5.15/5.37 thf(fact_1888_mod__mult__self1__is__0,axiom,
% 5.15/5.37 ! [B: code_integer,A: code_integer] :
% 5.15/5.37 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % mod_mult_self1_is_0
% 5.15/5.37 thf(fact_1889_bits__mod__by__1,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_by_1
% 5.15/5.37 thf(fact_1890_bits__mod__by__1,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_by_1
% 5.15/5.37 thf(fact_1891_bits__mod__by__1,axiom,
% 5.15/5.37 ! [A: code_integer] :
% 5.15/5.37 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_by_1
% 5.15/5.37 thf(fact_1892_mod__by__1,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % mod_by_1
% 5.15/5.37 thf(fact_1893_mod__by__1,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % mod_by_1
% 5.15/5.37 thf(fact_1894_mod__by__1,axiom,
% 5.15/5.37 ! [A: code_integer] :
% 5.15/5.37 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % mod_by_1
% 5.15/5.37 thf(fact_1895_power__Suc0__right,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % power_Suc0_right
% 5.15/5.37 thf(fact_1896_power__Suc0__right,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % power_Suc0_right
% 5.15/5.37 thf(fact_1897_power__Suc0__right,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % power_Suc0_right
% 5.15/5.37 thf(fact_1898_power__Suc0__right,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % power_Suc0_right
% 5.15/5.37 thf(fact_1899_bits__mod__div__trivial,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_div_trivial
% 5.15/5.37 thf(fact_1900_bits__mod__div__trivial,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_div_trivial
% 5.15/5.37 thf(fact_1901_bits__mod__div__trivial,axiom,
% 5.15/5.37 ! [A: code_integer,B: code_integer] :
% 5.15/5.37 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % bits_mod_div_trivial
% 5.15/5.37 thf(fact_1902_mod__div__trivial,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % mod_div_trivial
% 5.15/5.37 thf(fact_1903_mod__div__trivial,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % mod_div_trivial
% 5.15/5.37 thf(fact_1904_mod__div__trivial,axiom,
% 5.15/5.37 ! [A: code_integer,B: code_integer] :
% 5.15/5.37 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ).
% 5.15/5.37
% 5.15/5.37 % mod_div_trivial
% 5.15/5.37 thf(fact_1905_zero__less__Suc,axiom,
% 5.15/5.37 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_Suc
% 5.15/5.37 thf(fact_1906_less__Suc0,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.15/5.37 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_Suc0
% 5.15/5.37 thf(fact_1907_add__gr__0,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.37 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.37 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % add_gr_0
% 5.15/5.37 thf(fact_1908_mult__eq__1__iff,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ( times_times_nat @ M @ N2 )
% 5.15/5.37 = ( suc @ zero_zero_nat ) )
% 5.15/5.37 = ( ( M
% 5.15/5.37 = ( suc @ zero_zero_nat ) )
% 5.15/5.37 & ( N2
% 5.15/5.37 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_eq_1_iff
% 5.15/5.37 thf(fact_1909_one__eq__mult__iff,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ( suc @ zero_zero_nat )
% 5.15/5.37 = ( times_times_nat @ M @ N2 ) )
% 5.15/5.37 = ( ( M
% 5.15/5.37 = ( suc @ zero_zero_nat ) )
% 5.15/5.37 & ( N2
% 5.15/5.37 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % one_eq_mult_iff
% 5.15/5.37 thf(fact_1910_less__one,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ N2 @ one_one_nat )
% 5.15/5.37 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_one
% 5.15/5.37 thf(fact_1911_div__by__Suc__0,axiom,
% 5.15/5.37 ! [M: nat] :
% 5.15/5.37 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.15/5.37 = M ) ).
% 5.15/5.37
% 5.15/5.37 % div_by_Suc_0
% 5.15/5.37 thf(fact_1912_zero__less__diff,axiom,
% 5.15/5.37 ! [N2: nat,M: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 5.15/5.37 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_diff
% 5.15/5.37 thf(fact_1913_mult__less__cancel2,axiom,
% 5.15/5.37 ! [M: nat,K: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.15/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.37 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_less_cancel2
% 5.15/5.37 thf(fact_1914_nat__0__less__mult__iff,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.37 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.37 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nat_0_less_mult_iff
% 5.15/5.37 thf(fact_1915_nat__mult__less__cancel__disj,axiom,
% 5.15/5.37 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.37 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nat_mult_less_cancel_disj
% 5.15/5.37 thf(fact_1916_div__less,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.37 => ( ( divide_divide_nat @ M @ N2 )
% 5.15/5.37 = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_less
% 5.15/5.37 thf(fact_1917_diff__is__0__eq,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ( minus_minus_nat @ M @ N2 )
% 5.15/5.37 = zero_zero_nat )
% 5.15/5.37 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % diff_is_0_eq
% 5.15/5.37 thf(fact_1918_diff__is__0__eq_H,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.37 => ( ( minus_minus_nat @ M @ N2 )
% 5.15/5.37 = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % diff_is_0_eq'
% 5.15/5.37 thf(fact_1919_power__Suc__0,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.37 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_Suc_0
% 5.15/5.37 thf(fact_1920_nat__power__eq__Suc__0__iff,axiom,
% 5.15/5.37 ! [X: nat,M: nat] :
% 5.15/5.37 ( ( ( power_power_nat @ X @ M )
% 5.15/5.37 = ( suc @ zero_zero_nat ) )
% 5.15/5.37 = ( ( M = zero_zero_nat )
% 5.15/5.37 | ( X
% 5.15/5.37 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nat_power_eq_Suc_0_iff
% 5.15/5.37 thf(fact_1921_nat__zero__less__power__iff,axiom,
% 5.15/5.37 ! [X: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N2 ) )
% 5.15/5.37 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.15/5.37 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nat_zero_less_power_iff
% 5.15/5.37 thf(fact_1922_nat__mult__div__cancel__disj,axiom,
% 5.15/5.37 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.37 ( ( ( K = zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.37 = zero_zero_nat ) )
% 5.15/5.37 & ( ( K != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.37 = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nat_mult_div_cancel_disj
% 5.15/5.37 thf(fact_1923_mod__by__Suc__0,axiom,
% 5.15/5.37 ! [M: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % mod_by_Suc_0
% 5.15/5.37 thf(fact_1924_zero__le__divide__1__iff,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.15/5.37 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_le_divide_1_iff
% 5.15/5.37 thf(fact_1925_zero__le__divide__1__iff,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.15/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_le_divide_1_iff
% 5.15/5.37 thf(fact_1926_divide__le__0__1__iff,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.15/5.37 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_le_0_1_iff
% 5.15/5.37 thf(fact_1927_divide__le__0__1__iff,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.15/5.37 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_le_0_1_iff
% 5.15/5.37 thf(fact_1928_zero__less__divide__1__iff,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.15/5.37 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_divide_1_iff
% 5.15/5.37 thf(fact_1929_zero__less__divide__1__iff,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.15/5.37 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_divide_1_iff
% 5.15/5.37 thf(fact_1930_less__divide__eq__1__pos,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.37 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.15/5.37 = ( ord_less_real @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_divide_eq_1_pos
% 5.15/5.37 thf(fact_1931_less__divide__eq__1__pos,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.37 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.15/5.37 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_divide_eq_1_pos
% 5.15/5.37 thf(fact_1932_less__divide__eq__1__neg,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.37 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.15/5.37 = ( ord_less_real @ B @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_divide_eq_1_neg
% 5.15/5.37 thf(fact_1933_less__divide__eq__1__neg,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.37 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.15/5.37 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % less_divide_eq_1_neg
% 5.15/5.37 thf(fact_1934_divide__less__eq__1__pos,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.37 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.15/5.37 = ( ord_less_real @ B @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_less_eq_1_pos
% 5.15/5.37 thf(fact_1935_divide__less__eq__1__pos,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.37 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.15/5.37 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_less_eq_1_pos
% 5.15/5.37 thf(fact_1936_divide__less__eq__1__neg,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.37 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.15/5.37 = ( ord_less_real @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_less_eq_1_neg
% 5.15/5.37 thf(fact_1937_divide__less__eq__1__neg,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.37 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.15/5.37 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_less_eq_1_neg
% 5.15/5.37 thf(fact_1938_divide__less__0__1__iff,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.15/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_less_0_1_iff
% 5.15/5.37 thf(fact_1939_divide__less__0__1__iff,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.15/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_less_0_1_iff
% 5.15/5.37 thf(fact_1940_eq__divide__eq__numeral1_I1_J,axiom,
% 5.15/5.37 ! [A: complex,B: complex,W: num] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.37 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.15/5.37 != zero_zero_complex )
% 5.15/5.37 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.37 = B ) )
% 5.15/5.37 & ( ( ( numera6690914467698888265omplex @ W )
% 5.15/5.37 = zero_zero_complex )
% 5.15/5.37 => ( A = zero_zero_complex ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % eq_divide_eq_numeral1(1)
% 5.15/5.37 thf(fact_1941_eq__divide__eq__numeral1_I1_J,axiom,
% 5.15/5.37 ! [A: real,B: real,W: num] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.37 = ( ( ( ( numeral_numeral_real @ W )
% 5.15/5.37 != zero_zero_real )
% 5.15/5.37 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.15/5.37 = B ) )
% 5.15/5.37 & ( ( ( numeral_numeral_real @ W )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 => ( A = zero_zero_real ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % eq_divide_eq_numeral1(1)
% 5.15/5.37 thf(fact_1942_eq__divide__eq__numeral1_I1_J,axiom,
% 5.15/5.37 ! [A: rat,B: rat,W: num] :
% 5.15/5.37 ( ( A
% 5.15/5.37 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.15/5.37 = ( ( ( ( numeral_numeral_rat @ W )
% 5.15/5.37 != zero_zero_rat )
% 5.15/5.37 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.15/5.37 = B ) )
% 5.15/5.37 & ( ( ( numeral_numeral_rat @ W )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 => ( A = zero_zero_rat ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % eq_divide_eq_numeral1(1)
% 5.15/5.37 thf(fact_1943_divide__eq__eq__numeral1_I1_J,axiom,
% 5.15/5.37 ! [B: complex,W: num,A: complex] :
% 5.15/5.37 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.37 = A )
% 5.15/5.37 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.15/5.37 != zero_zero_complex )
% 5.15/5.37 => ( B
% 5.15/5.37 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.15/5.37 & ( ( ( numera6690914467698888265omplex @ W )
% 5.15/5.37 = zero_zero_complex )
% 5.15/5.37 => ( A = zero_zero_complex ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_eq_numeral1(1)
% 5.15/5.37 thf(fact_1944_divide__eq__eq__numeral1_I1_J,axiom,
% 5.15/5.37 ! [B: real,W: num,A: real] :
% 5.15/5.37 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.15/5.37 = A )
% 5.15/5.37 = ( ( ( ( numeral_numeral_real @ W )
% 5.15/5.37 != zero_zero_real )
% 5.15/5.37 => ( B
% 5.15/5.37 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.15/5.37 & ( ( ( numeral_numeral_real @ W )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 => ( A = zero_zero_real ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_eq_numeral1(1)
% 5.15/5.37 thf(fact_1945_divide__eq__eq__numeral1_I1_J,axiom,
% 5.15/5.37 ! [B: rat,W: num,A: rat] :
% 5.15/5.37 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.15/5.37 = A )
% 5.15/5.37 = ( ( ( ( numeral_numeral_rat @ W )
% 5.15/5.37 != zero_zero_rat )
% 5.15/5.37 => ( B
% 5.15/5.37 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.15/5.37 & ( ( ( numeral_numeral_rat @ W )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 => ( A = zero_zero_rat ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_eq_eq_numeral1(1)
% 5.15/5.37 thf(fact_1946_nonzero__divide__mult__cancel__right,axiom,
% 5.15/5.37 ! [B: complex,A: complex] :
% 5.15/5.37 ( ( B != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.15/5.37 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_divide_mult_cancel_right
% 5.15/5.37 thf(fact_1947_nonzero__divide__mult__cancel__right,axiom,
% 5.15/5.37 ! [B: real,A: real] :
% 5.15/5.37 ( ( B != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.15/5.37 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_divide_mult_cancel_right
% 5.15/5.37 thf(fact_1948_nonzero__divide__mult__cancel__right,axiom,
% 5.15/5.37 ! [B: rat,A: rat] :
% 5.15/5.37 ( ( B != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.15/5.37 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_divide_mult_cancel_right
% 5.15/5.37 thf(fact_1949_nonzero__divide__mult__cancel__left,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( A != zero_zero_complex )
% 5.15/5.37 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.15/5.37 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_divide_mult_cancel_left
% 5.15/5.37 thf(fact_1950_nonzero__divide__mult__cancel__left,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( A != zero_zero_real )
% 5.15/5.37 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.15/5.37 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_divide_mult_cancel_left
% 5.15/5.37 thf(fact_1951_nonzero__divide__mult__cancel__left,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( A != zero_zero_rat )
% 5.15/5.37 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.15/5.37 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nonzero_divide_mult_cancel_left
% 5.15/5.37 thf(fact_1952_div__mult__self4,axiom,
% 5.15/5.37 ! [B: nat,C: nat,A: nat] :
% 5.15/5.37 ( ( B != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.15/5.37 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self4
% 5.15/5.37 thf(fact_1953_div__mult__self4,axiom,
% 5.15/5.37 ! [B: int,C: int,A: int] :
% 5.15/5.37 ( ( B != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.15/5.37 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self4
% 5.15/5.37 thf(fact_1954_div__mult__self3,axiom,
% 5.15/5.37 ! [B: nat,C: nat,A: nat] :
% 5.15/5.37 ( ( B != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.15/5.37 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self3
% 5.15/5.37 thf(fact_1955_div__mult__self3,axiom,
% 5.15/5.37 ! [B: int,C: int,A: int] :
% 5.15/5.37 ( ( B != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.15/5.37 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self3
% 5.15/5.37 thf(fact_1956_div__mult__self2,axiom,
% 5.15/5.37 ! [B: nat,A: nat,C: nat] :
% 5.15/5.37 ( ( B != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.15/5.37 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self2
% 5.15/5.37 thf(fact_1957_div__mult__self2,axiom,
% 5.15/5.37 ! [B: int,A: int,C: int] :
% 5.15/5.37 ( ( B != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.15/5.37 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self2
% 5.15/5.37 thf(fact_1958_div__mult__self1,axiom,
% 5.15/5.37 ! [B: nat,A: nat,C: nat] :
% 5.15/5.37 ( ( B != zero_zero_nat )
% 5.15/5.37 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.15/5.37 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self1
% 5.15/5.37 thf(fact_1959_div__mult__self1,axiom,
% 5.15/5.37 ! [B: int,A: int,C: int] :
% 5.15/5.37 ( ( B != zero_zero_int )
% 5.15/5.37 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.15/5.37 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self1
% 5.15/5.37 thf(fact_1960_power__eq__0__iff,axiom,
% 5.15/5.37 ! [A: rat,N2: nat] :
% 5.15/5.37 ( ( ( power_power_rat @ A @ N2 )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 = ( ( A = zero_zero_rat )
% 5.15/5.37 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_eq_0_iff
% 5.15/5.37 thf(fact_1961_power__eq__0__iff,axiom,
% 5.15/5.37 ! [A: nat,N2: nat] :
% 5.15/5.37 ( ( ( power_power_nat @ A @ N2 )
% 5.15/5.37 = zero_zero_nat )
% 5.15/5.37 = ( ( A = zero_zero_nat )
% 5.15/5.37 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_eq_0_iff
% 5.15/5.37 thf(fact_1962_power__eq__0__iff,axiom,
% 5.15/5.37 ! [A: real,N2: nat] :
% 5.15/5.37 ( ( ( power_power_real @ A @ N2 )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 = ( ( A = zero_zero_real )
% 5.15/5.37 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_eq_0_iff
% 5.15/5.37 thf(fact_1963_power__eq__0__iff,axiom,
% 5.15/5.37 ! [A: complex,N2: nat] :
% 5.15/5.37 ( ( ( power_power_complex @ A @ N2 )
% 5.15/5.37 = zero_zero_complex )
% 5.15/5.37 = ( ( A = zero_zero_complex )
% 5.15/5.37 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_eq_0_iff
% 5.15/5.37 thf(fact_1964_power__eq__0__iff,axiom,
% 5.15/5.37 ! [A: int,N2: nat] :
% 5.15/5.37 ( ( ( power_power_int @ A @ N2 )
% 5.15/5.37 = zero_zero_int )
% 5.15/5.37 = ( ( A = zero_zero_int )
% 5.15/5.37 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_eq_0_iff
% 5.15/5.37 thf(fact_1965_Suc__pred,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.15/5.37 = N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % Suc_pred
% 5.15/5.37 thf(fact_1966_one__le__mult__iff,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.37 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.15/5.37 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % one_le_mult_iff
% 5.15/5.37 thf(fact_1967_mult__le__cancel2,axiom,
% 5.15/5.37 ! [M: nat,K: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.15/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.37 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_le_cancel2
% 5.15/5.37 thf(fact_1968_nat__mult__le__cancel__disj,axiom,
% 5.15/5.37 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.37 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % nat_mult_le_cancel_disj
% 5.15/5.37 thf(fact_1969_div__mult__self1__is__m,axiom,
% 5.15/5.37 ! [N2: nat,M: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 5.15/5.37 = M ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self1_is_m
% 5.15/5.37 thf(fact_1970_div__mult__self__is__m,axiom,
% 5.15/5.37 ! [N2: nat,M: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 5.15/5.37 = M ) ) ).
% 5.15/5.37
% 5.15/5.37 % div_mult_self_is_m
% 5.15/5.37 thf(fact_1971_le__divide__eq__1__pos,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.37 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.15/5.37 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_divide_eq_1_pos
% 5.15/5.37 thf(fact_1972_le__divide__eq__1__pos,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.37 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.15/5.37 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_divide_eq_1_pos
% 5.15/5.37 thf(fact_1973_le__divide__eq__1__neg,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.37 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.15/5.37 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_divide_eq_1_neg
% 5.15/5.37 thf(fact_1974_le__divide__eq__1__neg,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.37 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.15/5.37 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % le_divide_eq_1_neg
% 5.15/5.37 thf(fact_1975_divide__le__eq__1__pos,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.37 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.15/5.37 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_le_eq_1_pos
% 5.15/5.37 thf(fact_1976_divide__le__eq__1__pos,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.37 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.15/5.37 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_le_eq_1_pos
% 5.15/5.37 thf(fact_1977_divide__le__eq__1__neg,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.37 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.15/5.37 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_le_eq_1_neg
% 5.15/5.37 thf(fact_1978_divide__le__eq__1__neg,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.37 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.15/5.37 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divide_le_eq_1_neg
% 5.15/5.37 thf(fact_1979_power__strict__decreasing__iff,axiom,
% 5.15/5.37 ! [B: real,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.37 => ( ( ord_less_real @ B @ one_one_real )
% 5.15/5.37 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_strict_decreasing_iff
% 5.15/5.37 thf(fact_1980_power__strict__decreasing__iff,axiom,
% 5.15/5.37 ! [B: rat,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.15/5.37 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.15/5.37 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_strict_decreasing_iff
% 5.15/5.37 thf(fact_1981_power__strict__decreasing__iff,axiom,
% 5.15/5.37 ! [B: nat,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.37 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.15/5.37 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_strict_decreasing_iff
% 5.15/5.37 thf(fact_1982_power__strict__decreasing__iff,axiom,
% 5.15/5.37 ! [B: int,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.37 => ( ( ord_less_int @ B @ one_one_int )
% 5.15/5.37 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_strict_decreasing_iff
% 5.15/5.37 thf(fact_1983_power__mono__iff,axiom,
% 5.15/5.37 ! [A: real,B: real,N2: nat] :
% 5.15/5.37 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_mono_iff
% 5.15/5.37 thf(fact_1984_power__mono__iff,axiom,
% 5.15/5.37 ! [A: rat,B: rat,N2: nat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.37 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_mono_iff
% 5.15/5.37 thf(fact_1985_power__mono__iff,axiom,
% 5.15/5.37 ! [A: nat,B: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.37 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_mono_iff
% 5.15/5.37 thf(fact_1986_power__mono__iff,axiom,
% 5.15/5.37 ! [A: int,B: int,N2: nat] :
% 5.15/5.37 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.37 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_mono_iff
% 5.15/5.37 thf(fact_1987_zero__eq__power2,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 = ( A = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_eq_power2
% 5.15/5.37 thf(fact_1988_zero__eq__power2,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_nat )
% 5.15/5.37 = ( A = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_eq_power2
% 5.15/5.37 thf(fact_1989_zero__eq__power2,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 = ( A = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_eq_power2
% 5.15/5.37 thf(fact_1990_zero__eq__power2,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_complex )
% 5.15/5.37 = ( A = zero_zero_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_eq_power2
% 5.15/5.37 thf(fact_1991_zero__eq__power2,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_int )
% 5.15/5.37 = ( A = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_eq_power2
% 5.15/5.37 thf(fact_1992_Suc__diff__1,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.15/5.37 = N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % Suc_diff_1
% 5.15/5.37 thf(fact_1993_bits__1__div__2,axiom,
% 5.15/5.37 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % bits_1_div_2
% 5.15/5.37 thf(fact_1994_bits__1__div__2,axiom,
% 5.15/5.37 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % bits_1_div_2
% 5.15/5.37 thf(fact_1995_one__div__two__eq__zero,axiom,
% 5.15/5.37 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % one_div_two_eq_zero
% 5.15/5.37 thf(fact_1996_one__div__two__eq__zero,axiom,
% 5.15/5.37 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % one_div_two_eq_zero
% 5.15/5.37 thf(fact_1997_power__decreasing__iff,axiom,
% 5.15/5.37 ! [B: real,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.37 => ( ( ord_less_real @ B @ one_one_real )
% 5.15/5.37 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_decreasing_iff
% 5.15/5.37 thf(fact_1998_power__decreasing__iff,axiom,
% 5.15/5.37 ! [B: rat,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.15/5.37 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.15/5.37 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_decreasing_iff
% 5.15/5.37 thf(fact_1999_power__decreasing__iff,axiom,
% 5.15/5.37 ! [B: nat,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.37 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.15/5.37 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_decreasing_iff
% 5.15/5.37 thf(fact_2000_power__decreasing__iff,axiom,
% 5.15/5.37 ! [B: int,M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.37 => ( ( ord_less_int @ B @ one_one_int )
% 5.15/5.37 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.15/5.37 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_decreasing_iff
% 5.15/5.37 thf(fact_2001_power2__eq__iff__nonneg,axiom,
% 5.15/5.37 ! [X: real,Y: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.37 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = ( X = Y ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power2_eq_iff_nonneg
% 5.15/5.37 thf(fact_2002_power2__eq__iff__nonneg,axiom,
% 5.15/5.37 ! [X: rat,Y: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.37 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.37 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = ( X = Y ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power2_eq_iff_nonneg
% 5.15/5.37 thf(fact_2003_power2__eq__iff__nonneg,axiom,
% 5.15/5.37 ! [X: nat,Y: nat] :
% 5.15/5.37 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.15/5.37 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.15/5.37 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = ( X = Y ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power2_eq_iff_nonneg
% 5.15/5.37 thf(fact_2004_power2__eq__iff__nonneg,axiom,
% 5.15/5.37 ! [X: int,Y: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.37 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.37 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = ( X = Y ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power2_eq_iff_nonneg
% 5.15/5.37 thf(fact_2005_power2__less__eq__zero__iff,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.15/5.37 = ( A = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % power2_less_eq_zero_iff
% 5.15/5.37 thf(fact_2006_power2__less__eq__zero__iff,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.15/5.37 = ( A = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % power2_less_eq_zero_iff
% 5.15/5.37 thf(fact_2007_power2__less__eq__zero__iff,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.15/5.37 = ( A = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % power2_less_eq_zero_iff
% 5.15/5.37 thf(fact_2008_zero__less__power2,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = ( A != zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_power2
% 5.15/5.37 thf(fact_2009_zero__less__power2,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = ( A != zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_power2
% 5.15/5.37 thf(fact_2010_zero__less__power2,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = ( A != zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_power2
% 5.15/5.37 thf(fact_2011_sum__power2__eq__zero__iff,axiom,
% 5.15/5.37 ! [X: rat,Y: rat] :
% 5.15/5.37 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 = ( ( X = zero_zero_rat )
% 5.15/5.37 & ( Y = zero_zero_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % sum_power2_eq_zero_iff
% 5.15/5.37 thf(fact_2012_sum__power2__eq__zero__iff,axiom,
% 5.15/5.37 ! [X: real,Y: real] :
% 5.15/5.37 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 = ( ( X = zero_zero_real )
% 5.15/5.37 & ( Y = zero_zero_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % sum_power2_eq_zero_iff
% 5.15/5.37 thf(fact_2013_sum__power2__eq__zero__iff,axiom,
% 5.15/5.37 ! [X: int,Y: int] :
% 5.15/5.37 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = zero_zero_int )
% 5.15/5.37 = ( ( X = zero_zero_int )
% 5.15/5.37 & ( Y = zero_zero_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % sum_power2_eq_zero_iff
% 5.15/5.37 thf(fact_2014_not__mod__2__eq__1__eq__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 != one_one_nat )
% 5.15/5.37 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % not_mod_2_eq_1_eq_0
% 5.15/5.37 thf(fact_2015_not__mod__2__eq__1__eq__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.37 != one_one_int )
% 5.15/5.37 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % not_mod_2_eq_1_eq_0
% 5.15/5.37 thf(fact_2016_not__mod__2__eq__1__eq__0,axiom,
% 5.15/5.37 ! [A: code_integer] :
% 5.15/5.37 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.37 != one_one_Code_integer )
% 5.15/5.37 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.37
% 5.15/5.37 % not_mod_2_eq_1_eq_0
% 5.15/5.37 thf(fact_2017_not__mod__2__eq__0__eq__1,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 != zero_zero_nat )
% 5.15/5.37 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = one_one_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % not_mod_2_eq_0_eq_1
% 5.15/5.37 thf(fact_2018_not__mod__2__eq__0__eq__1,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.37 != zero_zero_int )
% 5.15/5.37 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.37 = one_one_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % not_mod_2_eq_0_eq_1
% 5.15/5.37 thf(fact_2019_not__mod__2__eq__0__eq__1,axiom,
% 5.15/5.37 ! [A: code_integer] :
% 5.15/5.37 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.37 != zero_z3403309356797280102nteger )
% 5.15/5.37 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.37 = one_one_Code_integer ) ) ).
% 5.15/5.37
% 5.15/5.37 % not_mod_2_eq_0_eq_1
% 5.15/5.37 thf(fact_2020_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 != ( suc @ zero_zero_nat ) )
% 5.15/5.37 = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % not_mod2_eq_Suc_0_eq_0
% 5.15/5.37 thf(fact_2021_add__self__mod__2,axiom,
% 5.15/5.37 ! [M: nat] :
% 5.15/5.37 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % add_self_mod_2
% 5.15/5.37 thf(fact_2022_mod2__gr__0,axiom,
% 5.15/5.37 ! [M: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.37 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.37 = one_one_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % mod2_gr_0
% 5.15/5.37 thf(fact_2023_zero__reorient,axiom,
% 5.15/5.37 ! [X: complex] :
% 5.15/5.37 ( ( zero_zero_complex = X )
% 5.15/5.37 = ( X = zero_zero_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_reorient
% 5.15/5.37 thf(fact_2024_zero__reorient,axiom,
% 5.15/5.37 ! [X: real] :
% 5.15/5.37 ( ( zero_zero_real = X )
% 5.15/5.37 = ( X = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_reorient
% 5.15/5.37 thf(fact_2025_zero__reorient,axiom,
% 5.15/5.37 ! [X: rat] :
% 5.15/5.37 ( ( zero_zero_rat = X )
% 5.15/5.37 = ( X = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_reorient
% 5.15/5.37 thf(fact_2026_zero__reorient,axiom,
% 5.15/5.37 ! [X: nat] :
% 5.15/5.37 ( ( zero_zero_nat = X )
% 5.15/5.37 = ( X = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_reorient
% 5.15/5.37 thf(fact_2027_zero__reorient,axiom,
% 5.15/5.37 ! [X: int] :
% 5.15/5.37 ( ( zero_zero_int = X )
% 5.15/5.37 = ( X = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_reorient
% 5.15/5.37 thf(fact_2028_power__0__left,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ( N2 = zero_zero_nat )
% 5.15/5.37 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.15/5.37 = one_one_rat ) )
% 5.15/5.37 & ( ( N2 != zero_zero_nat )
% 5.15/5.37 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.15/5.37 = zero_zero_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_left
% 5.15/5.37 thf(fact_2029_power__0__left,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ( N2 = zero_zero_nat )
% 5.15/5.37 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 = one_one_nat ) )
% 5.15/5.37 & ( ( N2 != zero_zero_nat )
% 5.15/5.37 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_left
% 5.15/5.37 thf(fact_2030_power__0__left,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ( N2 = zero_zero_nat )
% 5.15/5.37 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.15/5.37 = one_one_real ) )
% 5.15/5.37 & ( ( N2 != zero_zero_nat )
% 5.15/5.37 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.15/5.37 = zero_zero_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_left
% 5.15/5.37 thf(fact_2031_power__0__left,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ( N2 = zero_zero_nat )
% 5.15/5.37 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.15/5.37 = one_one_complex ) )
% 5.15/5.37 & ( ( N2 != zero_zero_nat )
% 5.15/5.37 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.15/5.37 = zero_zero_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_left
% 5.15/5.37 thf(fact_2032_power__0__left,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ( N2 = zero_zero_nat )
% 5.15/5.37 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.15/5.37 = one_one_int ) )
% 5.15/5.37 & ( ( N2 != zero_zero_nat )
% 5.15/5.37 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.15/5.37 = zero_zero_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % power_0_left
% 5.15/5.37 thf(fact_2033_zero__power,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.15/5.37 = zero_zero_rat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_power
% 5.15/5.37 thf(fact_2034_zero__power,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 = zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_power
% 5.15/5.37 thf(fact_2035_zero__power,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.15/5.37 = zero_zero_real ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_power
% 5.15/5.37 thf(fact_2036_zero__power,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.15/5.37 = zero_zero_complex ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_power
% 5.15/5.37 thf(fact_2037_zero__power,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.15/5.37 = zero_zero_int ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_power
% 5.15/5.37 thf(fact_2038_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.15/5.37 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.15/5.37 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.15/5.37 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % VEBT_internal.option_shift.simps(3)
% 5.15/5.37 thf(fact_2039_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.15/5.37 ! [F: num > num > num,A: num,B: num] :
% 5.15/5.37 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.15/5.37 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % VEBT_internal.option_shift.simps(3)
% 5.15/5.37 thf(fact_2040_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.15/5.37 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.15/5.37 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.15/5.37 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % VEBT_internal.option_shift.simps(3)
% 5.15/5.37 thf(fact_2041_le__numeral__extra_I3_J,axiom,
% 5.15/5.37 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.15/5.37
% 5.15/5.37 % le_numeral_extra(3)
% 5.15/5.37 thf(fact_2042_le__numeral__extra_I3_J,axiom,
% 5.15/5.37 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.15/5.37
% 5.15/5.37 % le_numeral_extra(3)
% 5.15/5.37 thf(fact_2043_le__numeral__extra_I3_J,axiom,
% 5.15/5.37 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.15/5.37
% 5.15/5.37 % le_numeral_extra(3)
% 5.15/5.37 thf(fact_2044_le__numeral__extra_I3_J,axiom,
% 5.15/5.37 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.15/5.37
% 5.15/5.37 % le_numeral_extra(3)
% 5.15/5.37 thf(fact_2045_zero__le,axiom,
% 5.15/5.37 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.15/5.37
% 5.15/5.37 % zero_le
% 5.15/5.37 thf(fact_2046_field__lbound__gt__zero,axiom,
% 5.15/5.37 ! [D1: real,D22: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.15/5.37 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.15/5.37 => ? [E2: real] :
% 5.15/5.37 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.15/5.37 & ( ord_less_real @ E2 @ D1 )
% 5.15/5.37 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % field_lbound_gt_zero
% 5.15/5.37 thf(fact_2047_field__lbound__gt__zero,axiom,
% 5.15/5.37 ! [D1: rat,D22: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.15/5.37 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.15/5.37 => ? [E2: rat] :
% 5.15/5.37 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.15/5.37 & ( ord_less_rat @ E2 @ D1 )
% 5.15/5.37 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % field_lbound_gt_zero
% 5.15/5.37 thf(fact_2048_less__numeral__extra_I3_J,axiom,
% 5.15/5.37 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.15/5.37
% 5.15/5.37 % less_numeral_extra(3)
% 5.15/5.37 thf(fact_2049_less__numeral__extra_I3_J,axiom,
% 5.15/5.37 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.15/5.37
% 5.15/5.37 % less_numeral_extra(3)
% 5.15/5.37 thf(fact_2050_less__numeral__extra_I3_J,axiom,
% 5.15/5.37 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % less_numeral_extra(3)
% 5.15/5.37 thf(fact_2051_less__numeral__extra_I3_J,axiom,
% 5.15/5.37 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.15/5.37
% 5.15/5.37 % less_numeral_extra(3)
% 5.15/5.37 thf(fact_2052_zero__less__iff__neq__zero,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.37 = ( N2 != zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_less_iff_neq_zero
% 5.15/5.37 thf(fact_2053_gr__implies__not__zero,axiom,
% 5.15/5.37 ! [M: nat,N2: nat] :
% 5.15/5.37 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.37 => ( N2 != zero_zero_nat ) ) ).
% 5.15/5.37
% 5.15/5.37 % gr_implies_not_zero
% 5.15/5.37 thf(fact_2054_not__less__zero,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.15/5.37
% 5.15/5.37 % not_less_zero
% 5.15/5.37 thf(fact_2055_gr__zeroI,axiom,
% 5.15/5.37 ! [N2: nat] :
% 5.15/5.37 ( ( N2 != zero_zero_nat )
% 5.15/5.37 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % gr_zeroI
% 5.15/5.37 thf(fact_2056_zero__neq__numeral,axiom,
% 5.15/5.37 ! [N2: num] :
% 5.15/5.37 ( zero_zero_complex
% 5.15/5.37 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_numeral
% 5.15/5.37 thf(fact_2057_zero__neq__numeral,axiom,
% 5.15/5.37 ! [N2: num] :
% 5.15/5.37 ( zero_zero_real
% 5.15/5.37 != ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_numeral
% 5.15/5.37 thf(fact_2058_zero__neq__numeral,axiom,
% 5.15/5.37 ! [N2: num] :
% 5.15/5.37 ( zero_zero_rat
% 5.15/5.37 != ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_numeral
% 5.15/5.37 thf(fact_2059_zero__neq__numeral,axiom,
% 5.15/5.37 ! [N2: num] :
% 5.15/5.37 ( zero_zero_nat
% 5.15/5.37 != ( numeral_numeral_nat @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_numeral
% 5.15/5.37 thf(fact_2060_zero__neq__numeral,axiom,
% 5.15/5.37 ! [N2: num] :
% 5.15/5.37 ( zero_zero_int
% 5.15/5.37 != ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_numeral
% 5.15/5.37 thf(fact_2061_mult__right__cancel,axiom,
% 5.15/5.37 ! [C: complex,A: complex,B: complex] :
% 5.15/5.37 ( ( C != zero_zero_complex )
% 5.15/5.37 => ( ( ( times_times_complex @ A @ C )
% 5.15/5.37 = ( times_times_complex @ B @ C ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_right_cancel
% 5.15/5.37 thf(fact_2062_mult__right__cancel,axiom,
% 5.15/5.37 ! [C: real,A: real,B: real] :
% 5.15/5.37 ( ( C != zero_zero_real )
% 5.15/5.37 => ( ( ( times_times_real @ A @ C )
% 5.15/5.37 = ( times_times_real @ B @ C ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_right_cancel
% 5.15/5.37 thf(fact_2063_mult__right__cancel,axiom,
% 5.15/5.37 ! [C: rat,A: rat,B: rat] :
% 5.15/5.37 ( ( C != zero_zero_rat )
% 5.15/5.37 => ( ( ( times_times_rat @ A @ C )
% 5.15/5.37 = ( times_times_rat @ B @ C ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_right_cancel
% 5.15/5.37 thf(fact_2064_mult__right__cancel,axiom,
% 5.15/5.37 ! [C: nat,A: nat,B: nat] :
% 5.15/5.37 ( ( C != zero_zero_nat )
% 5.15/5.37 => ( ( ( times_times_nat @ A @ C )
% 5.15/5.37 = ( times_times_nat @ B @ C ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_right_cancel
% 5.15/5.37 thf(fact_2065_mult__right__cancel,axiom,
% 5.15/5.37 ! [C: int,A: int,B: int] :
% 5.15/5.37 ( ( C != zero_zero_int )
% 5.15/5.37 => ( ( ( times_times_int @ A @ C )
% 5.15/5.37 = ( times_times_int @ B @ C ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_right_cancel
% 5.15/5.37 thf(fact_2066_mult__left__cancel,axiom,
% 5.15/5.37 ! [C: complex,A: complex,B: complex] :
% 5.15/5.37 ( ( C != zero_zero_complex )
% 5.15/5.37 => ( ( ( times_times_complex @ C @ A )
% 5.15/5.37 = ( times_times_complex @ C @ B ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_left_cancel
% 5.15/5.37 thf(fact_2067_mult__left__cancel,axiom,
% 5.15/5.37 ! [C: real,A: real,B: real] :
% 5.15/5.37 ( ( C != zero_zero_real )
% 5.15/5.37 => ( ( ( times_times_real @ C @ A )
% 5.15/5.37 = ( times_times_real @ C @ B ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_left_cancel
% 5.15/5.37 thf(fact_2068_mult__left__cancel,axiom,
% 5.15/5.37 ! [C: rat,A: rat,B: rat] :
% 5.15/5.37 ( ( C != zero_zero_rat )
% 5.15/5.37 => ( ( ( times_times_rat @ C @ A )
% 5.15/5.37 = ( times_times_rat @ C @ B ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_left_cancel
% 5.15/5.37 thf(fact_2069_mult__left__cancel,axiom,
% 5.15/5.37 ! [C: nat,A: nat,B: nat] :
% 5.15/5.37 ( ( C != zero_zero_nat )
% 5.15/5.37 => ( ( ( times_times_nat @ C @ A )
% 5.15/5.37 = ( times_times_nat @ C @ B ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_left_cancel
% 5.15/5.37 thf(fact_2070_mult__left__cancel,axiom,
% 5.15/5.37 ! [C: int,A: int,B: int] :
% 5.15/5.37 ( ( C != zero_zero_int )
% 5.15/5.37 => ( ( ( times_times_int @ C @ A )
% 5.15/5.37 = ( times_times_int @ C @ B ) )
% 5.15/5.37 = ( A = B ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_left_cancel
% 5.15/5.37 thf(fact_2071_no__zero__divisors,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( A != zero_zero_complex )
% 5.15/5.37 => ( ( B != zero_zero_complex )
% 5.15/5.37 => ( ( times_times_complex @ A @ B )
% 5.15/5.37 != zero_zero_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % no_zero_divisors
% 5.15/5.37 thf(fact_2072_no__zero__divisors,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( A != zero_zero_real )
% 5.15/5.37 => ( ( B != zero_zero_real )
% 5.15/5.37 => ( ( times_times_real @ A @ B )
% 5.15/5.37 != zero_zero_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % no_zero_divisors
% 5.15/5.37 thf(fact_2073_no__zero__divisors,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( A != zero_zero_rat )
% 5.15/5.37 => ( ( B != zero_zero_rat )
% 5.15/5.37 => ( ( times_times_rat @ A @ B )
% 5.15/5.37 != zero_zero_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % no_zero_divisors
% 5.15/5.37 thf(fact_2074_no__zero__divisors,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( A != zero_zero_nat )
% 5.15/5.37 => ( ( B != zero_zero_nat )
% 5.15/5.37 => ( ( times_times_nat @ A @ B )
% 5.15/5.37 != zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % no_zero_divisors
% 5.15/5.37 thf(fact_2075_no__zero__divisors,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( A != zero_zero_int )
% 5.15/5.37 => ( ( B != zero_zero_int )
% 5.15/5.37 => ( ( times_times_int @ A @ B )
% 5.15/5.37 != zero_zero_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % no_zero_divisors
% 5.15/5.37 thf(fact_2076_divisors__zero,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( ( times_times_complex @ A @ B )
% 5.15/5.37 = zero_zero_complex )
% 5.15/5.37 => ( ( A = zero_zero_complex )
% 5.15/5.37 | ( B = zero_zero_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divisors_zero
% 5.15/5.37 thf(fact_2077_divisors__zero,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ( times_times_real @ A @ B )
% 5.15/5.37 = zero_zero_real )
% 5.15/5.37 => ( ( A = zero_zero_real )
% 5.15/5.37 | ( B = zero_zero_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divisors_zero
% 5.15/5.37 thf(fact_2078_divisors__zero,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ( times_times_rat @ A @ B )
% 5.15/5.37 = zero_zero_rat )
% 5.15/5.37 => ( ( A = zero_zero_rat )
% 5.15/5.37 | ( B = zero_zero_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divisors_zero
% 5.15/5.37 thf(fact_2079_divisors__zero,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ( times_times_nat @ A @ B )
% 5.15/5.37 = zero_zero_nat )
% 5.15/5.37 => ( ( A = zero_zero_nat )
% 5.15/5.37 | ( B = zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divisors_zero
% 5.15/5.37 thf(fact_2080_divisors__zero,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ( times_times_int @ A @ B )
% 5.15/5.37 = zero_zero_int )
% 5.15/5.37 => ( ( A = zero_zero_int )
% 5.15/5.37 | ( B = zero_zero_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % divisors_zero
% 5.15/5.37 thf(fact_2081_mult__not__zero,axiom,
% 5.15/5.37 ! [A: complex,B: complex] :
% 5.15/5.37 ( ( ( times_times_complex @ A @ B )
% 5.15/5.37 != zero_zero_complex )
% 5.15/5.37 => ( ( A != zero_zero_complex )
% 5.15/5.37 & ( B != zero_zero_complex ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_not_zero
% 5.15/5.37 thf(fact_2082_mult__not__zero,axiom,
% 5.15/5.37 ! [A: real,B: real] :
% 5.15/5.37 ( ( ( times_times_real @ A @ B )
% 5.15/5.37 != zero_zero_real )
% 5.15/5.37 => ( ( A != zero_zero_real )
% 5.15/5.37 & ( B != zero_zero_real ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_not_zero
% 5.15/5.37 thf(fact_2083_mult__not__zero,axiom,
% 5.15/5.37 ! [A: rat,B: rat] :
% 5.15/5.37 ( ( ( times_times_rat @ A @ B )
% 5.15/5.37 != zero_zero_rat )
% 5.15/5.37 => ( ( A != zero_zero_rat )
% 5.15/5.37 & ( B != zero_zero_rat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_not_zero
% 5.15/5.37 thf(fact_2084_mult__not__zero,axiom,
% 5.15/5.37 ! [A: nat,B: nat] :
% 5.15/5.37 ( ( ( times_times_nat @ A @ B )
% 5.15/5.37 != zero_zero_nat )
% 5.15/5.37 => ( ( A != zero_zero_nat )
% 5.15/5.37 & ( B != zero_zero_nat ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_not_zero
% 5.15/5.37 thf(fact_2085_mult__not__zero,axiom,
% 5.15/5.37 ! [A: int,B: int] :
% 5.15/5.37 ( ( ( times_times_int @ A @ B )
% 5.15/5.37 != zero_zero_int )
% 5.15/5.37 => ( ( A != zero_zero_int )
% 5.15/5.37 & ( B != zero_zero_int ) ) ) ).
% 5.15/5.37
% 5.15/5.37 % mult_not_zero
% 5.15/5.37 thf(fact_2086_zero__neq__one,axiom,
% 5.15/5.37 zero_zero_complex != one_one_complex ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_one
% 5.15/5.37 thf(fact_2087_zero__neq__one,axiom,
% 5.15/5.37 zero_zero_real != one_one_real ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_one
% 5.15/5.37 thf(fact_2088_zero__neq__one,axiom,
% 5.15/5.37 zero_zero_rat != one_one_rat ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_one
% 5.15/5.37 thf(fact_2089_zero__neq__one,axiom,
% 5.15/5.37 zero_zero_nat != one_one_nat ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_one
% 5.15/5.37 thf(fact_2090_zero__neq__one,axiom,
% 5.15/5.37 zero_zero_int != one_one_int ).
% 5.15/5.37
% 5.15/5.37 % zero_neq_one
% 5.15/5.37 thf(fact_2091_add_Ogroup__left__neutral,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.group_left_neutral
% 5.15/5.37 thf(fact_2092_add_Ogroup__left__neutral,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.group_left_neutral
% 5.15/5.37 thf(fact_2093_add_Ogroup__left__neutral,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.group_left_neutral
% 5.15/5.37 thf(fact_2094_add_Ogroup__left__neutral,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.group_left_neutral
% 5.15/5.37 thf(fact_2095_add_Ocomm__neutral,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.comm_neutral
% 5.15/5.37 thf(fact_2096_add_Ocomm__neutral,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.comm_neutral
% 5.15/5.37 thf(fact_2097_add_Ocomm__neutral,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.comm_neutral
% 5.15/5.37 thf(fact_2098_add_Ocomm__neutral,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.comm_neutral
% 5.15/5.37 thf(fact_2099_add_Ocomm__neutral,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % add.comm_neutral
% 5.15/5.37 thf(fact_2100_comm__monoid__add__class_Oadd__0,axiom,
% 5.15/5.37 ! [A: complex] :
% 5.15/5.37 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % comm_monoid_add_class.add_0
% 5.15/5.37 thf(fact_2101_comm__monoid__add__class_Oadd__0,axiom,
% 5.15/5.37 ! [A: real] :
% 5.15/5.37 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % comm_monoid_add_class.add_0
% 5.15/5.37 thf(fact_2102_comm__monoid__add__class_Oadd__0,axiom,
% 5.15/5.37 ! [A: rat] :
% 5.15/5.37 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % comm_monoid_add_class.add_0
% 5.15/5.37 thf(fact_2103_comm__monoid__add__class_Oadd__0,axiom,
% 5.15/5.37 ! [A: nat] :
% 5.15/5.37 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % comm_monoid_add_class.add_0
% 5.15/5.37 thf(fact_2104_comm__monoid__add__class_Oadd__0,axiom,
% 5.15/5.37 ! [A: int] :
% 5.15/5.37 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.15/5.37 = A ) ).
% 5.15/5.37
% 5.15/5.37 % comm_monoid_add_class.add_0
% 5.15/5.37 thf(fact_2105_eq__iff__diff__eq__0,axiom,
% 5.15/5.37 ( ( ^ [Y5: complex,Z5: complex] : ( Y5 = Z5 ) )
% 5.15/5.37 = ( ^ [A3: complex,B2: complex] :
% 5.15/5.38 ( ( minus_minus_complex @ A3 @ B2 )
% 5.15/5.38 = zero_zero_complex ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_iff_diff_eq_0
% 5.15/5.38 thf(fact_2106_eq__iff__diff__eq__0,axiom,
% 5.15/5.38 ( ( ^ [Y5: real,Z5: real] : ( Y5 = Z5 ) )
% 5.15/5.38 = ( ^ [A3: real,B2: real] :
% 5.15/5.38 ( ( minus_minus_real @ A3 @ B2 )
% 5.15/5.38 = zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_iff_diff_eq_0
% 5.15/5.38 thf(fact_2107_eq__iff__diff__eq__0,axiom,
% 5.15/5.38 ( ( ^ [Y5: rat,Z5: rat] : ( Y5 = Z5 ) )
% 5.15/5.38 = ( ^ [A3: rat,B2: rat] :
% 5.15/5.38 ( ( minus_minus_rat @ A3 @ B2 )
% 5.15/5.38 = zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_iff_diff_eq_0
% 5.15/5.38 thf(fact_2108_eq__iff__diff__eq__0,axiom,
% 5.15/5.38 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.15/5.38 = ( ^ [A3: int,B2: int] :
% 5.15/5.38 ( ( minus_minus_int @ A3 @ B2 )
% 5.15/5.38 = zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_iff_diff_eq_0
% 5.15/5.38 thf(fact_2109_power__not__zero,axiom,
% 5.15/5.38 ! [A: rat,N2: nat] :
% 5.15/5.38 ( ( A != zero_zero_rat )
% 5.15/5.38 => ( ( power_power_rat @ A @ N2 )
% 5.15/5.38 != zero_zero_rat ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_not_zero
% 5.15/5.38 thf(fact_2110_power__not__zero,axiom,
% 5.15/5.38 ! [A: nat,N2: nat] :
% 5.15/5.38 ( ( A != zero_zero_nat )
% 5.15/5.38 => ( ( power_power_nat @ A @ N2 )
% 5.15/5.38 != zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_not_zero
% 5.15/5.38 thf(fact_2111_power__not__zero,axiom,
% 5.15/5.38 ! [A: real,N2: nat] :
% 5.15/5.38 ( ( A != zero_zero_real )
% 5.15/5.38 => ( ( power_power_real @ A @ N2 )
% 5.15/5.38 != zero_zero_real ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_not_zero
% 5.15/5.38 thf(fact_2112_power__not__zero,axiom,
% 5.15/5.38 ! [A: complex,N2: nat] :
% 5.15/5.38 ( ( A != zero_zero_complex )
% 5.15/5.38 => ( ( power_power_complex @ A @ N2 )
% 5.15/5.38 != zero_zero_complex ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_not_zero
% 5.15/5.38 thf(fact_2113_power__not__zero,axiom,
% 5.15/5.38 ! [A: int,N2: nat] :
% 5.15/5.38 ( ( A != zero_zero_int )
% 5.15/5.38 => ( ( power_power_int @ A @ N2 )
% 5.15/5.38 != zero_zero_int ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_not_zero
% 5.15/5.38 thf(fact_2114_num_Osize_I4_J,axiom,
% 5.15/5.38 ( ( size_size_num @ one )
% 5.15/5.38 = zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % num.size(4)
% 5.15/5.38 thf(fact_2115_nat_Odistinct_I1_J,axiom,
% 5.15/5.38 ! [X22: nat] :
% 5.15/5.38 ( zero_zero_nat
% 5.15/5.38 != ( suc @ X22 ) ) ).
% 5.15/5.38
% 5.15/5.38 % nat.distinct(1)
% 5.15/5.38 thf(fact_2116_old_Onat_Odistinct_I2_J,axiom,
% 5.15/5.38 ! [Nat2: nat] :
% 5.15/5.38 ( ( suc @ Nat2 )
% 5.15/5.38 != zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % old.nat.distinct(2)
% 5.15/5.38 thf(fact_2117_old_Onat_Odistinct_I1_J,axiom,
% 5.15/5.38 ! [Nat2: nat] :
% 5.15/5.38 ( zero_zero_nat
% 5.15/5.38 != ( suc @ Nat2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % old.nat.distinct(1)
% 5.15/5.38 thf(fact_2118_nat_OdiscI,axiom,
% 5.15/5.38 ! [Nat: nat,X22: nat] :
% 5.15/5.38 ( ( Nat
% 5.15/5.38 = ( suc @ X22 ) )
% 5.15/5.38 => ( Nat != zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % nat.discI
% 5.15/5.38 thf(fact_2119_old_Onat_Oexhaust,axiom,
% 5.15/5.38 ! [Y: nat] :
% 5.15/5.38 ( ( Y != zero_zero_nat )
% 5.15/5.38 => ~ ! [Nat3: nat] :
% 5.15/5.38 ( Y
% 5.15/5.38 != ( suc @ Nat3 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % old.nat.exhaust
% 5.15/5.38 thf(fact_2120_nat__induct,axiom,
% 5.15/5.38 ! [P: nat > $o,N2: nat] :
% 5.15/5.38 ( ( P @ zero_zero_nat )
% 5.15/5.38 => ( ! [N: nat] :
% 5.15/5.38 ( ( P @ N )
% 5.15/5.38 => ( P @ ( suc @ N ) ) )
% 5.15/5.38 => ( P @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nat_induct
% 5.15/5.38 thf(fact_2121_diff__induct,axiom,
% 5.15/5.38 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.15/5.38 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 5.15/5.38 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.15/5.38 => ( ! [X3: nat,Y3: nat] :
% 5.15/5.38 ( ( P @ X3 @ Y3 )
% 5.15/5.38 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 5.15/5.38 => ( P @ M @ N2 ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % diff_induct
% 5.15/5.38 thf(fact_2122_zero__induct,axiom,
% 5.15/5.38 ! [P: nat > $o,K: nat] :
% 5.15/5.38 ( ( P @ K )
% 5.15/5.38 => ( ! [N: nat] :
% 5.15/5.38 ( ( P @ ( suc @ N ) )
% 5.15/5.38 => ( P @ N ) )
% 5.15/5.38 => ( P @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_induct
% 5.15/5.38 thf(fact_2123_Suc__neq__Zero,axiom,
% 5.15/5.38 ! [M: nat] :
% 5.15/5.38 ( ( suc @ M )
% 5.15/5.38 != zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % Suc_neq_Zero
% 5.15/5.38 thf(fact_2124_Zero__neq__Suc,axiom,
% 5.15/5.38 ! [M: nat] :
% 5.15/5.38 ( zero_zero_nat
% 5.15/5.38 != ( suc @ M ) ) ).
% 5.15/5.38
% 5.15/5.38 % Zero_neq_Suc
% 5.15/5.38 thf(fact_2125_Zero__not__Suc,axiom,
% 5.15/5.38 ! [M: nat] :
% 5.15/5.38 ( zero_zero_nat
% 5.15/5.38 != ( suc @ M ) ) ).
% 5.15/5.38
% 5.15/5.38 % Zero_not_Suc
% 5.15/5.38 thf(fact_2126_not0__implies__Suc,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ( ( N2 != zero_zero_nat )
% 5.15/5.38 => ? [M3: nat] :
% 5.15/5.38 ( N2
% 5.15/5.38 = ( suc @ M3 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % not0_implies_Suc
% 5.15/5.38 thf(fact_2127_vebt__buildup_Ocases,axiom,
% 5.15/5.38 ! [X: nat] :
% 5.15/5.38 ( ( X != zero_zero_nat )
% 5.15/5.38 => ( ( X
% 5.15/5.38 != ( suc @ zero_zero_nat ) )
% 5.15/5.38 => ~ ! [Va3: nat] :
% 5.15/5.38 ( X
% 5.15/5.38 != ( suc @ ( suc @ Va3 ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % vebt_buildup.cases
% 5.15/5.38 thf(fact_2128_infinite__descent0,axiom,
% 5.15/5.38 ! [P: nat > $o,N2: nat] :
% 5.15/5.38 ( ( P @ zero_zero_nat )
% 5.15/5.38 => ( ! [N: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.15/5.38 => ( ~ ( P @ N )
% 5.15/5.38 => ? [M4: nat] :
% 5.15/5.38 ( ( ord_less_nat @ M4 @ N )
% 5.15/5.38 & ~ ( P @ M4 ) ) ) )
% 5.15/5.38 => ( P @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % infinite_descent0
% 5.15/5.38 thf(fact_2129_gr__implies__not0,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.38 => ( N2 != zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % gr_implies_not0
% 5.15/5.38 thf(fact_2130_less__zeroE,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % less_zeroE
% 5.15/5.38 thf(fact_2131_not__less0,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % not_less0
% 5.15/5.38 thf(fact_2132_not__gr0,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.38 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % not_gr0
% 5.15/5.38 thf(fact_2133_gr0I,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ( ( N2 != zero_zero_nat )
% 5.15/5.38 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % gr0I
% 5.15/5.38 thf(fact_2134_bot__nat__0_Oextremum__strict,axiom,
% 5.15/5.38 ! [A: nat] :
% 5.15/5.38 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % bot_nat_0.extremum_strict
% 5.15/5.38 thf(fact_2135_less__eq__nat_Osimps_I1_J,axiom,
% 5.15/5.38 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.15/5.38
% 5.15/5.38 % less_eq_nat.simps(1)
% 5.15/5.38 thf(fact_2136_bot__nat__0_Oextremum__unique,axiom,
% 5.15/5.38 ! [A: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.15/5.38 = ( A = zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % bot_nat_0.extremum_unique
% 5.15/5.38 thf(fact_2137_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.15/5.38 ! [A: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.15/5.38 => ( A = zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % bot_nat_0.extremum_uniqueI
% 5.15/5.38 thf(fact_2138_le__0__eq,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.15/5.38 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % le_0_eq
% 5.15/5.38 thf(fact_2139_add__eq__self__zero,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( ( plus_plus_nat @ M @ N2 )
% 5.15/5.38 = M )
% 5.15/5.38 => ( N2 = zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_eq_self_zero
% 5.15/5.38 thf(fact_2140_plus__nat_Oadd__0,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 = N2 ) ).
% 5.15/5.38
% 5.15/5.38 % plus_nat.add_0
% 5.15/5.38 thf(fact_2141_minus__nat_Odiff__0,axiom,
% 5.15/5.38 ! [M: nat] :
% 5.15/5.38 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.15/5.38 = M ) ).
% 5.15/5.38
% 5.15/5.38 % minus_nat.diff_0
% 5.15/5.38 thf(fact_2142_diffs0__imp__equal,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( ( minus_minus_nat @ M @ N2 )
% 5.15/5.38 = zero_zero_nat )
% 5.15/5.38 => ( ( ( minus_minus_nat @ N2 @ M )
% 5.15/5.38 = zero_zero_nat )
% 5.15/5.38 => ( M = N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % diffs0_imp_equal
% 5.15/5.38 thf(fact_2143_nat__mult__eq__cancel__disj,axiom,
% 5.15/5.38 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.38 ( ( ( times_times_nat @ K @ M )
% 5.15/5.38 = ( times_times_nat @ K @ N2 ) )
% 5.15/5.38 = ( ( K = zero_zero_nat )
% 5.15/5.38 | ( M = N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nat_mult_eq_cancel_disj
% 5.15/5.38 thf(fact_2144_mult__0,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 = zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % mult_0
% 5.15/5.38 thf(fact_2145_power__eq__iff__eq__base,axiom,
% 5.15/5.38 ! [N2: nat,A: real,B: real] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ( ( power_power_real @ A @ N2 )
% 5.15/5.38 = ( power_power_real @ B @ N2 ) )
% 5.15/5.38 = ( A = B ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_eq_iff_eq_base
% 5.15/5.38 thf(fact_2146_power__eq__iff__eq__base,axiom,
% 5.15/5.38 ! [N2: nat,A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ( ( power_power_rat @ A @ N2 )
% 5.15/5.38 = ( power_power_rat @ B @ N2 ) )
% 5.15/5.38 = ( A = B ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_eq_iff_eq_base
% 5.15/5.38 thf(fact_2147_power__eq__iff__eq__base,axiom,
% 5.15/5.38 ! [N2: nat,A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ( ( power_power_nat @ A @ N2 )
% 5.15/5.38 = ( power_power_nat @ B @ N2 ) )
% 5.15/5.38 = ( A = B ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_eq_iff_eq_base
% 5.15/5.38 thf(fact_2148_power__eq__iff__eq__base,axiom,
% 5.15/5.38 ! [N2: nat,A: int,B: int] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ( ( power_power_int @ A @ N2 )
% 5.15/5.38 = ( power_power_int @ B @ N2 ) )
% 5.15/5.38 = ( A = B ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_eq_iff_eq_base
% 5.15/5.38 thf(fact_2149_power__eq__imp__eq__base,axiom,
% 5.15/5.38 ! [A: real,N2: nat,B: real] :
% 5.15/5.38 ( ( ( power_power_real @ A @ N2 )
% 5.15/5.38 = ( power_power_real @ B @ N2 ) )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( A = B ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_eq_imp_eq_base
% 5.15/5.38 thf(fact_2150_power__eq__imp__eq__base,axiom,
% 5.15/5.38 ! [A: rat,N2: nat,B: rat] :
% 5.15/5.38 ( ( ( power_power_rat @ A @ N2 )
% 5.15/5.38 = ( power_power_rat @ B @ N2 ) )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( A = B ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_eq_imp_eq_base
% 5.15/5.38 thf(fact_2151_power__eq__imp__eq__base,axiom,
% 5.15/5.38 ! [A: nat,N2: nat,B: nat] :
% 5.15/5.38 ( ( ( power_power_nat @ A @ N2 )
% 5.15/5.38 = ( power_power_nat @ B @ N2 ) )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( A = B ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_eq_imp_eq_base
% 5.15/5.38 thf(fact_2152_power__eq__imp__eq__base,axiom,
% 5.15/5.38 ! [A: int,N2: nat,B: int] :
% 5.15/5.38 ( ( ( power_power_int @ A @ N2 )
% 5.15/5.38 = ( power_power_int @ B @ N2 ) )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( A = B ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_eq_imp_eq_base
% 5.15/5.38 thf(fact_2153_lambda__zero,axiom,
% 5.15/5.38 ( ( ^ [H: complex] : zero_zero_complex )
% 5.15/5.38 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.15/5.38
% 5.15/5.38 % lambda_zero
% 5.15/5.38 thf(fact_2154_lambda__zero,axiom,
% 5.15/5.38 ( ( ^ [H: real] : zero_zero_real )
% 5.15/5.38 = ( times_times_real @ zero_zero_real ) ) ).
% 5.15/5.38
% 5.15/5.38 % lambda_zero
% 5.15/5.38 thf(fact_2155_lambda__zero,axiom,
% 5.15/5.38 ( ( ^ [H: rat] : zero_zero_rat )
% 5.15/5.38 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.15/5.38
% 5.15/5.38 % lambda_zero
% 5.15/5.38 thf(fact_2156_lambda__zero,axiom,
% 5.15/5.38 ( ( ^ [H: nat] : zero_zero_nat )
% 5.15/5.38 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % lambda_zero
% 5.15/5.38 thf(fact_2157_lambda__zero,axiom,
% 5.15/5.38 ( ( ^ [H: int] : zero_zero_int )
% 5.15/5.38 = ( times_times_int @ zero_zero_int ) ) ).
% 5.15/5.38
% 5.15/5.38 % lambda_zero
% 5.15/5.38 thf(fact_2158_power__strict__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,N2: nat] :
% 5.15/5.38 ( ( ord_less_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_strict_mono
% 5.15/5.38 thf(fact_2159_power__strict__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,N2: nat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_strict_mono
% 5.15/5.38 thf(fact_2160_power__strict__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_strict_mono
% 5.15/5.38 thf(fact_2161_power__strict__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,N2: nat] :
% 5.15/5.38 ( ( ord_less_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_strict_mono
% 5.15/5.38 thf(fact_2162_finite__has__minimal,axiom,
% 5.15/5.38 ! [A2: set_real] :
% 5.15/5.38 ( ( finite_finite_real @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_real )
% 5.15/5.38 => ? [X3: real] :
% 5.15/5.38 ( ( member_real @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: real] :
% 5.15/5.38 ( ( member_real @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_minimal
% 5.15/5.38 thf(fact_2163_finite__has__minimal,axiom,
% 5.15/5.38 ! [A2: set_set_nat] :
% 5.15/5.38 ( ( finite1152437895449049373et_nat @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_set_nat )
% 5.15/5.38 => ? [X3: set_nat] :
% 5.15/5.38 ( ( member_set_nat @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: set_nat] :
% 5.15/5.38 ( ( member_set_nat @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_minimal
% 5.15/5.38 thf(fact_2164_finite__has__minimal,axiom,
% 5.15/5.38 ! [A2: set_rat] :
% 5.15/5.38 ( ( finite_finite_rat @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_rat )
% 5.15/5.38 => ? [X3: rat] :
% 5.15/5.38 ( ( member_rat @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: rat] :
% 5.15/5.38 ( ( member_rat @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_minimal
% 5.15/5.38 thf(fact_2165_finite__has__minimal,axiom,
% 5.15/5.38 ! [A2: set_num] :
% 5.15/5.38 ( ( finite_finite_num @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_num )
% 5.15/5.38 => ? [X3: num] :
% 5.15/5.38 ( ( member_num @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: num] :
% 5.15/5.38 ( ( member_num @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_minimal
% 5.15/5.38 thf(fact_2166_finite__has__minimal,axiom,
% 5.15/5.38 ! [A2: set_nat] :
% 5.15/5.38 ( ( finite_finite_nat @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_nat )
% 5.15/5.38 => ? [X3: nat] :
% 5.15/5.38 ( ( member_nat @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: nat] :
% 5.15/5.38 ( ( member_nat @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_minimal
% 5.15/5.38 thf(fact_2167_finite__has__minimal,axiom,
% 5.15/5.38 ! [A2: set_int] :
% 5.15/5.38 ( ( finite_finite_int @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_int )
% 5.15/5.38 => ? [X3: int] :
% 5.15/5.38 ( ( member_int @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: int] :
% 5.15/5.38 ( ( member_int @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_minimal
% 5.15/5.38 thf(fact_2168_finite__has__maximal,axiom,
% 5.15/5.38 ! [A2: set_real] :
% 5.15/5.38 ( ( finite_finite_real @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_real )
% 5.15/5.38 => ? [X3: real] :
% 5.15/5.38 ( ( member_real @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: real] :
% 5.15/5.38 ( ( member_real @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_maximal
% 5.15/5.38 thf(fact_2169_finite__has__maximal,axiom,
% 5.15/5.38 ! [A2: set_set_nat] :
% 5.15/5.38 ( ( finite1152437895449049373et_nat @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_set_nat )
% 5.15/5.38 => ? [X3: set_nat] :
% 5.15/5.38 ( ( member_set_nat @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: set_nat] :
% 5.15/5.38 ( ( member_set_nat @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_maximal
% 5.15/5.38 thf(fact_2170_finite__has__maximal,axiom,
% 5.15/5.38 ! [A2: set_rat] :
% 5.15/5.38 ( ( finite_finite_rat @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_rat )
% 5.15/5.38 => ? [X3: rat] :
% 5.15/5.38 ( ( member_rat @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: rat] :
% 5.15/5.38 ( ( member_rat @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_maximal
% 5.15/5.38 thf(fact_2171_finite__has__maximal,axiom,
% 5.15/5.38 ! [A2: set_num] :
% 5.15/5.38 ( ( finite_finite_num @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_num )
% 5.15/5.38 => ? [X3: num] :
% 5.15/5.38 ( ( member_num @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: num] :
% 5.15/5.38 ( ( member_num @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_maximal
% 5.15/5.38 thf(fact_2172_finite__has__maximal,axiom,
% 5.15/5.38 ! [A2: set_nat] :
% 5.15/5.38 ( ( finite_finite_nat @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_nat )
% 5.15/5.38 => ? [X3: nat] :
% 5.15/5.38 ( ( member_nat @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: nat] :
% 5.15/5.38 ( ( member_nat @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_maximal
% 5.15/5.38 thf(fact_2173_finite__has__maximal,axiom,
% 5.15/5.38 ! [A2: set_int] :
% 5.15/5.38 ( ( finite_finite_int @ A2 )
% 5.15/5.38 => ( ( A2 != bot_bot_set_int )
% 5.15/5.38 => ? [X3: int] :
% 5.15/5.38 ( ( member_int @ X3 @ A2 )
% 5.15/5.38 & ! [Xa: int] :
% 5.15/5.38 ( ( member_int @ Xa @ A2 )
% 5.15/5.38 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.15/5.38 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % finite_has_maximal
% 5.15/5.38 thf(fact_2174_zero__le__numeral,axiom,
% 5.15/5.38 ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_numeral
% 5.15/5.38 thf(fact_2175_zero__le__numeral,axiom,
% 5.15/5.38 ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_numeral
% 5.15/5.38 thf(fact_2176_zero__le__numeral,axiom,
% 5.15/5.38 ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_numeral
% 5.15/5.38 thf(fact_2177_zero__le__numeral,axiom,
% 5.15/5.38 ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_numeral
% 5.15/5.38 thf(fact_2178_not__numeral__le__zero,axiom,
% 5.15/5.38 ! [N2: num] :
% 5.15/5.38 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 5.15/5.38
% 5.15/5.38 % not_numeral_le_zero
% 5.15/5.38 thf(fact_2179_not__numeral__le__zero,axiom,
% 5.15/5.38 ! [N2: num] :
% 5.15/5.38 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 5.15/5.38
% 5.15/5.38 % not_numeral_le_zero
% 5.15/5.38 thf(fact_2180_not__numeral__le__zero,axiom,
% 5.15/5.38 ! [N2: num] :
% 5.15/5.38 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % not_numeral_le_zero
% 5.15/5.38 thf(fact_2181_not__numeral__le__zero,axiom,
% 5.15/5.38 ! [N2: num] :
% 5.15/5.38 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.15/5.38
% 5.15/5.38 % not_numeral_le_zero
% 5.15/5.38 thf(fact_2182_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.15/5.38 thf(fact_2183_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.15/5.38 thf(fact_2184_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.15/5.38 thf(fact_2185_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.15/5.38 thf(fact_2186_zero__le__mult__iff,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.15/5.38 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_mult_iff
% 5.15/5.38 thf(fact_2187_zero__le__mult__iff,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.15/5.38 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_mult_iff
% 5.15/5.38 thf(fact_2188_zero__le__mult__iff,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.15/5.38 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.38 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_mult_iff
% 5.15/5.38 thf(fact_2189_mult__nonneg__nonpos2,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonpos2
% 5.15/5.38 thf(fact_2190_mult__nonneg__nonpos2,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonpos2
% 5.15/5.38 thf(fact_2191_mult__nonneg__nonpos2,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonpos2
% 5.15/5.38 thf(fact_2192_mult__nonneg__nonpos2,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonpos2
% 5.15/5.38 thf(fact_2193_mult__nonpos__nonneg,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonpos_nonneg
% 5.15/5.38 thf(fact_2194_mult__nonpos__nonneg,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonpos_nonneg
% 5.15/5.38 thf(fact_2195_mult__nonpos__nonneg,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonpos_nonneg
% 5.15/5.38 thf(fact_2196_mult__nonpos__nonneg,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonpos_nonneg
% 5.15/5.38 thf(fact_2197_mult__nonneg__nonpos,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonpos
% 5.15/5.38 thf(fact_2198_mult__nonneg__nonpos,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonpos
% 5.15/5.38 thf(fact_2199_mult__nonneg__nonpos,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonpos
% 5.15/5.38 thf(fact_2200_mult__nonneg__nonpos,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonpos
% 5.15/5.38 thf(fact_2201_mult__nonneg__nonneg,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonneg
% 5.15/5.38 thf(fact_2202_mult__nonneg__nonneg,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonneg
% 5.15/5.38 thf(fact_2203_mult__nonneg__nonneg,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonneg
% 5.15/5.38 thf(fact_2204_mult__nonneg__nonneg,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonneg_nonneg
% 5.15/5.38 thf(fact_2205_split__mult__neg__le,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.15/5.38 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.15/5.38
% 5.15/5.38 % split_mult_neg_le
% 5.15/5.38 thf(fact_2206_split__mult__neg__le,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.15/5.38 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.15/5.38
% 5.15/5.38 % split_mult_neg_le
% 5.15/5.38 thf(fact_2207_split__mult__neg__le,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.15/5.38 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.15/5.38 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % split_mult_neg_le
% 5.15/5.38 thf(fact_2208_split__mult__neg__le,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.15/5.38 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.38 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.15/5.38
% 5.15/5.38 % split_mult_neg_le
% 5.15/5.38 thf(fact_2209_mult__le__0__iff,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.15/5.38 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.15/5.38 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_0_iff
% 5.15/5.38 thf(fact_2210_mult__le__0__iff,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.15/5.38 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.15/5.38 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_0_iff
% 5.15/5.38 thf(fact_2211_mult__le__0__iff,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.15/5.38 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.15/5.38 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.38 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_0_iff
% 5.15/5.38 thf(fact_2212_mult__right__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_right_mono
% 5.15/5.38 thf(fact_2213_mult__right__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_right_mono
% 5.15/5.38 thf(fact_2214_mult__right__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_right_mono
% 5.15/5.38 thf(fact_2215_mult__right__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_right_mono
% 5.15/5.38 thf(fact_2216_mult__right__mono__neg,axiom,
% 5.15/5.38 ! [B: real,A: real,C: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ B @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_right_mono_neg
% 5.15/5.38 thf(fact_2217_mult__right__mono__neg,axiom,
% 5.15/5.38 ! [B: rat,A: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_right_mono_neg
% 5.15/5.38 thf(fact_2218_mult__right__mono__neg,axiom,
% 5.15/5.38 ! [B: int,A: int,C: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ B @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_right_mono_neg
% 5.15/5.38 thf(fact_2219_mult__left__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_mono
% 5.15/5.38 thf(fact_2220_mult__left__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_mono
% 5.15/5.38 thf(fact_2221_mult__left__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_mono
% 5.15/5.38 thf(fact_2222_mult__left__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_mono
% 5.15/5.38 thf(fact_2223_mult__nonpos__nonpos,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonpos_nonpos
% 5.15/5.38 thf(fact_2224_mult__nonpos__nonpos,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonpos_nonpos
% 5.15/5.38 thf(fact_2225_mult__nonpos__nonpos,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.15/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_nonpos_nonpos
% 5.15/5.38 thf(fact_2226_mult__left__mono__neg,axiom,
% 5.15/5.38 ! [B: real,A: real,C: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ B @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_mono_neg
% 5.15/5.38 thf(fact_2227_mult__left__mono__neg,axiom,
% 5.15/5.38 ! [B: rat,A: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_mono_neg
% 5.15/5.38 thf(fact_2228_mult__left__mono__neg,axiom,
% 5.15/5.38 ! [B: int,A: int,C: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ B @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_mono_neg
% 5.15/5.38 thf(fact_2229_split__mult__pos__le,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.15/5.38 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.15/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % split_mult_pos_le
% 5.15/5.38 thf(fact_2230_split__mult__pos__le,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.15/5.38 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.15/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % split_mult_pos_le
% 5.15/5.38 thf(fact_2231_split__mult__pos__le,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.15/5.38 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.38 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.15/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % split_mult_pos_le
% 5.15/5.38 thf(fact_2232_zero__le__square,axiom,
% 5.15/5.38 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_square
% 5.15/5.38 thf(fact_2233_zero__le__square,axiom,
% 5.15/5.38 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_square
% 5.15/5.38 thf(fact_2234_zero__le__square,axiom,
% 5.15/5.38 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_square
% 5.15/5.38 thf(fact_2235_mult__mono_H,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ C @ D )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_mono'
% 5.15/5.38 thf(fact_2236_mult__mono_H,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ C @ D )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_mono'
% 5.15/5.38 thf(fact_2237_mult__mono_H,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ C @ D )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_mono'
% 5.15/5.38 thf(fact_2238_mult__mono_H,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ C @ D )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_mono'
% 5.15/5.38 thf(fact_2239_mult__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ C @ D )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_mono
% 5.15/5.38 thf(fact_2240_mult__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ C @ D )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_mono
% 5.15/5.38 thf(fact_2241_mult__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ C @ D )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_mono
% 5.15/5.38 thf(fact_2242_mult__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ C @ D )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_mono
% 5.15/5.38 thf(fact_2243_not__numeral__less__zero,axiom,
% 5.15/5.38 ! [N2: num] :
% 5.15/5.38 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 5.15/5.38
% 5.15/5.38 % not_numeral_less_zero
% 5.15/5.38 thf(fact_2244_not__numeral__less__zero,axiom,
% 5.15/5.38 ! [N2: num] :
% 5.15/5.38 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 5.15/5.38
% 5.15/5.38 % not_numeral_less_zero
% 5.15/5.38 thf(fact_2245_not__numeral__less__zero,axiom,
% 5.15/5.38 ! [N2: num] :
% 5.15/5.38 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % not_numeral_less_zero
% 5.15/5.38 thf(fact_2246_not__numeral__less__zero,axiom,
% 5.15/5.38 ! [N2: num] :
% 5.15/5.38 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.15/5.38
% 5.15/5.38 % not_numeral_less_zero
% 5.15/5.38 thf(fact_2247_zero__less__numeral,axiom,
% 5.15/5.38 ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_numeral
% 5.15/5.38 thf(fact_2248_zero__less__numeral,axiom,
% 5.15/5.38 ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_numeral
% 5.15/5.38 thf(fact_2249_zero__less__numeral,axiom,
% 5.15/5.38 ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_numeral
% 5.15/5.38 thf(fact_2250_zero__less__numeral,axiom,
% 5.15/5.38 ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_numeral
% 5.15/5.38 thf(fact_2251_zero__less__one__class_Ozero__le__one,axiom,
% 5.15/5.38 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.15/5.38
% 5.15/5.38 % zero_less_one_class.zero_le_one
% 5.15/5.38 thf(fact_2252_zero__less__one__class_Ozero__le__one,axiom,
% 5.15/5.38 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.15/5.38
% 5.15/5.38 % zero_less_one_class.zero_le_one
% 5.15/5.38 thf(fact_2253_zero__less__one__class_Ozero__le__one,axiom,
% 5.15/5.38 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.15/5.38
% 5.15/5.38 % zero_less_one_class.zero_le_one
% 5.15/5.38 thf(fact_2254_zero__less__one__class_Ozero__le__one,axiom,
% 5.15/5.38 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.15/5.38
% 5.15/5.38 % zero_less_one_class.zero_le_one
% 5.15/5.38 thf(fact_2255_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.15/5.38 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.15/5.38
% 5.15/5.38 % linordered_nonzero_semiring_class.zero_le_one
% 5.15/5.38 thf(fact_2256_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.15/5.38 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.15/5.38
% 5.15/5.38 % linordered_nonzero_semiring_class.zero_le_one
% 5.15/5.38 thf(fact_2257_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.15/5.38 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.15/5.38
% 5.15/5.38 % linordered_nonzero_semiring_class.zero_le_one
% 5.15/5.38 thf(fact_2258_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.15/5.38 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.15/5.38
% 5.15/5.38 % linordered_nonzero_semiring_class.zero_le_one
% 5.15/5.38 thf(fact_2259_not__one__le__zero,axiom,
% 5.15/5.38 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.15/5.38
% 5.15/5.38 % not_one_le_zero
% 5.15/5.38 thf(fact_2260_not__one__le__zero,axiom,
% 5.15/5.38 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.15/5.38
% 5.15/5.38 % not_one_le_zero
% 5.15/5.38 thf(fact_2261_not__one__le__zero,axiom,
% 5.15/5.38 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % not_one_le_zero
% 5.15/5.38 thf(fact_2262_not__one__le__zero,axiom,
% 5.15/5.38 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.15/5.38
% 5.15/5.38 % not_one_le_zero
% 5.15/5.38 thf(fact_2263_add__decreasing,axiom,
% 5.15/5.38 ! [A: real,C: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_eq_real @ C @ B )
% 5.15/5.38 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_decreasing
% 5.15/5.38 thf(fact_2264_add__decreasing,axiom,
% 5.15/5.38 ! [A: rat,C: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_eq_rat @ C @ B )
% 5.15/5.38 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_decreasing
% 5.15/5.38 thf(fact_2265_add__decreasing,axiom,
% 5.15/5.38 ! [A: nat,C: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.15/5.38 => ( ( ord_less_eq_nat @ C @ B )
% 5.15/5.38 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_decreasing
% 5.15/5.38 thf(fact_2266_add__decreasing,axiom,
% 5.15/5.38 ! [A: int,C: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_eq_int @ C @ B )
% 5.15/5.38 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_decreasing
% 5.15/5.38 thf(fact_2267_add__increasing,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ B @ C )
% 5.15/5.38 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_increasing
% 5.15/5.38 thf(fact_2268_add__increasing,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ B @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_increasing
% 5.15/5.38 thf(fact_2269_add__increasing,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_eq_nat @ B @ C )
% 5.15/5.38 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_increasing
% 5.15/5.38 thf(fact_2270_add__increasing,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ B @ C )
% 5.15/5.38 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_increasing
% 5.15/5.38 thf(fact_2271_add__decreasing2,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_decreasing2
% 5.15/5.38 thf(fact_2272_add__decreasing2,axiom,
% 5.15/5.38 ! [C: rat,A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_decreasing2
% 5.15/5.38 thf(fact_2273_add__decreasing2,axiom,
% 5.15/5.38 ! [C: nat,A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.15/5.38 => ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.38 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_decreasing2
% 5.15/5.38 thf(fact_2274_add__decreasing2,axiom,
% 5.15/5.38 ! [C: int,A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_eq_int @ A @ B )
% 5.15/5.38 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_decreasing2
% 5.15/5.38 thf(fact_2275_add__increasing2,axiom,
% 5.15/5.38 ! [C: real,B: real,A: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ( ord_less_eq_real @ B @ A )
% 5.15/5.38 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_increasing2
% 5.15/5.38 thf(fact_2276_add__increasing2,axiom,
% 5.15/5.38 ! [C: rat,B: rat,A: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.38 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_increasing2
% 5.15/5.38 thf(fact_2277_add__increasing2,axiom,
% 5.15/5.38 ! [C: nat,B: nat,A: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.38 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_increasing2
% 5.15/5.38 thf(fact_2278_add__increasing2,axiom,
% 5.15/5.38 ! [C: int,B: int,A: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ( ord_less_eq_int @ B @ A )
% 5.15/5.38 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_increasing2
% 5.15/5.38 thf(fact_2279_add__nonneg__nonneg,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonneg_nonneg
% 5.15/5.38 thf(fact_2280_add__nonneg__nonneg,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonneg_nonneg
% 5.15/5.38 thf(fact_2281_add__nonneg__nonneg,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonneg_nonneg
% 5.15/5.38 thf(fact_2282_add__nonneg__nonneg,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonneg_nonneg
% 5.15/5.38 thf(fact_2283_add__nonpos__nonpos,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonpos_nonpos
% 5.15/5.38 thf(fact_2284_add__nonpos__nonpos,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonpos_nonpos
% 5.15/5.38 thf(fact_2285_add__nonpos__nonpos,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.15/5.38 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.15/5.38 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonpos_nonpos
% 5.15/5.38 thf(fact_2286_add__nonpos__nonpos,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.15/5.38 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonpos_nonpos
% 5.15/5.38 thf(fact_2287_add__nonneg__eq__0__iff,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.38 => ( ( ( plus_plus_real @ X @ Y )
% 5.15/5.38 = zero_zero_real )
% 5.15/5.38 = ( ( X = zero_zero_real )
% 5.15/5.38 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonneg_eq_0_iff
% 5.15/5.38 thf(fact_2288_add__nonneg__eq__0__iff,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.38 => ( ( ( plus_plus_rat @ X @ Y )
% 5.15/5.38 = zero_zero_rat )
% 5.15/5.38 = ( ( X = zero_zero_rat )
% 5.15/5.38 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonneg_eq_0_iff
% 5.15/5.38 thf(fact_2289_add__nonneg__eq__0__iff,axiom,
% 5.15/5.38 ! [X: nat,Y: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.15/5.38 => ( ( ( plus_plus_nat @ X @ Y )
% 5.15/5.38 = zero_zero_nat )
% 5.15/5.38 = ( ( X = zero_zero_nat )
% 5.15/5.38 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonneg_eq_0_iff
% 5.15/5.38 thf(fact_2290_add__nonneg__eq__0__iff,axiom,
% 5.15/5.38 ! [X: int,Y: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.38 => ( ( ( plus_plus_int @ X @ Y )
% 5.15/5.38 = zero_zero_int )
% 5.15/5.38 = ( ( X = zero_zero_int )
% 5.15/5.38 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonneg_eq_0_iff
% 5.15/5.38 thf(fact_2291_add__nonpos__eq__0__iff,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.15/5.38 => ( ( ( plus_plus_real @ X @ Y )
% 5.15/5.38 = zero_zero_real )
% 5.15/5.38 = ( ( X = zero_zero_real )
% 5.15/5.38 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonpos_eq_0_iff
% 5.15/5.38 thf(fact_2292_add__nonpos__eq__0__iff,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.15/5.38 => ( ( ( plus_plus_rat @ X @ Y )
% 5.15/5.38 = zero_zero_rat )
% 5.15/5.38 = ( ( X = zero_zero_rat )
% 5.15/5.38 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonpos_eq_0_iff
% 5.15/5.38 thf(fact_2293_add__nonpos__eq__0__iff,axiom,
% 5.15/5.38 ! [X: nat,Y: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.15/5.38 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.15/5.38 => ( ( ( plus_plus_nat @ X @ Y )
% 5.15/5.38 = zero_zero_nat )
% 5.15/5.38 = ( ( X = zero_zero_nat )
% 5.15/5.38 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonpos_eq_0_iff
% 5.15/5.38 thf(fact_2294_add__nonpos__eq__0__iff,axiom,
% 5.15/5.38 ! [X: int,Y: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.15/5.38 => ( ( ( plus_plus_int @ X @ Y )
% 5.15/5.38 = zero_zero_int )
% 5.15/5.38 = ( ( X = zero_zero_int )
% 5.15/5.38 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_nonpos_eq_0_iff
% 5.15/5.38 thf(fact_2295_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.15/5.38 thf(fact_2296_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.15/5.38 thf(fact_2297_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat] :
% 5.15/5.38 ( ( ord_less_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.15/5.38 thf(fact_2298_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int] :
% 5.15/5.38 ( ( ord_less_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.15/5.38 thf(fact_2299_mult__less__cancel__right__disj,axiom,
% 5.15/5.38 ! [A: real,C: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 & ( ord_less_real @ A @ B ) )
% 5.15/5.38 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_right_disj
% 5.15/5.38 thf(fact_2300_mult__less__cancel__right__disj,axiom,
% 5.15/5.38 ! [A: rat,C: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 & ( ord_less_rat @ A @ B ) )
% 5.15/5.38 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_right_disj
% 5.15/5.38 thf(fact_2301_mult__less__cancel__right__disj,axiom,
% 5.15/5.38 ! [A: int,C: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.15/5.38 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.38 & ( ord_less_int @ A @ B ) )
% 5.15/5.38 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.38 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_right_disj
% 5.15/5.38 thf(fact_2302_mult__strict__right__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_right_mono
% 5.15/5.38 thf(fact_2303_mult__strict__right__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_right_mono
% 5.15/5.38 thf(fact_2304_mult__strict__right__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat] :
% 5.15/5.38 ( ( ord_less_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_right_mono
% 5.15/5.38 thf(fact_2305_mult__strict__right__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int] :
% 5.15/5.38 ( ( ord_less_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_right_mono
% 5.15/5.38 thf(fact_2306_mult__strict__right__mono__neg,axiom,
% 5.15/5.38 ! [B: real,A: real,C: real] :
% 5.15/5.38 ( ( ord_less_real @ B @ A )
% 5.15/5.38 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_right_mono_neg
% 5.15/5.38 thf(fact_2307_mult__strict__right__mono__neg,axiom,
% 5.15/5.38 ! [B: rat,A: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_rat @ B @ A )
% 5.15/5.38 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_right_mono_neg
% 5.15/5.38 thf(fact_2308_mult__strict__right__mono__neg,axiom,
% 5.15/5.38 ! [B: int,A: int,C: int] :
% 5.15/5.38 ( ( ord_less_int @ B @ A )
% 5.15/5.38 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_right_mono_neg
% 5.15/5.38 thf(fact_2309_mult__less__cancel__left__disj,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 & ( ord_less_real @ A @ B ) )
% 5.15/5.38 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_disj
% 5.15/5.38 thf(fact_2310_mult__less__cancel__left__disj,axiom,
% 5.15/5.38 ! [C: rat,A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 & ( ord_less_rat @ A @ B ) )
% 5.15/5.38 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_disj
% 5.15/5.38 thf(fact_2311_mult__less__cancel__left__disj,axiom,
% 5.15/5.38 ! [C: int,A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.38 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.38 & ( ord_less_int @ A @ B ) )
% 5.15/5.38 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.38 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_disj
% 5.15/5.38 thf(fact_2312_mult__strict__left__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_left_mono
% 5.15/5.38 thf(fact_2313_mult__strict__left__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_left_mono
% 5.15/5.38 thf(fact_2314_mult__strict__left__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat] :
% 5.15/5.38 ( ( ord_less_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_left_mono
% 5.15/5.38 thf(fact_2315_mult__strict__left__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int] :
% 5.15/5.38 ( ( ord_less_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_left_mono
% 5.15/5.38 thf(fact_2316_mult__strict__left__mono__neg,axiom,
% 5.15/5.38 ! [B: real,A: real,C: real] :
% 5.15/5.38 ( ( ord_less_real @ B @ A )
% 5.15/5.38 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_left_mono_neg
% 5.15/5.38 thf(fact_2317_mult__strict__left__mono__neg,axiom,
% 5.15/5.38 ! [B: rat,A: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_rat @ B @ A )
% 5.15/5.38 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_left_mono_neg
% 5.15/5.38 thf(fact_2318_mult__strict__left__mono__neg,axiom,
% 5.15/5.38 ! [B: int,A: int,C: int] :
% 5.15/5.38 ( ( ord_less_int @ B @ A )
% 5.15/5.38 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_left_mono_neg
% 5.15/5.38 thf(fact_2319_mult__less__cancel__left__pos,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.38 = ( ord_less_real @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_pos
% 5.15/5.38 thf(fact_2320_mult__less__cancel__left__pos,axiom,
% 5.15/5.38 ! [C: rat,A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.38 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_pos
% 5.15/5.38 thf(fact_2321_mult__less__cancel__left__pos,axiom,
% 5.15/5.38 ! [C: int,A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.38 = ( ord_less_int @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_pos
% 5.15/5.38 thf(fact_2322_mult__less__cancel__left__neg,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.38 = ( ord_less_real @ B @ A ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_neg
% 5.15/5.38 thf(fact_2323_mult__less__cancel__left__neg,axiom,
% 5.15/5.38 ! [C: rat,A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.38 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_neg
% 5.15/5.38 thf(fact_2324_mult__less__cancel__left__neg,axiom,
% 5.15/5.38 ! [C: int,A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.38 = ( ord_less_int @ B @ A ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left_neg
% 5.15/5.38 thf(fact_2325_zero__less__mult__pos2,axiom,
% 5.15/5.38 ! [B: real,A: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_pos2
% 5.15/5.38 thf(fact_2326_zero__less__mult__pos2,axiom,
% 5.15/5.38 ! [B: rat,A: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_pos2
% 5.15/5.38 thf(fact_2327_zero__less__mult__pos2,axiom,
% 5.15/5.38 ! [B: nat,A: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_pos2
% 5.15/5.38 thf(fact_2328_zero__less__mult__pos2,axiom,
% 5.15/5.38 ! [B: int,A: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_pos2
% 5.15/5.38 thf(fact_2329_zero__less__mult__pos,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_pos
% 5.15/5.38 thf(fact_2330_zero__less__mult__pos,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_pos
% 5.15/5.38 thf(fact_2331_zero__less__mult__pos,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_pos
% 5.15/5.38 thf(fact_2332_zero__less__mult__pos,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_pos
% 5.15/5.38 thf(fact_2333_zero__less__mult__iff,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.15/5.38 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_iff
% 5.15/5.38 thf(fact_2334_zero__less__mult__iff,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.15/5.38 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_iff
% 5.15/5.38 thf(fact_2335_zero__less__mult__iff,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.15/5.38 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.38 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_mult_iff
% 5.15/5.38 thf(fact_2336_mult__pos__neg2,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_neg2
% 5.15/5.38 thf(fact_2337_mult__pos__neg2,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_neg2
% 5.15/5.38 thf(fact_2338_mult__pos__neg2,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_neg2
% 5.15/5.38 thf(fact_2339_mult__pos__neg2,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_neg2
% 5.15/5.38 thf(fact_2340_mult__pos__pos,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_pos
% 5.15/5.38 thf(fact_2341_mult__pos__pos,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_pos
% 5.15/5.38 thf(fact_2342_mult__pos__pos,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_pos
% 5.15/5.38 thf(fact_2343_mult__pos__pos,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_pos
% 5.15/5.38 thf(fact_2344_mult__pos__neg,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_neg
% 5.15/5.38 thf(fact_2345_mult__pos__neg,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_neg
% 5.15/5.38 thf(fact_2346_mult__pos__neg,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_neg
% 5.15/5.38 thf(fact_2347_mult__pos__neg,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_pos_neg
% 5.15/5.38 thf(fact_2348_mult__neg__pos,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_neg_pos
% 5.15/5.38 thf(fact_2349_mult__neg__pos,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_neg_pos
% 5.15/5.38 thf(fact_2350_mult__neg__pos,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_neg_pos
% 5.15/5.38 thf(fact_2351_mult__neg__pos,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_neg_pos
% 5.15/5.38 thf(fact_2352_mult__less__0__iff,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.15/5.38 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_0_iff
% 5.15/5.38 thf(fact_2353_mult__less__0__iff,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.15/5.38 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_0_iff
% 5.15/5.38 thf(fact_2354_mult__less__0__iff,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.15/5.38 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.15/5.38 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.38 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_0_iff
% 5.15/5.38 thf(fact_2355_not__square__less__zero,axiom,
% 5.15/5.38 ! [A: real] :
% 5.15/5.38 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.15/5.38
% 5.15/5.38 % not_square_less_zero
% 5.15/5.38 thf(fact_2356_not__square__less__zero,axiom,
% 5.15/5.38 ! [A: rat] :
% 5.15/5.38 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.15/5.38
% 5.15/5.38 % not_square_less_zero
% 5.15/5.38 thf(fact_2357_not__square__less__zero,axiom,
% 5.15/5.38 ! [A: int] :
% 5.15/5.38 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.15/5.38
% 5.15/5.38 % not_square_less_zero
% 5.15/5.38 thf(fact_2358_mult__neg__neg,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_neg_neg
% 5.15/5.38 thf(fact_2359_mult__neg__neg,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_neg_neg
% 5.15/5.38 thf(fact_2360_mult__neg__neg,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.38 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_neg_neg
% 5.15/5.38 thf(fact_2361_less__numeral__extra_I1_J,axiom,
% 5.15/5.38 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.15/5.38
% 5.15/5.38 % less_numeral_extra(1)
% 5.15/5.38 thf(fact_2362_less__numeral__extra_I1_J,axiom,
% 5.15/5.38 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.15/5.38
% 5.15/5.38 % less_numeral_extra(1)
% 5.15/5.38 thf(fact_2363_less__numeral__extra_I1_J,axiom,
% 5.15/5.38 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.15/5.38
% 5.15/5.38 % less_numeral_extra(1)
% 5.15/5.38 thf(fact_2364_less__numeral__extra_I1_J,axiom,
% 5.15/5.38 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.15/5.38
% 5.15/5.38 % less_numeral_extra(1)
% 5.15/5.38 thf(fact_2365_not__one__less__zero,axiom,
% 5.15/5.38 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.15/5.38
% 5.15/5.38 % not_one_less_zero
% 5.15/5.38 thf(fact_2366_not__one__less__zero,axiom,
% 5.15/5.38 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.15/5.38
% 5.15/5.38 % not_one_less_zero
% 5.15/5.38 thf(fact_2367_not__one__less__zero,axiom,
% 5.15/5.38 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % not_one_less_zero
% 5.15/5.38 thf(fact_2368_not__one__less__zero,axiom,
% 5.15/5.38 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.15/5.38
% 5.15/5.38 % not_one_less_zero
% 5.15/5.38 thf(fact_2369_zero__less__one,axiom,
% 5.15/5.38 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.15/5.38
% 5.15/5.38 % zero_less_one
% 5.15/5.38 thf(fact_2370_zero__less__one,axiom,
% 5.15/5.38 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.15/5.38
% 5.15/5.38 % zero_less_one
% 5.15/5.38 thf(fact_2371_zero__less__one,axiom,
% 5.15/5.38 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.15/5.38
% 5.15/5.38 % zero_less_one
% 5.15/5.38 thf(fact_2372_zero__less__one,axiom,
% 5.15/5.38 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.15/5.38
% 5.15/5.38 % zero_less_one
% 5.15/5.38 thf(fact_2373_add__less__zeroD,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.38 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_less_zeroD
% 5.15/5.38 thf(fact_2374_add__less__zeroD,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.15/5.38 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_less_zeroD
% 5.15/5.38 thf(fact_2375_add__less__zeroD,axiom,
% 5.15/5.38 ! [X: int,Y: int] :
% 5.15/5.38 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.15/5.38 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_less_zeroD
% 5.15/5.38 thf(fact_2376_pos__add__strict,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_real @ B @ C )
% 5.15/5.38 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % pos_add_strict
% 5.15/5.38 thf(fact_2377_pos__add__strict,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_rat @ B @ C )
% 5.15/5.38 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % pos_add_strict
% 5.15/5.38 thf(fact_2378_pos__add__strict,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_nat @ B @ C )
% 5.15/5.38 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % pos_add_strict
% 5.15/5.38 thf(fact_2379_pos__add__strict,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_int @ B @ C )
% 5.15/5.38 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % pos_add_strict
% 5.15/5.38 thf(fact_2380_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ A @ B )
% 5.15/5.38 => ~ ! [C2: nat] :
% 5.15/5.38 ( ( B
% 5.15/5.38 = ( plus_plus_nat @ A @ C2 ) )
% 5.15/5.38 => ( C2 = zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % canonically_ordered_monoid_add_class.lessE
% 5.15/5.38 thf(fact_2381_add__pos__pos,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_pos_pos
% 5.15/5.38 thf(fact_2382_add__pos__pos,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_pos_pos
% 5.15/5.38 thf(fact_2383_add__pos__pos,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_pos_pos
% 5.15/5.38 thf(fact_2384_add__pos__pos,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_pos_pos
% 5.15/5.38 thf(fact_2385_add__neg__neg,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_neg_neg
% 5.15/5.38 thf(fact_2386_add__neg__neg,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_neg_neg
% 5.15/5.38 thf(fact_2387_add__neg__neg,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.15/5.38 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.15/5.38 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_neg_neg
% 5.15/5.38 thf(fact_2388_add__neg__neg,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.38 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.38 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_neg_neg
% 5.15/5.38 thf(fact_2389_le__iff__diff__le__0,axiom,
% 5.15/5.38 ( ord_less_eq_real
% 5.15/5.38 = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % le_iff_diff_le_0
% 5.15/5.38 thf(fact_2390_le__iff__diff__le__0,axiom,
% 5.15/5.38 ( ord_less_eq_rat
% 5.15/5.38 = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % le_iff_diff_le_0
% 5.15/5.38 thf(fact_2391_le__iff__diff__le__0,axiom,
% 5.15/5.38 ( ord_less_eq_int
% 5.15/5.38 = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % le_iff_diff_le_0
% 5.15/5.38 thf(fact_2392_divide__le__0__iff,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.15/5.38 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.15/5.38 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_le_0_iff
% 5.15/5.38 thf(fact_2393_divide__le__0__iff,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.15/5.38 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.15/5.38 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_le_0_iff
% 5.15/5.38 thf(fact_2394_divide__right__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_right_mono
% 5.15/5.38 thf(fact_2395_divide__right__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_right_mono
% 5.15/5.38 thf(fact_2396_zero__le__divide__iff,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.15/5.38 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_divide_iff
% 5.15/5.38 thf(fact_2397_zero__le__divide__iff,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.15/5.38 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_divide_iff
% 5.15/5.38 thf(fact_2398_divide__nonneg__nonneg,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_nonneg_nonneg
% 5.15/5.38 thf(fact_2399_divide__nonneg__nonneg,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_nonneg_nonneg
% 5.15/5.38 thf(fact_2400_divide__nonneg__nonpos,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.38 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_nonneg_nonpos
% 5.15/5.38 thf(fact_2401_divide__nonneg__nonpos,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.38 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_nonneg_nonpos
% 5.15/5.38 thf(fact_2402_divide__nonpos__nonneg,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.38 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_nonpos_nonneg
% 5.15/5.38 thf(fact_2403_divide__nonpos__nonneg,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.38 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_nonpos_nonneg
% 5.15/5.38 thf(fact_2404_divide__nonpos__nonpos,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_nonpos_nonpos
% 5.15/5.38 thf(fact_2405_divide__nonpos__nonpos,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_nonpos_nonpos
% 5.15/5.38 thf(fact_2406_divide__right__mono__neg,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_right_mono_neg
% 5.15/5.38 thf(fact_2407_divide__right__mono__neg,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_right_mono_neg
% 5.15/5.38 thf(fact_2408_less__iff__diff__less__0,axiom,
% 5.15/5.38 ( ord_less_real
% 5.15/5.38 = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % less_iff_diff_less_0
% 5.15/5.38 thf(fact_2409_less__iff__diff__less__0,axiom,
% 5.15/5.38 ( ord_less_rat
% 5.15/5.38 = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % less_iff_diff_less_0
% 5.15/5.38 thf(fact_2410_less__iff__diff__less__0,axiom,
% 5.15/5.38 ( ord_less_int
% 5.15/5.38 = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % less_iff_diff_less_0
% 5.15/5.38 thf(fact_2411_divide__strict__right__mono__neg,axiom,
% 5.15/5.38 ! [B: real,A: real,C: real] :
% 5.15/5.38 ( ( ord_less_real @ B @ A )
% 5.15/5.38 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_strict_right_mono_neg
% 5.15/5.38 thf(fact_2412_divide__strict__right__mono__neg,axiom,
% 5.15/5.38 ! [B: rat,A: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_rat @ B @ A )
% 5.15/5.38 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_strict_right_mono_neg
% 5.15/5.38 thf(fact_2413_divide__strict__right__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( ord_less_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_strict_right_mono
% 5.15/5.38 thf(fact_2414_divide__strict__right__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_strict_right_mono
% 5.15/5.38 thf(fact_2415_zero__less__divide__iff,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.15/5.38 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_divide_iff
% 5.15/5.38 thf(fact_2416_zero__less__divide__iff,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.15/5.38 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_divide_iff
% 5.15/5.38 thf(fact_2417_divide__less__cancel,axiom,
% 5.15/5.38 ! [A: real,C: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_real @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ B @ A ) )
% 5.15/5.38 & ( C != zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_less_cancel
% 5.15/5.38 thf(fact_2418_divide__less__cancel,axiom,
% 5.15/5.38 ! [A: rat,C: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_rat @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ B @ A ) )
% 5.15/5.38 & ( C != zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_less_cancel
% 5.15/5.38 thf(fact_2419_divide__less__0__iff,axiom,
% 5.15/5.38 ! [A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.15/5.38 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.38 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_less_0_iff
% 5.15/5.38 thf(fact_2420_divide__less__0__iff,axiom,
% 5.15/5.38 ! [A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.15/5.38 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.38 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_less_0_iff
% 5.15/5.38 thf(fact_2421_divide__pos__pos,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.38 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_pos_pos
% 5.15/5.38 thf(fact_2422_divide__pos__pos,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.38 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_pos_pos
% 5.15/5.38 thf(fact_2423_divide__pos__neg,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.38 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_pos_neg
% 5.15/5.38 thf(fact_2424_divide__pos__neg,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.15/5.38 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_pos_neg
% 5.15/5.38 thf(fact_2425_divide__neg__pos,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.38 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_neg_pos
% 5.15/5.38 thf(fact_2426_divide__neg__pos,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.38 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_neg_pos
% 5.15/5.38 thf(fact_2427_divide__neg__neg,axiom,
% 5.15/5.38 ! [X: real,Y: real] :
% 5.15/5.38 ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.38 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_neg_neg
% 5.15/5.38 thf(fact_2428_divide__neg__neg,axiom,
% 5.15/5.38 ! [X: rat,Y: rat] :
% 5.15/5.38 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.15/5.38 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_neg_neg
% 5.15/5.38 thf(fact_2429_power__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_mono
% 5.15/5.38 thf(fact_2430_power__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_mono
% 5.15/5.38 thf(fact_2431_power__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_mono
% 5.15/5.38 thf(fact_2432_power__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % power_mono
% 5.15/5.38 thf(fact_2433_zero__le__power,axiom,
% 5.15/5.38 ! [A: real,N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_power
% 5.15/5.38 thf(fact_2434_zero__le__power,axiom,
% 5.15/5.38 ! [A: rat,N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_power
% 5.15/5.38 thf(fact_2435_zero__le__power,axiom,
% 5.15/5.38 ! [A: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_power
% 5.15/5.38 thf(fact_2436_zero__le__power,axiom,
% 5.15/5.38 ! [A: int,N2: nat] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_le_power
% 5.15/5.38 thf(fact_2437_zero__less__power,axiom,
% 5.15/5.38 ! [A: real,N2: nat] :
% 5.15/5.38 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.38 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_power
% 5.15/5.38 thf(fact_2438_zero__less__power,axiom,
% 5.15/5.38 ! [A: rat,N2: nat] :
% 5.15/5.38 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.38 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_power
% 5.15/5.38 thf(fact_2439_zero__less__power,axiom,
% 5.15/5.38 ! [A: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_power
% 5.15/5.38 thf(fact_2440_zero__less__power,axiom,
% 5.15/5.38 ! [A: int,N2: nat] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % zero_less_power
% 5.15/5.38 thf(fact_2441_nonzero__eq__divide__eq,axiom,
% 5.15/5.38 ! [C: complex,A: complex,B: complex] :
% 5.15/5.38 ( ( C != zero_zero_complex )
% 5.15/5.38 => ( ( A
% 5.15/5.38 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.38 = ( ( times_times_complex @ A @ C )
% 5.15/5.38 = B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nonzero_eq_divide_eq
% 5.15/5.38 thf(fact_2442_nonzero__eq__divide__eq,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( C != zero_zero_real )
% 5.15/5.38 => ( ( A
% 5.15/5.38 = ( divide_divide_real @ B @ C ) )
% 5.15/5.38 = ( ( times_times_real @ A @ C )
% 5.15/5.38 = B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nonzero_eq_divide_eq
% 5.15/5.38 thf(fact_2443_nonzero__eq__divide__eq,axiom,
% 5.15/5.38 ! [C: rat,A: rat,B: rat] :
% 5.15/5.38 ( ( C != zero_zero_rat )
% 5.15/5.38 => ( ( A
% 5.15/5.38 = ( divide_divide_rat @ B @ C ) )
% 5.15/5.38 = ( ( times_times_rat @ A @ C )
% 5.15/5.38 = B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nonzero_eq_divide_eq
% 5.15/5.38 thf(fact_2444_nonzero__divide__eq__eq,axiom,
% 5.15/5.38 ! [C: complex,B: complex,A: complex] :
% 5.15/5.38 ( ( C != zero_zero_complex )
% 5.15/5.38 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.15/5.38 = A )
% 5.15/5.38 = ( B
% 5.15/5.38 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nonzero_divide_eq_eq
% 5.15/5.38 thf(fact_2445_nonzero__divide__eq__eq,axiom,
% 5.15/5.38 ! [C: real,B: real,A: real] :
% 5.15/5.38 ( ( C != zero_zero_real )
% 5.15/5.38 => ( ( ( divide_divide_real @ B @ C )
% 5.15/5.38 = A )
% 5.15/5.38 = ( B
% 5.15/5.38 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nonzero_divide_eq_eq
% 5.15/5.38 thf(fact_2446_nonzero__divide__eq__eq,axiom,
% 5.15/5.38 ! [C: rat,B: rat,A: rat] :
% 5.15/5.38 ( ( C != zero_zero_rat )
% 5.15/5.38 => ( ( ( divide_divide_rat @ B @ C )
% 5.15/5.38 = A )
% 5.15/5.38 = ( B
% 5.15/5.38 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nonzero_divide_eq_eq
% 5.15/5.38 thf(fact_2447_eq__divide__imp,axiom,
% 5.15/5.38 ! [C: complex,A: complex,B: complex] :
% 5.15/5.38 ( ( C != zero_zero_complex )
% 5.15/5.38 => ( ( ( times_times_complex @ A @ C )
% 5.15/5.38 = B )
% 5.15/5.38 => ( A
% 5.15/5.38 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_divide_imp
% 5.15/5.38 thf(fact_2448_eq__divide__imp,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( C != zero_zero_real )
% 5.15/5.38 => ( ( ( times_times_real @ A @ C )
% 5.15/5.38 = B )
% 5.15/5.38 => ( A
% 5.15/5.38 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_divide_imp
% 5.15/5.38 thf(fact_2449_eq__divide__imp,axiom,
% 5.15/5.38 ! [C: rat,A: rat,B: rat] :
% 5.15/5.38 ( ( C != zero_zero_rat )
% 5.15/5.38 => ( ( ( times_times_rat @ A @ C )
% 5.15/5.38 = B )
% 5.15/5.38 => ( A
% 5.15/5.38 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_divide_imp
% 5.15/5.38 thf(fact_2450_divide__eq__imp,axiom,
% 5.15/5.38 ! [C: complex,B: complex,A: complex] :
% 5.15/5.38 ( ( C != zero_zero_complex )
% 5.15/5.38 => ( ( B
% 5.15/5.38 = ( times_times_complex @ A @ C ) )
% 5.15/5.38 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.15/5.38 = A ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_eq_imp
% 5.15/5.38 thf(fact_2451_divide__eq__imp,axiom,
% 5.15/5.38 ! [C: real,B: real,A: real] :
% 5.15/5.38 ( ( C != zero_zero_real )
% 5.15/5.38 => ( ( B
% 5.15/5.38 = ( times_times_real @ A @ C ) )
% 5.15/5.38 => ( ( divide_divide_real @ B @ C )
% 5.15/5.38 = A ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_eq_imp
% 5.15/5.38 thf(fact_2452_divide__eq__imp,axiom,
% 5.15/5.38 ! [C: rat,B: rat,A: rat] :
% 5.15/5.38 ( ( C != zero_zero_rat )
% 5.15/5.38 => ( ( B
% 5.15/5.38 = ( times_times_rat @ A @ C ) )
% 5.15/5.38 => ( ( divide_divide_rat @ B @ C )
% 5.15/5.38 = A ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_eq_imp
% 5.15/5.38 thf(fact_2453_eq__divide__eq,axiom,
% 5.15/5.38 ! [A: complex,B: complex,C: complex] :
% 5.15/5.38 ( ( A
% 5.15/5.38 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.38 = ( ( ( C != zero_zero_complex )
% 5.15/5.38 => ( ( times_times_complex @ A @ C )
% 5.15/5.38 = B ) )
% 5.15/5.38 & ( ( C = zero_zero_complex )
% 5.15/5.38 => ( A = zero_zero_complex ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_divide_eq
% 5.15/5.38 thf(fact_2454_eq__divide__eq,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real] :
% 5.15/5.38 ( ( A
% 5.15/5.38 = ( divide_divide_real @ B @ C ) )
% 5.15/5.38 = ( ( ( C != zero_zero_real )
% 5.15/5.38 => ( ( times_times_real @ A @ C )
% 5.15/5.38 = B ) )
% 5.15/5.38 & ( ( C = zero_zero_real )
% 5.15/5.38 => ( A = zero_zero_real ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_divide_eq
% 5.15/5.38 thf(fact_2455_eq__divide__eq,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat] :
% 5.15/5.38 ( ( A
% 5.15/5.38 = ( divide_divide_rat @ B @ C ) )
% 5.15/5.38 = ( ( ( C != zero_zero_rat )
% 5.15/5.38 => ( ( times_times_rat @ A @ C )
% 5.15/5.38 = B ) )
% 5.15/5.38 & ( ( C = zero_zero_rat )
% 5.15/5.38 => ( A = zero_zero_rat ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % eq_divide_eq
% 5.15/5.38 thf(fact_2456_divide__eq__eq,axiom,
% 5.15/5.38 ! [B: complex,C: complex,A: complex] :
% 5.15/5.38 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.15/5.38 = A )
% 5.15/5.38 = ( ( ( C != zero_zero_complex )
% 5.15/5.38 => ( B
% 5.15/5.38 = ( times_times_complex @ A @ C ) ) )
% 5.15/5.38 & ( ( C = zero_zero_complex )
% 5.15/5.38 => ( A = zero_zero_complex ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_eq_eq
% 5.15/5.38 thf(fact_2457_divide__eq__eq,axiom,
% 5.15/5.38 ! [B: real,C: real,A: real] :
% 5.15/5.38 ( ( ( divide_divide_real @ B @ C )
% 5.15/5.38 = A )
% 5.15/5.38 = ( ( ( C != zero_zero_real )
% 5.15/5.38 => ( B
% 5.15/5.38 = ( times_times_real @ A @ C ) ) )
% 5.15/5.38 & ( ( C = zero_zero_real )
% 5.15/5.38 => ( A = zero_zero_real ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_eq_eq
% 5.15/5.38 thf(fact_2458_divide__eq__eq,axiom,
% 5.15/5.38 ! [B: rat,C: rat,A: rat] :
% 5.15/5.38 ( ( ( divide_divide_rat @ B @ C )
% 5.15/5.38 = A )
% 5.15/5.38 = ( ( ( C != zero_zero_rat )
% 5.15/5.38 => ( B
% 5.15/5.38 = ( times_times_rat @ A @ C ) ) )
% 5.15/5.38 & ( ( C = zero_zero_rat )
% 5.15/5.38 => ( A = zero_zero_rat ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % divide_eq_eq
% 5.15/5.38 thf(fact_2459_frac__eq__eq,axiom,
% 5.15/5.38 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.15/5.38 ( ( Y != zero_zero_complex )
% 5.15/5.38 => ( ( Z != zero_zero_complex )
% 5.15/5.38 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 5.15/5.38 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.15/5.38 = ( ( times_times_complex @ X @ Z )
% 5.15/5.38 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % frac_eq_eq
% 5.15/5.38 thf(fact_2460_frac__eq__eq,axiom,
% 5.15/5.38 ! [Y: real,Z: real,X: real,W: real] :
% 5.15/5.38 ( ( Y != zero_zero_real )
% 5.15/5.38 => ( ( Z != zero_zero_real )
% 5.15/5.38 => ( ( ( divide_divide_real @ X @ Y )
% 5.15/5.38 = ( divide_divide_real @ W @ Z ) )
% 5.15/5.38 = ( ( times_times_real @ X @ Z )
% 5.15/5.38 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % frac_eq_eq
% 5.15/5.38 thf(fact_2461_frac__eq__eq,axiom,
% 5.15/5.38 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.15/5.38 ( ( Y != zero_zero_rat )
% 5.15/5.38 => ( ( Z != zero_zero_rat )
% 5.15/5.38 => ( ( ( divide_divide_rat @ X @ Y )
% 5.15/5.38 = ( divide_divide_rat @ W @ Z ) )
% 5.15/5.38 = ( ( times_times_rat @ X @ Z )
% 5.15/5.38 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % frac_eq_eq
% 5.15/5.38 thf(fact_2462_right__inverse__eq,axiom,
% 5.15/5.38 ! [B: complex,A: complex] :
% 5.15/5.38 ( ( B != zero_zero_complex )
% 5.15/5.38 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.15/5.38 = one_one_complex )
% 5.15/5.38 = ( A = B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % right_inverse_eq
% 5.15/5.38 thf(fact_2463_right__inverse__eq,axiom,
% 5.15/5.38 ! [B: real,A: real] :
% 5.15/5.38 ( ( B != zero_zero_real )
% 5.15/5.38 => ( ( ( divide_divide_real @ A @ B )
% 5.15/5.38 = one_one_real )
% 5.15/5.38 = ( A = B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % right_inverse_eq
% 5.15/5.38 thf(fact_2464_right__inverse__eq,axiom,
% 5.15/5.38 ! [B: rat,A: rat] :
% 5.15/5.38 ( ( B != zero_zero_rat )
% 5.15/5.38 => ( ( ( divide_divide_rat @ A @ B )
% 5.15/5.38 = one_one_rat )
% 5.15/5.38 = ( A = B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % right_inverse_eq
% 5.15/5.38 thf(fact_2465_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.15/5.38 ! [A: code_integer,B: code_integer] :
% 5.15/5.38 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.38 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.15/5.38
% 5.15/5.38 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.15/5.38 thf(fact_2466_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.38 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.15/5.38
% 5.15/5.38 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.15/5.38 thf(fact_2467_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.38 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.15/5.38
% 5.15/5.38 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.15/5.38 thf(fact_2468_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.15/5.38 ! [B: nat,A: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.15/5.38
% 5.15/5.38 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.15/5.38 thf(fact_2469_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.15/5.38 ! [B: int,A: int] :
% 5.15/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.15/5.38
% 5.15/5.38 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.15/5.38 thf(fact_2470_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.15/5.38 ! [B: code_integer,A: code_integer] :
% 5.15/5.38 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.38 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.15/5.38
% 5.15/5.38 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.15/5.38 thf(fact_2471_power__0,axiom,
% 5.15/5.38 ! [A: rat] :
% 5.15/5.38 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.15/5.38 = one_one_rat ) ).
% 5.15/5.38
% 5.15/5.38 % power_0
% 5.15/5.38 thf(fact_2472_power__0,axiom,
% 5.15/5.38 ! [A: nat] :
% 5.15/5.38 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.15/5.38 = one_one_nat ) ).
% 5.15/5.38
% 5.15/5.38 % power_0
% 5.15/5.38 thf(fact_2473_power__0,axiom,
% 5.15/5.38 ! [A: real] :
% 5.15/5.38 ( ( power_power_real @ A @ zero_zero_nat )
% 5.15/5.38 = one_one_real ) ).
% 5.15/5.38
% 5.15/5.38 % power_0
% 5.15/5.38 thf(fact_2474_power__0,axiom,
% 5.15/5.38 ! [A: complex] :
% 5.15/5.38 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.15/5.38 = one_one_complex ) ).
% 5.15/5.38
% 5.15/5.38 % power_0
% 5.15/5.38 thf(fact_2475_power__0,axiom,
% 5.15/5.38 ! [A: int] :
% 5.15/5.38 ( ( power_power_int @ A @ zero_zero_nat )
% 5.15/5.38 = one_one_int ) ).
% 5.15/5.38
% 5.15/5.38 % power_0
% 5.15/5.38 thf(fact_2476_mod__eq__self__iff__div__eq__0,axiom,
% 5.15/5.38 ! [A: nat,B: nat] :
% 5.15/5.38 ( ( ( modulo_modulo_nat @ A @ B )
% 5.15/5.38 = A )
% 5.15/5.38 = ( ( divide_divide_nat @ A @ B )
% 5.15/5.38 = zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % mod_eq_self_iff_div_eq_0
% 5.15/5.38 thf(fact_2477_mod__eq__self__iff__div__eq__0,axiom,
% 5.15/5.38 ! [A: int,B: int] :
% 5.15/5.38 ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.38 = A )
% 5.15/5.38 = ( ( divide_divide_int @ A @ B )
% 5.15/5.38 = zero_zero_int ) ) ).
% 5.15/5.38
% 5.15/5.38 % mod_eq_self_iff_div_eq_0
% 5.15/5.38 thf(fact_2478_mod__eq__self__iff__div__eq__0,axiom,
% 5.15/5.38 ! [A: code_integer,B: code_integer] :
% 5.15/5.38 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.15/5.38 = A )
% 5.15/5.38 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.15/5.38 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.38
% 5.15/5.38 % mod_eq_self_iff_div_eq_0
% 5.15/5.38 thf(fact_2479_less__Suc__eq__0__disj,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.15/5.38 = ( ( M = zero_zero_nat )
% 5.15/5.38 | ? [J3: nat] :
% 5.15/5.38 ( ( M
% 5.15/5.38 = ( suc @ J3 ) )
% 5.15/5.38 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % less_Suc_eq_0_disj
% 5.15/5.38 thf(fact_2480_gr0__implies__Suc,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ? [M3: nat] :
% 5.15/5.38 ( N2
% 5.15/5.38 = ( suc @ M3 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % gr0_implies_Suc
% 5.15/5.38 thf(fact_2481_All__less__Suc2,axiom,
% 5.15/5.38 ! [N2: nat,P: nat > $o] :
% 5.15/5.38 ( ( ! [I3: nat] :
% 5.15/5.38 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 5.15/5.38 => ( P @ I3 ) ) )
% 5.15/5.38 = ( ( P @ zero_zero_nat )
% 5.15/5.38 & ! [I3: nat] :
% 5.15/5.38 ( ( ord_less_nat @ I3 @ N2 )
% 5.15/5.38 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % All_less_Suc2
% 5.15/5.38 thf(fact_2482_gr0__conv__Suc,axiom,
% 5.15/5.38 ! [N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 = ( ? [M5: nat] :
% 5.15/5.38 ( N2
% 5.15/5.38 = ( suc @ M5 ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % gr0_conv_Suc
% 5.15/5.38 thf(fact_2483_Ex__less__Suc2,axiom,
% 5.15/5.38 ! [N2: nat,P: nat > $o] :
% 5.15/5.38 ( ( ? [I3: nat] :
% 5.15/5.38 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 5.15/5.38 & ( P @ I3 ) ) )
% 5.15/5.38 = ( ( P @ zero_zero_nat )
% 5.15/5.38 | ? [I3: nat] :
% 5.15/5.38 ( ( ord_less_nat @ I3 @ N2 )
% 5.15/5.38 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % Ex_less_Suc2
% 5.15/5.38 thf(fact_2484_one__is__add,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( ( suc @ zero_zero_nat )
% 5.15/5.38 = ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.38 = ( ( ( M
% 5.15/5.38 = ( suc @ zero_zero_nat ) )
% 5.15/5.38 & ( N2 = zero_zero_nat ) )
% 5.15/5.38 | ( ( M = zero_zero_nat )
% 5.15/5.38 & ( N2
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % one_is_add
% 5.15/5.38 thf(fact_2485_add__is__1,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( ( plus_plus_nat @ M @ N2 )
% 5.15/5.38 = ( suc @ zero_zero_nat ) )
% 5.15/5.38 = ( ( ( M
% 5.15/5.38 = ( suc @ zero_zero_nat ) )
% 5.15/5.38 & ( N2 = zero_zero_nat ) )
% 5.15/5.38 | ( ( M = zero_zero_nat )
% 5.15/5.38 & ( N2
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % add_is_1
% 5.15/5.38 thf(fact_2486_option_Osize_I4_J,axiom,
% 5.15/5.38 ! [X22: product_prod_nat_nat] :
% 5.15/5.38 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % option.size(4)
% 5.15/5.38 thf(fact_2487_option_Osize_I4_J,axiom,
% 5.15/5.38 ! [X22: nat] :
% 5.15/5.38 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % option.size(4)
% 5.15/5.38 thf(fact_2488_option_Osize_I4_J,axiom,
% 5.15/5.38 ! [X22: num] :
% 5.15/5.38 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % option.size(4)
% 5.15/5.38 thf(fact_2489_ex__least__nat__le,axiom,
% 5.15/5.38 ! [P: nat > $o,N2: nat] :
% 5.15/5.38 ( ( P @ N2 )
% 5.15/5.38 => ( ~ ( P @ zero_zero_nat )
% 5.15/5.38 => ? [K3: nat] :
% 5.15/5.38 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.15/5.38 & ! [I4: nat] :
% 5.15/5.38 ( ( ord_less_nat @ I4 @ K3 )
% 5.15/5.38 => ~ ( P @ I4 ) )
% 5.15/5.38 & ( P @ K3 ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % ex_least_nat_le
% 5.15/5.38 thf(fact_2490_less__imp__add__positive,axiom,
% 5.15/5.38 ! [I: nat,J: nat] :
% 5.15/5.38 ( ( ord_less_nat @ I @ J )
% 5.15/5.38 => ? [K3: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 5.15/5.38 & ( ( plus_plus_nat @ I @ K3 )
% 5.15/5.38 = J ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % less_imp_add_positive
% 5.15/5.38 thf(fact_2491_One__nat__def,axiom,
% 5.15/5.38 ( one_one_nat
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % One_nat_def
% 5.15/5.38 thf(fact_2492_option_Osize_I3_J,axiom,
% 5.15/5.38 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % option.size(3)
% 5.15/5.38 thf(fact_2493_option_Osize_I3_J,axiom,
% 5.15/5.38 ( ( size_size_option_nat @ none_nat )
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % option.size(3)
% 5.15/5.38 thf(fact_2494_option_Osize_I3_J,axiom,
% 5.15/5.38 ( ( size_size_option_num @ none_num )
% 5.15/5.38 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.38
% 5.15/5.38 % option.size(3)
% 5.15/5.38 thf(fact_2495_diff__less,axiom,
% 5.15/5.38 ! [N2: nat,M: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.38 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % diff_less
% 5.15/5.38 thf(fact_2496_mult__less__mono1,axiom,
% 5.15/5.38 ! [I: nat,J: nat,K: nat] :
% 5.15/5.38 ( ( ord_less_nat @ I @ J )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_mono1
% 5.15/5.38 thf(fact_2497_mult__less__mono2,axiom,
% 5.15/5.38 ! [I: nat,J: nat,K: nat] :
% 5.15/5.38 ( ( ord_less_nat @ I @ J )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_mono2
% 5.15/5.38 thf(fact_2498_nat__mult__eq__cancel1,axiom,
% 5.15/5.38 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.38 => ( ( ( times_times_nat @ K @ M )
% 5.15/5.38 = ( times_times_nat @ K @ N2 ) )
% 5.15/5.38 = ( M = N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nat_mult_eq_cancel1
% 5.15/5.38 thf(fact_2499_nat__mult__less__cancel1,axiom,
% 5.15/5.38 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.38 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.38 = ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nat_mult_less_cancel1
% 5.15/5.38 thf(fact_2500_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( ( divide_divide_nat @ M @ N2 )
% 5.15/5.38 = zero_zero_nat )
% 5.15/5.38 = ( ( ord_less_nat @ M @ N2 )
% 5.15/5.38 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % Euclidean_Division.div_eq_0_iff
% 5.15/5.38 thf(fact_2501_diff__add__0,axiom,
% 5.15/5.38 ! [N2: nat,M: nat] :
% 5.15/5.38 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.38 = zero_zero_nat ) ).
% 5.15/5.38
% 5.15/5.38 % diff_add_0
% 5.15/5.38 thf(fact_2502_nat__power__less__imp__less,axiom,
% 5.15/5.38 ! [I: nat,M: nat,N2: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.15/5.38 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N2 ) )
% 5.15/5.38 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % nat_power_less_imp_less
% 5.15/5.38 thf(fact_2503_mult__eq__self__implies__10,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( M
% 5.15/5.38 = ( times_times_nat @ M @ N2 ) )
% 5.15/5.38 => ( ( N2 = one_one_nat )
% 5.15/5.38 | ( M = zero_zero_nat ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_eq_self_implies_10
% 5.15/5.38 thf(fact_2504_mod__Suc,axiom,
% 5.15/5.38 ! [M: nat,N2: nat] :
% 5.15/5.38 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.15/5.38 = N2 )
% 5.15/5.38 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 5.15/5.38 = zero_zero_nat ) )
% 5.15/5.38 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.15/5.38 != N2 )
% 5.15/5.38 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 5.15/5.38 = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mod_Suc
% 5.15/5.38 thf(fact_2505_mod__less__divisor,axiom,
% 5.15/5.38 ! [N2: nat,M: nat] :
% 5.15/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.38 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.15/5.38
% 5.15/5.38 % mod_less_divisor
% 5.15/5.38 thf(fact_2506_mod__eq__0D,axiom,
% 5.15/5.38 ! [M: nat,D: nat] :
% 5.15/5.38 ( ( ( modulo_modulo_nat @ M @ D )
% 5.15/5.38 = zero_zero_nat )
% 5.15/5.38 => ? [Q2: nat] :
% 5.15/5.38 ( M
% 5.15/5.38 = ( times_times_nat @ D @ Q2 ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mod_eq_0D
% 5.15/5.38 thf(fact_2507_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.15/5.38 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.15/5.38 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.15/5.38 = none_P5556105721700978146at_nat ) ).
% 5.15/5.38
% 5.15/5.38 % VEBT_internal.option_shift.simps(2)
% 5.15/5.38 thf(fact_2508_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.15/5.38 ! [Uw: num > num > num,V: num] :
% 5.15/5.38 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.15/5.38 = none_num ) ).
% 5.15/5.38
% 5.15/5.38 % VEBT_internal.option_shift.simps(2)
% 5.15/5.38 thf(fact_2509_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.15/5.38 ! [Uw: nat > nat > nat,V: nat] :
% 5.15/5.38 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.15/5.38 = none_nat ) ).
% 5.15/5.38
% 5.15/5.38 % VEBT_internal.option_shift.simps(2)
% 5.15/5.38 thf(fact_2510_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.15/5.38 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 5.15/5.38 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 5.15/5.38 = Y )
% 5.15/5.38 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.15/5.38 => ( Y != none_P5556105721700978146at_nat ) )
% 5.15/5.38 => ( ( ? [V2: product_prod_nat_nat] :
% 5.15/5.38 ( Xa2
% 5.15/5.38 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.15/5.38 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.15/5.38 => ( Y != none_P5556105721700978146at_nat ) ) )
% 5.15/5.38 => ~ ! [A5: product_prod_nat_nat] :
% 5.15/5.38 ( ( Xa2
% 5.15/5.38 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.15/5.38 => ! [B6: product_prod_nat_nat] :
% 5.15/5.38 ( ( Xb
% 5.15/5.38 = ( some_P7363390416028606310at_nat @ B6 ) )
% 5.15/5.38 => ( Y
% 5.15/5.38 != ( some_P7363390416028606310at_nat @ ( X @ A5 @ B6 ) ) ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % VEBT_internal.option_shift.elims
% 5.15/5.38 thf(fact_2511_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.15/5.38 ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y: option_num] :
% 5.15/5.38 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 5.15/5.38 = Y )
% 5.15/5.38 => ( ( ( Xa2 = none_num )
% 5.15/5.38 => ( Y != none_num ) )
% 5.15/5.38 => ( ( ? [V2: num] :
% 5.15/5.38 ( Xa2
% 5.15/5.38 = ( some_num @ V2 ) )
% 5.15/5.38 => ( ( Xb = none_num )
% 5.15/5.38 => ( Y != none_num ) ) )
% 5.15/5.38 => ~ ! [A5: num] :
% 5.15/5.38 ( ( Xa2
% 5.15/5.38 = ( some_num @ A5 ) )
% 5.15/5.38 => ! [B6: num] :
% 5.15/5.38 ( ( Xb
% 5.15/5.38 = ( some_num @ B6 ) )
% 5.15/5.38 => ( Y
% 5.15/5.38 != ( some_num @ ( X @ A5 @ B6 ) ) ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % VEBT_internal.option_shift.elims
% 5.15/5.38 thf(fact_2512_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.15/5.38 ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y: option_nat] :
% 5.15/5.38 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 5.15/5.38 = Y )
% 5.15/5.38 => ( ( ( Xa2 = none_nat )
% 5.15/5.38 => ( Y != none_nat ) )
% 5.15/5.38 => ( ( ? [V2: nat] :
% 5.15/5.38 ( Xa2
% 5.15/5.38 = ( some_nat @ V2 ) )
% 5.15/5.38 => ( ( Xb = none_nat )
% 5.15/5.38 => ( Y != none_nat ) ) )
% 5.15/5.38 => ~ ! [A5: nat] :
% 5.15/5.38 ( ( Xa2
% 5.15/5.38 = ( some_nat @ A5 ) )
% 5.15/5.38 => ! [B6: nat] :
% 5.15/5.38 ( ( Xb
% 5.15/5.38 = ( some_nat @ B6 ) )
% 5.15/5.38 => ( Y
% 5.15/5.38 != ( some_nat @ ( X @ A5 @ B6 ) ) ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % VEBT_internal.option_shift.elims
% 5.15/5.38 thf(fact_2513_vebt__insert_Osimps_I2_J,axiom,
% 5.15/5.38 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.15/5.38 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 5.15/5.38 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 5.15/5.38
% 5.15/5.38 % vebt_insert.simps(2)
% 5.15/5.38 thf(fact_2514_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.15/5.38 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.15/5.38 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.15/5.38
% 5.15/5.38 % VEBT_internal.naive_member.simps(2)
% 5.15/5.38 thf(fact_2515_mult__le__cancel__left,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_eq_real @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_cancel_left
% 5.15/5.38 thf(fact_2516_mult__le__cancel__left,axiom,
% 5.15/5.38 ! [C: rat,A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_cancel_left
% 5.15/5.38 thf(fact_2517_mult__le__cancel__left,axiom,
% 5.15/5.38 ! [C: int,A: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.38 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_eq_int @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.38 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_cancel_left
% 5.15/5.38 thf(fact_2518_mult__le__cancel__right,axiom,
% 5.15/5.38 ! [A: real,C: real,B: real] :
% 5.15/5.38 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.15/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_eq_real @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_cancel_right
% 5.15/5.38 thf(fact_2519_mult__le__cancel__right,axiom,
% 5.15/5.38 ! [A: rat,C: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.15/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_eq_rat @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.38 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_cancel_right
% 5.15/5.38 thf(fact_2520_mult__le__cancel__right,axiom,
% 5.15/5.38 ! [A: int,C: int,B: int] :
% 5.15/5.38 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.15/5.38 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_eq_int @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.38 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_le_cancel_right
% 5.15/5.38 thf(fact_2521_mult__left__less__imp__less,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_real @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_less_imp_less
% 5.15/5.38 thf(fact_2522_mult__left__less__imp__less,axiom,
% 5.15/5.38 ! [C: rat,A: rat,B: rat] :
% 5.15/5.38 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_less_imp_less
% 5.15/5.38 thf(fact_2523_mult__left__less__imp__less,axiom,
% 5.15/5.38 ! [C: nat,A: nat,B: nat] :
% 5.15/5.38 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_less_imp_less
% 5.15/5.38 thf(fact_2524_mult__left__less__imp__less,axiom,
% 5.15/5.38 ! [C: int,A: int,B: int] :
% 5.15/5.38 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_int @ A @ B ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_left_less_imp_less
% 5.15/5.38 thf(fact_2525_mult__strict__mono,axiom,
% 5.15/5.38 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.38 ( ( ord_less_real @ A @ B )
% 5.15/5.38 => ( ( ord_less_real @ C @ D )
% 5.15/5.38 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.38 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_mono
% 5.15/5.38 thf(fact_2526_mult__strict__mono,axiom,
% 5.15/5.38 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.38 ( ( ord_less_rat @ A @ B )
% 5.15/5.38 => ( ( ord_less_rat @ C @ D )
% 5.15/5.38 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.15/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.38 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_mono
% 5.15/5.38 thf(fact_2527_mult__strict__mono,axiom,
% 5.15/5.38 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.38 ( ( ord_less_nat @ A @ B )
% 5.15/5.38 => ( ( ord_less_nat @ C @ D )
% 5.15/5.38 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.38 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.38 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_mono
% 5.15/5.38 thf(fact_2528_mult__strict__mono,axiom,
% 5.15/5.38 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.38 ( ( ord_less_int @ A @ B )
% 5.15/5.38 => ( ( ord_less_int @ C @ D )
% 5.15/5.38 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.38 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_strict_mono
% 5.15/5.38 thf(fact_2529_mult__less__cancel__left,axiom,
% 5.15/5.38 ! [C: real,A: real,B: real] :
% 5.15/5.38 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.38 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.38 => ( ord_less_real @ A @ B ) )
% 5.15/5.38 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.38 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.15/5.38
% 5.15/5.38 % mult_less_cancel_left
% 5.15/5.38 thf(fact_2530_mult__less__cancel__left,axiom,
% 5.15/5.39 ! [C: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.39 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ A @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_left
% 5.15/5.39 thf(fact_2531_mult__less__cancel__left,axiom,
% 5.15/5.39 ! [C: int,A: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ A @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_left
% 5.15/5.39 thf(fact_2532_mult__right__less__imp__less,axiom,
% 5.15/5.39 ! [A: real,C: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_less_imp_less
% 5.15/5.39 thf(fact_2533_mult__right__less__imp__less,axiom,
% 5.15/5.39 ! [A: rat,C: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_less_imp_less
% 5.15/5.39 thf(fact_2534_mult__right__less__imp__less,axiom,
% 5.15/5.39 ! [A: nat,C: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.39 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_less_imp_less
% 5.15/5.39 thf(fact_2535_mult__right__less__imp__less,axiom,
% 5.15/5.39 ! [A: int,C: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_less_imp_less
% 5.15/5.39 thf(fact_2536_mult__strict__mono_H,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.39 ( ( ord_less_real @ A @ B )
% 5.15/5.39 => ( ( ord_less_real @ C @ D )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_strict_mono'
% 5.15/5.39 thf(fact_2537_mult__strict__mono_H,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.39 ( ( ord_less_rat @ A @ B )
% 5.15/5.39 => ( ( ord_less_rat @ C @ D )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_strict_mono'
% 5.15/5.39 thf(fact_2538_mult__strict__mono_H,axiom,
% 5.15/5.39 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.39 ( ( ord_less_nat @ A @ B )
% 5.15/5.39 => ( ( ord_less_nat @ C @ D )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_strict_mono'
% 5.15/5.39 thf(fact_2539_mult__strict__mono_H,axiom,
% 5.15/5.39 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.39 ( ( ord_less_int @ A @ B )
% 5.15/5.39 => ( ( ord_less_int @ C @ D )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_strict_mono'
% 5.15/5.39 thf(fact_2540_mult__less__cancel__right,axiom,
% 5.15/5.39 ! [A: real,C: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ A @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right
% 5.15/5.39 thf(fact_2541_mult__less__cancel__right,axiom,
% 5.15/5.39 ! [A: rat,C: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ A @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right
% 5.15/5.39 thf(fact_2542_mult__less__cancel__right,axiom,
% 5.15/5.39 ! [A: int,C: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ A @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right
% 5.15/5.39 thf(fact_2543_mult__le__cancel__left__neg,axiom,
% 5.15/5.39 ! [C: real,A: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.39 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left_neg
% 5.15/5.39 thf(fact_2544_mult__le__cancel__left__neg,axiom,
% 5.15/5.39 ! [C: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.39 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left_neg
% 5.15/5.39 thf(fact_2545_mult__le__cancel__left__neg,axiom,
% 5.15/5.39 ! [C: int,A: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.39 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left_neg
% 5.15/5.39 thf(fact_2546_mult__le__cancel__left__pos,axiom,
% 5.15/5.39 ! [C: real,A: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.39 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left_pos
% 5.15/5.39 thf(fact_2547_mult__le__cancel__left__pos,axiom,
% 5.15/5.39 ! [C: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.39 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left_pos
% 5.15/5.39 thf(fact_2548_mult__le__cancel__left__pos,axiom,
% 5.15/5.39 ! [C: int,A: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.39 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left_pos
% 5.15/5.39 thf(fact_2549_mult__left__le__imp__le,axiom,
% 5.15/5.39 ! [C: real,A: real,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le_imp_le
% 5.15/5.39 thf(fact_2550_mult__left__le__imp__le,axiom,
% 5.15/5.39 ! [C: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le_imp_le
% 5.15/5.39 thf(fact_2551_mult__left__le__imp__le,axiom,
% 5.15/5.39 ! [C: nat,A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.15/5.39 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le_imp_le
% 5.15/5.39 thf(fact_2552_mult__left__le__imp__le,axiom,
% 5.15/5.39 ! [C: int,A: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le_imp_le
% 5.15/5.39 thf(fact_2553_mult__right__le__imp__le,axiom,
% 5.15/5.39 ! [A: real,C: real,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_le_imp_le
% 5.15/5.39 thf(fact_2554_mult__right__le__imp__le,axiom,
% 5.15/5.39 ! [A: rat,C: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_le_imp_le
% 5.15/5.39 thf(fact_2555_mult__right__le__imp__le,axiom,
% 5.15/5.39 ! [A: nat,C: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.15/5.39 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_le_imp_le
% 5.15/5.39 thf(fact_2556_mult__right__le__imp__le,axiom,
% 5.15/5.39 ! [A: int,C: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.15/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_le_imp_le
% 5.15/5.39 thf(fact_2557_mult__le__less__imp__less,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.39 => ( ( ord_less_real @ C @ D )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_less_imp_less
% 5.15/5.39 thf(fact_2558_mult__le__less__imp__less,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.39 => ( ( ord_less_rat @ C @ D )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_less_imp_less
% 5.15/5.39 thf(fact_2559_mult__le__less__imp__less,axiom,
% 5.15/5.39 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.39 => ( ( ord_less_nat @ C @ D )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_less_imp_less
% 5.15/5.39 thf(fact_2560_mult__le__less__imp__less,axiom,
% 5.15/5.39 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.39 => ( ( ord_less_int @ C @ D )
% 5.15/5.39 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_less_imp_less
% 5.15/5.39 thf(fact_2561_mult__less__le__imp__less,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.39 ( ( ord_less_real @ A @ B )
% 5.15/5.39 => ( ( ord_less_eq_real @ C @ D )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_le_imp_less
% 5.15/5.39 thf(fact_2562_mult__less__le__imp__less,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.39 ( ( ord_less_rat @ A @ B )
% 5.15/5.39 => ( ( ord_less_eq_rat @ C @ D )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_le_imp_less
% 5.15/5.39 thf(fact_2563_mult__less__le__imp__less,axiom,
% 5.15/5.39 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.39 ( ( ord_less_nat @ A @ B )
% 5.15/5.39 => ( ( ord_less_eq_nat @ C @ D )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.15/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_le_imp_less
% 5.15/5.39 thf(fact_2564_mult__less__le__imp__less,axiom,
% 5.15/5.39 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.39 ( ( ord_less_int @ A @ B )
% 5.15/5.39 => ( ( ord_less_eq_int @ C @ D )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_le_imp_less
% 5.15/5.39 thf(fact_2565_field__le__epsilon,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ! [E2: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.15/5.39 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 5.15/5.39 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.15/5.39
% 5.15/5.39 % field_le_epsilon
% 5.15/5.39 thf(fact_2566_field__le__epsilon,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ! [E2: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.15/5.39 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 5.15/5.39 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.15/5.39
% 5.15/5.39 % field_le_epsilon
% 5.15/5.39 thf(fact_2567_add__strict__increasing2,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_real @ B @ C )
% 5.15/5.39 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_strict_increasing2
% 5.15/5.39 thf(fact_2568_add__strict__increasing2,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_rat @ B @ C )
% 5.15/5.39 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_strict_increasing2
% 5.15/5.39 thf(fact_2569_add__strict__increasing2,axiom,
% 5.15/5.39 ! [A: nat,B: nat,C: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ B @ C )
% 5.15/5.39 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_strict_increasing2
% 5.15/5.39 thf(fact_2570_add__strict__increasing2,axiom,
% 5.15/5.39 ! [A: int,B: int,C: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_int @ B @ C )
% 5.15/5.39 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_strict_increasing2
% 5.15/5.39 thf(fact_2571_add__strict__increasing,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ B @ C )
% 5.15/5.39 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_strict_increasing
% 5.15/5.39 thf(fact_2572_add__strict__increasing,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ B @ C )
% 5.15/5.39 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_strict_increasing
% 5.15/5.39 thf(fact_2573_add__strict__increasing,axiom,
% 5.15/5.39 ! [A: nat,B: nat,C: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_eq_nat @ B @ C )
% 5.15/5.39 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_strict_increasing
% 5.15/5.39 thf(fact_2574_add__strict__increasing,axiom,
% 5.15/5.39 ! [A: int,B: int,C: int] :
% 5.15/5.39 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ B @ C )
% 5.15/5.39 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_strict_increasing
% 5.15/5.39 thf(fact_2575_add__pos__nonneg,axiom,
% 5.15/5.39 ! [A: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.39 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_pos_nonneg
% 5.15/5.39 thf(fact_2576_add__pos__nonneg,axiom,
% 5.15/5.39 ! [A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.39 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_pos_nonneg
% 5.15/5.39 thf(fact_2577_add__pos__nonneg,axiom,
% 5.15/5.39 ! [A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_pos_nonneg
% 5.15/5.39 thf(fact_2578_add__pos__nonneg,axiom,
% 5.15/5.39 ! [A: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.39 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_pos_nonneg
% 5.15/5.39 thf(fact_2579_add__nonpos__neg,axiom,
% 5.15/5.39 ! [A: real,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_nonpos_neg
% 5.15/5.39 thf(fact_2580_add__nonpos__neg,axiom,
% 5.15/5.39 ! [A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_nonpos_neg
% 5.15/5.39 thf(fact_2581_add__nonpos__neg,axiom,
% 5.15/5.39 ! [A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.15/5.39 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.15/5.39 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_nonpos_neg
% 5.15/5.39 thf(fact_2582_add__nonpos__neg,axiom,
% 5.15/5.39 ! [A: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.39 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.39 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_nonpos_neg
% 5.15/5.39 thf(fact_2583_add__nonneg__pos,axiom,
% 5.15/5.39 ! [A: real,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.39 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_nonneg_pos
% 5.15/5.39 thf(fact_2584_add__nonneg__pos,axiom,
% 5.15/5.39 ! [A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.15/5.39 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_nonneg_pos
% 5.15/5.39 thf(fact_2585_add__nonneg__pos,axiom,
% 5.15/5.39 ! [A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_nonneg_pos
% 5.15/5.39 thf(fact_2586_add__nonneg__pos,axiom,
% 5.15/5.39 ! [A: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.39 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_nonneg_pos
% 5.15/5.39 thf(fact_2587_add__neg__nonpos,axiom,
% 5.15/5.39 ! [A: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_neg_nonpos
% 5.15/5.39 thf(fact_2588_add__neg__nonpos,axiom,
% 5.15/5.39 ! [A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_neg_nonpos
% 5.15/5.39 thf(fact_2589_add__neg__nonpos,axiom,
% 5.15/5.39 ! [A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.15/5.39 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.15/5.39 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_neg_nonpos
% 5.15/5.39 thf(fact_2590_add__neg__nonpos,axiom,
% 5.15/5.39 ! [A: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.39 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.15/5.39 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_neg_nonpos
% 5.15/5.39 thf(fact_2591_mult__left__le__one__le,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le_one_le
% 5.15/5.39 thf(fact_2592_mult__left__le__one__le,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le_one_le
% 5.15/5.39 thf(fact_2593_mult__left__le__one__le,axiom,
% 5.15/5.39 ! [X: int,Y: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.39 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.15/5.39 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le_one_le
% 5.15/5.39 thf(fact_2594_mult__right__le__one__le,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_le_one_le
% 5.15/5.39 thf(fact_2595_mult__right__le__one__le,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_le_one_le
% 5.15/5.39 thf(fact_2596_mult__right__le__one__le,axiom,
% 5.15/5.39 ! [X: int,Y: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.39 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.15/5.39 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_right_le_one_le
% 5.15/5.39 thf(fact_2597_mult__le__one,axiom,
% 5.15/5.39 ! [A: real,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.39 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_one
% 5.15/5.39 thf(fact_2598_mult__le__one,axiom,
% 5.15/5.39 ! [A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.39 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_one
% 5.15/5.39 thf(fact_2599_mult__le__one,axiom,
% 5.15/5.39 ! [A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.39 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.15/5.39 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_one
% 5.15/5.39 thf(fact_2600_mult__le__one,axiom,
% 5.15/5.39 ! [A: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.39 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.15/5.39 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_one
% 5.15/5.39 thf(fact_2601_mult__left__le,axiom,
% 5.15/5.39 ! [C: real,A: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le
% 5.15/5.39 thf(fact_2602_mult__left__le,axiom,
% 5.15/5.39 ! [C: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le
% 5.15/5.39 thf(fact_2603_mult__left__le,axiom,
% 5.15/5.39 ! [C: nat,A: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le
% 5.15/5.39 thf(fact_2604_mult__left__le,axiom,
% 5.15/5.39 ! [C: int,A: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_left_le
% 5.15/5.39 thf(fact_2605_divide__nonpos__pos,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_nonpos_pos
% 5.15/5.39 thf(fact_2606_divide__nonpos__pos,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_nonpos_pos
% 5.15/5.39 thf(fact_2607_divide__nonpos__neg,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_nonpos_neg
% 5.15/5.39 thf(fact_2608_divide__nonpos__neg,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_nonpos_neg
% 5.15/5.39 thf(fact_2609_divide__nonneg__pos,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_nonneg_pos
% 5.15/5.39 thf(fact_2610_divide__nonneg__pos,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_nonneg_pos
% 5.15/5.39 thf(fact_2611_divide__nonneg__neg,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.39 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_nonneg_neg
% 5.15/5.39 thf(fact_2612_divide__nonneg__neg,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.39 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_nonneg_neg
% 5.15/5.39 thf(fact_2613_divide__le__cancel,axiom,
% 5.15/5.39 ! [A: real,C: real,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ A @ B ) )
% 5.15/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_le_cancel
% 5.15/5.39 thf(fact_2614_divide__le__cancel,axiom,
% 5.15/5.39 ! [A: rat,C: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ A @ B ) )
% 5.15/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_le_cancel
% 5.15/5.39 thf(fact_2615_frac__less2,axiom,
% 5.15/5.39 ! [X: real,Y: real,W: real,Z: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.39 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.15/5.39 => ( ( ord_less_real @ W @ Z )
% 5.15/5.39 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_less2
% 5.15/5.39 thf(fact_2616_frac__less2,axiom,
% 5.15/5.39 ! [X: rat,Y: rat,W: rat,Z: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.15/5.39 => ( ( ord_less_eq_rat @ X @ Y )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.15/5.39 => ( ( ord_less_rat @ W @ Z )
% 5.15/5.39 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_less2
% 5.15/5.39 thf(fact_2617_frac__less,axiom,
% 5.15/5.39 ! [X: real,Y: real,W: real,Z: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.39 => ( ( ord_less_real @ X @ Y )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.15/5.39 => ( ( ord_less_eq_real @ W @ Z )
% 5.15/5.39 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_less
% 5.15/5.39 thf(fact_2618_frac__less,axiom,
% 5.15/5.39 ! [X: rat,Y: rat,W: rat,Z: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.39 => ( ( ord_less_rat @ X @ Y )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.15/5.39 => ( ( ord_less_eq_rat @ W @ Z )
% 5.15/5.39 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_less
% 5.15/5.39 thf(fact_2619_frac__le,axiom,
% 5.15/5.39 ! [Y: real,X: real,W: real,Z: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.15/5.39 => ( ( ord_less_eq_real @ W @ Z )
% 5.15/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_le
% 5.15/5.39 thf(fact_2620_frac__le,axiom,
% 5.15/5.39 ! [Y: rat,X: rat,W: rat,Z: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ( ord_less_eq_rat @ X @ Y )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.15/5.39 => ( ( ord_less_eq_rat @ W @ Z )
% 5.15/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_le
% 5.15/5.39 thf(fact_2621_div__positive,axiom,
% 5.15/5.39 ! [B: nat,A: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.39 => ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_positive
% 5.15/5.39 thf(fact_2622_div__positive,axiom,
% 5.15/5.39 ! [B: int,A: int] :
% 5.15/5.39 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.39 => ( ( ord_less_eq_int @ B @ A )
% 5.15/5.39 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_positive
% 5.15/5.39 thf(fact_2623_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.15/5.39 ! [A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ A @ B )
% 5.15/5.39 => ( ( divide_divide_nat @ A @ B )
% 5.15/5.39 = zero_zero_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.div_less
% 5.15/5.39 thf(fact_2624_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.15/5.39 ! [A: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_int @ A @ B )
% 5.15/5.39 => ( ( divide_divide_int @ A @ B )
% 5.15/5.39 = zero_zero_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.div_less
% 5.15/5.39 thf(fact_2625_sum__squares__ge__zero,axiom,
% 5.15/5.39 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_ge_zero
% 5.15/5.39 thf(fact_2626_sum__squares__ge__zero,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_ge_zero
% 5.15/5.39 thf(fact_2627_sum__squares__ge__zero,axiom,
% 5.15/5.39 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_ge_zero
% 5.15/5.39 thf(fact_2628_sum__squares__le__zero__iff,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.15/5.39 = ( ( X = zero_zero_real )
% 5.15/5.39 & ( Y = zero_zero_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_le_zero_iff
% 5.15/5.39 thf(fact_2629_sum__squares__le__zero__iff,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.15/5.39 = ( ( X = zero_zero_rat )
% 5.15/5.39 & ( Y = zero_zero_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_le_zero_iff
% 5.15/5.39 thf(fact_2630_sum__squares__le__zero__iff,axiom,
% 5.15/5.39 ! [X: int,Y: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.15/5.39 = ( ( X = zero_zero_int )
% 5.15/5.39 & ( Y = zero_zero_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_le_zero_iff
% 5.15/5.39 thf(fact_2631_sum__squares__gt__zero__iff,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 5.15/5.39 = ( ( X != zero_zero_real )
% 5.15/5.39 | ( Y != zero_zero_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_gt_zero_iff
% 5.15/5.39 thf(fact_2632_sum__squares__gt__zero__iff,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.15/5.39 = ( ( X != zero_zero_rat )
% 5.15/5.39 | ( Y != zero_zero_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_gt_zero_iff
% 5.15/5.39 thf(fact_2633_sum__squares__gt__zero__iff,axiom,
% 5.15/5.39 ! [X: int,Y: int] :
% 5.15/5.39 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 5.15/5.39 = ( ( X != zero_zero_int )
% 5.15/5.39 | ( Y != zero_zero_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % sum_squares_gt_zero_iff
% 5.15/5.39 thf(fact_2634_not__sum__squares__lt__zero,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.15/5.39
% 5.15/5.39 % not_sum_squares_lt_zero
% 5.15/5.39 thf(fact_2635_not__sum__squares__lt__zero,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.15/5.39
% 5.15/5.39 % not_sum_squares_lt_zero
% 5.15/5.39 thf(fact_2636_not__sum__squares__lt__zero,axiom,
% 5.15/5.39 ! [X: int,Y: int] :
% 5.15/5.39 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.15/5.39
% 5.15/5.39 % not_sum_squares_lt_zero
% 5.15/5.39 thf(fact_2637_power__less__imp__less__base,axiom,
% 5.15/5.39 ! [A: real,N2: nat,B: real] :
% 5.15/5.39 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.39 => ( ord_less_real @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_less_imp_less_base
% 5.15/5.39 thf(fact_2638_power__less__imp__less__base,axiom,
% 5.15/5.39 ! [A: rat,N2: nat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.39 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_less_imp_less_base
% 5.15/5.39 thf(fact_2639_power__less__imp__less__base,axiom,
% 5.15/5.39 ! [A: nat,N2: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.39 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_less_imp_less_base
% 5.15/5.39 thf(fact_2640_power__less__imp__less__base,axiom,
% 5.15/5.39 ! [A: int,N2: nat,B: int] :
% 5.15/5.39 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.39 => ( ord_less_int @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_less_imp_less_base
% 5.15/5.39 thf(fact_2641_zero__less__two,axiom,
% 5.15/5.39 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.15/5.39
% 5.15/5.39 % zero_less_two
% 5.15/5.39 thf(fact_2642_zero__less__two,axiom,
% 5.15/5.39 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.15/5.39
% 5.15/5.39 % zero_less_two
% 5.15/5.39 thf(fact_2643_zero__less__two,axiom,
% 5.15/5.39 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.15/5.39
% 5.15/5.39 % zero_less_two
% 5.15/5.39 thf(fact_2644_zero__less__two,axiom,
% 5.15/5.39 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.15/5.39
% 5.15/5.39 % zero_less_two
% 5.15/5.39 thf(fact_2645_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.15/5.39 ! [C: nat,A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.39 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.15/5.39 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.15/5.39 thf(fact_2646_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.15/5.39 ! [C: int,A: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.39 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.15/5.39 thf(fact_2647_divide__strict__left__mono__neg,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real] :
% 5.15/5.39 ( ( ord_less_real @ A @ B )
% 5.15/5.39 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.15/5.39 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_strict_left_mono_neg
% 5.15/5.39 thf(fact_2648_divide__strict__left__mono__neg,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_rat @ A @ B )
% 5.15/5.39 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.39 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_strict_left_mono_neg
% 5.15/5.39 thf(fact_2649_divide__strict__left__mono,axiom,
% 5.15/5.39 ! [B: real,A: real,C: real] :
% 5.15/5.39 ( ( ord_less_real @ B @ A )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.15/5.39 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_strict_left_mono
% 5.15/5.39 thf(fact_2650_divide__strict__left__mono,axiom,
% 5.15/5.39 ! [B: rat,A: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_rat @ B @ A )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.39 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_strict_left_mono
% 5.15/5.39 thf(fact_2651_mult__imp__less__div__pos,axiom,
% 5.15/5.39 ! [Y: real,Z: real,X: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X )
% 5.15/5.39 => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_imp_less_div_pos
% 5.15/5.39 thf(fact_2652_mult__imp__less__div__pos,axiom,
% 5.15/5.39 ! [Y: rat,Z: rat,X: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 5.15/5.39 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_imp_less_div_pos
% 5.15/5.39 thf(fact_2653_mult__imp__div__pos__less,axiom,
% 5.15/5.39 ! [Y: real,X: real,Z: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y ) )
% 5.15/5.39 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_imp_div_pos_less
% 5.15/5.39 thf(fact_2654_mult__imp__div__pos__less,axiom,
% 5.15/5.39 ! [Y: rat,X: rat,Z: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 5.15/5.39 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_imp_div_pos_less
% 5.15/5.39 thf(fact_2655_pos__less__divide__eq,axiom,
% 5.15/5.39 ! [C: real,A: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos_less_divide_eq
% 5.15/5.39 thf(fact_2656_pos__less__divide__eq,axiom,
% 5.15/5.39 ! [C: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos_less_divide_eq
% 5.15/5.39 thf(fact_2657_pos__divide__less__eq,axiom,
% 5.15/5.39 ! [C: real,B: real,A: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.15/5.39 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos_divide_less_eq
% 5.15/5.39 thf(fact_2658_pos__divide__less__eq,axiom,
% 5.15/5.39 ! [C: rat,B: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.15/5.39 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos_divide_less_eq
% 5.15/5.39 thf(fact_2659_neg__less__divide__eq,axiom,
% 5.15/5.39 ! [C: real,A: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % neg_less_divide_eq
% 5.15/5.39 thf(fact_2660_neg__less__divide__eq,axiom,
% 5.15/5.39 ! [C: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % neg_less_divide_eq
% 5.15/5.39 thf(fact_2661_neg__divide__less__eq,axiom,
% 5.15/5.39 ! [C: real,B: real,A: real] :
% 5.15/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.15/5.39 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % neg_divide_less_eq
% 5.15/5.39 thf(fact_2662_neg__divide__less__eq,axiom,
% 5.15/5.39 ! [C: rat,B: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.15/5.39 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % neg_divide_less_eq
% 5.15/5.39 thf(fact_2663_less__divide__eq,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real] :
% 5.15/5.39 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % less_divide_eq
% 5.15/5.39 thf(fact_2664_less__divide__eq,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % less_divide_eq
% 5.15/5.39 thf(fact_2665_divide__less__eq,axiom,
% 5.15/5.39 ! [B: real,C: real,A: real] :
% 5.15/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_less_eq
% 5.15/5.39 thf(fact_2666_divide__less__eq,axiom,
% 5.15/5.39 ! [B: rat,C: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_less_eq
% 5.15/5.39 thf(fact_2667_less__divide__eq__1,axiom,
% 5.15/5.39 ! [B: real,A: real] :
% 5.15/5.39 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 & ( ord_less_real @ A @ B ) )
% 5.15/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.39 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % less_divide_eq_1
% 5.15/5.39 thf(fact_2668_less__divide__eq__1,axiom,
% 5.15/5.39 ! [B: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 & ( ord_less_rat @ A @ B ) )
% 5.15/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.39 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % less_divide_eq_1
% 5.15/5.39 thf(fact_2669_divide__less__eq__1,axiom,
% 5.15/5.39 ! [B: real,A: real] :
% 5.15/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 & ( ord_less_real @ B @ A ) )
% 5.15/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.39 & ( ord_less_real @ A @ B ) )
% 5.15/5.39 | ( A = zero_zero_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_less_eq_1
% 5.15/5.39 thf(fact_2670_divide__less__eq__1,axiom,
% 5.15/5.39 ! [B: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 & ( ord_less_rat @ B @ A ) )
% 5.15/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.39 & ( ord_less_rat @ A @ B ) )
% 5.15/5.39 | ( A = zero_zero_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_less_eq_1
% 5.15/5.39 thf(fact_2671_power__le__one,axiom,
% 5.15/5.39 ! [A: real,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_le_one
% 5.15/5.39 thf(fact_2672_power__le__one,axiom,
% 5.15/5.39 ! [A: rat,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_le_one
% 5.15/5.39 thf(fact_2673_power__le__one,axiom,
% 5.15/5.39 ! [A: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.15/5.39 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_le_one
% 5.15/5.39 thf(fact_2674_power__le__one,axiom,
% 5.15/5.39 ! [A: int,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.15/5.39 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_le_one
% 5.15/5.39 thf(fact_2675_eq__divide__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [W: num,B: complex,C: complex] :
% 5.15/5.39 ( ( ( numera6690914467698888265omplex @ W )
% 5.15/5.39 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.39 = ( ( ( C != zero_zero_complex )
% 5.15/5.39 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.15/5.39 = B ) )
% 5.15/5.39 & ( ( C = zero_zero_complex )
% 5.15/5.39 => ( ( numera6690914467698888265omplex @ W )
% 5.15/5.39 = zero_zero_complex ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % eq_divide_eq_numeral(1)
% 5.15/5.39 thf(fact_2676_eq__divide__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [W: num,B: real,C: real] :
% 5.15/5.39 ( ( ( numeral_numeral_real @ W )
% 5.15/5.39 = ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ( ( C != zero_zero_real )
% 5.15/5.39 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.15/5.39 = B ) )
% 5.15/5.39 & ( ( C = zero_zero_real )
% 5.15/5.39 => ( ( numeral_numeral_real @ W )
% 5.15/5.39 = zero_zero_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % eq_divide_eq_numeral(1)
% 5.15/5.39 thf(fact_2677_eq__divide__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [W: num,B: rat,C: rat] :
% 5.15/5.39 ( ( ( numeral_numeral_rat @ W )
% 5.15/5.39 = ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( C != zero_zero_rat )
% 5.15/5.39 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.15/5.39 = B ) )
% 5.15/5.39 & ( ( C = zero_zero_rat )
% 5.15/5.39 => ( ( numeral_numeral_rat @ W )
% 5.15/5.39 = zero_zero_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % eq_divide_eq_numeral(1)
% 5.15/5.39 thf(fact_2678_divide__eq__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [B: complex,C: complex,W: num] :
% 5.15/5.39 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.15/5.39 = ( numera6690914467698888265omplex @ W ) )
% 5.15/5.39 = ( ( ( C != zero_zero_complex )
% 5.15/5.39 => ( B
% 5.15/5.39 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.15/5.39 & ( ( C = zero_zero_complex )
% 5.15/5.39 => ( ( numera6690914467698888265omplex @ W )
% 5.15/5.39 = zero_zero_complex ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_eq_eq_numeral(1)
% 5.15/5.39 thf(fact_2679_divide__eq__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [B: real,C: real,W: num] :
% 5.15/5.39 ( ( ( divide_divide_real @ B @ C )
% 5.15/5.39 = ( numeral_numeral_real @ W ) )
% 5.15/5.39 = ( ( ( C != zero_zero_real )
% 5.15/5.39 => ( B
% 5.15/5.39 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.15/5.39 & ( ( C = zero_zero_real )
% 5.15/5.39 => ( ( numeral_numeral_real @ W )
% 5.15/5.39 = zero_zero_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_eq_eq_numeral(1)
% 5.15/5.39 thf(fact_2680_divide__eq__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [B: rat,C: rat,W: num] :
% 5.15/5.39 ( ( ( divide_divide_rat @ B @ C )
% 5.15/5.39 = ( numeral_numeral_rat @ W ) )
% 5.15/5.39 = ( ( ( C != zero_zero_rat )
% 5.15/5.39 => ( B
% 5.15/5.39 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.15/5.39 & ( ( C = zero_zero_rat )
% 5.15/5.39 => ( ( numeral_numeral_rat @ W )
% 5.15/5.39 = zero_zero_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_eq_eq_numeral(1)
% 5.15/5.39 thf(fact_2681_divide__add__eq__iff,axiom,
% 5.15/5.39 ! [Z: complex,X: complex,Y: complex] :
% 5.15/5.39 ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_add_eq_iff
% 5.15/5.39 thf(fact_2682_divide__add__eq__iff,axiom,
% 5.15/5.39 ! [Z: real,X: real,Y: real] :
% 5.15/5.39 ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 5.15/5.39 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_add_eq_iff
% 5.15/5.39 thf(fact_2683_divide__add__eq__iff,axiom,
% 5.15/5.39 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.39 ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 5.15/5.39 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_add_eq_iff
% 5.15/5.39 thf(fact_2684_add__divide__eq__iff,axiom,
% 5.15/5.39 ! [Z: complex,X: complex,Y: complex] :
% 5.15/5.39 ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_iff
% 5.15/5.39 thf(fact_2685_add__divide__eq__iff,axiom,
% 5.15/5.39 ! [Z: real,X: real,Y: real] :
% 5.15/5.39 ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 5.15/5.39 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_iff
% 5.15/5.39 thf(fact_2686_add__divide__eq__iff,axiom,
% 5.15/5.39 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.39 ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 5.15/5.39 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_iff
% 5.15/5.39 thf(fact_2687_add__num__frac,axiom,
% 5.15/5.39 ! [Y: complex,Z: complex,X: complex] :
% 5.15/5.39 ( ( Y != zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_num_frac
% 5.15/5.39 thf(fact_2688_add__num__frac,axiom,
% 5.15/5.39 ! [Y: real,Z: real,X: real] :
% 5.15/5.39 ( ( Y != zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.39 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_num_frac
% 5.15/5.39 thf(fact_2689_add__num__frac,axiom,
% 5.15/5.39 ! [Y: rat,Z: rat,X: rat] :
% 5.15/5.39 ( ( Y != zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 5.15/5.39 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_num_frac
% 5.15/5.39 thf(fact_2690_add__frac__num,axiom,
% 5.15/5.39 ! [Y: complex,X: complex,Z: complex] :
% 5.15/5.39 ( ( Y != zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_frac_num
% 5.15/5.39 thf(fact_2691_add__frac__num,axiom,
% 5.15/5.39 ! [Y: real,X: real,Z: real] :
% 5.15/5.39 ( ( Y != zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z )
% 5.15/5.39 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_frac_num
% 5.15/5.39 thf(fact_2692_add__frac__num,axiom,
% 5.15/5.39 ! [Y: rat,X: rat,Z: rat] :
% 5.15/5.39 ( ( Y != zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 5.15/5.39 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_frac_num
% 5.15/5.39 thf(fact_2693_add__frac__eq,axiom,
% 5.15/5.39 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.15/5.39 ( ( Y != zero_zero_complex )
% 5.15/5.39 => ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_frac_eq
% 5.15/5.39 thf(fact_2694_add__frac__eq,axiom,
% 5.15/5.39 ! [Y: real,Z: real,X: real,W: real] :
% 5.15/5.39 ( ( Y != zero_zero_real )
% 5.15/5.39 => ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.15/5.39 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_frac_eq
% 5.15/5.39 thf(fact_2695_add__frac__eq,axiom,
% 5.15/5.39 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.15/5.39 ( ( Y != zero_zero_rat )
% 5.15/5.39 => ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.15/5.39 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_frac_eq
% 5.15/5.39 thf(fact_2696_add__divide__eq__if__simps_I1_J,axiom,
% 5.15/5.39 ! [Z: complex,A: complex,B: complex] :
% 5.15/5.39 ( ( ( Z = zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.15/5.39 = A ) )
% 5.15/5.39 & ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(1)
% 5.15/5.39 thf(fact_2697_add__divide__eq__if__simps_I1_J,axiom,
% 5.15/5.39 ! [Z: real,A: real,B: real] :
% 5.15/5.39 ( ( ( Z = zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.15/5.39 = A ) )
% 5.15/5.39 & ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.15/5.39 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(1)
% 5.15/5.39 thf(fact_2698_add__divide__eq__if__simps_I1_J,axiom,
% 5.15/5.39 ! [Z: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ( Z = zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.15/5.39 = A ) )
% 5.15/5.39 & ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.15/5.39 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(1)
% 5.15/5.39 thf(fact_2699_add__divide__eq__if__simps_I2_J,axiom,
% 5.15/5.39 ! [Z: complex,A: complex,B: complex] :
% 5.15/5.39 ( ( ( Z = zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.15/5.39 = B ) )
% 5.15/5.39 & ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(2)
% 5.15/5.39 thf(fact_2700_add__divide__eq__if__simps_I2_J,axiom,
% 5.15/5.39 ! [Z: real,A: real,B: real] :
% 5.15/5.39 ( ( ( Z = zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.15/5.39 = B ) )
% 5.15/5.39 & ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.15/5.39 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(2)
% 5.15/5.39 thf(fact_2701_add__divide__eq__if__simps_I2_J,axiom,
% 5.15/5.39 ! [Z: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ( Z = zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.15/5.39 = B ) )
% 5.15/5.39 & ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.15/5.39 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(2)
% 5.15/5.39 thf(fact_2702_power__inject__base,axiom,
% 5.15/5.39 ! [A: real,N2: nat,B: real] :
% 5.15/5.39 ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.15/5.39 = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.39 => ( A = B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_inject_base
% 5.15/5.39 thf(fact_2703_power__inject__base,axiom,
% 5.15/5.39 ! [A: rat,N2: nat,B: rat] :
% 5.15/5.39 ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.15/5.39 = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.39 => ( A = B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_inject_base
% 5.15/5.39 thf(fact_2704_power__inject__base,axiom,
% 5.15/5.39 ! [A: nat,N2: nat,B: nat] :
% 5.15/5.39 ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.15/5.39 = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.39 => ( A = B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_inject_base
% 5.15/5.39 thf(fact_2705_power__inject__base,axiom,
% 5.15/5.39 ! [A: int,N2: nat,B: int] :
% 5.15/5.39 ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.15/5.39 = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.39 => ( A = B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_inject_base
% 5.15/5.39 thf(fact_2706_power__le__imp__le__base,axiom,
% 5.15/5.39 ! [A: real,N2: nat,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.39 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_le_imp_le_base
% 5.15/5.39 thf(fact_2707_power__le__imp__le__base,axiom,
% 5.15/5.39 ! [A: rat,N2: nat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.39 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_le_imp_le_base
% 5.15/5.39 thf(fact_2708_power__le__imp__le__base,axiom,
% 5.15/5.39 ! [A: nat,N2: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.15/5.39 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_le_imp_le_base
% 5.15/5.39 thf(fact_2709_power__le__imp__le__base,axiom,
% 5.15/5.39 ! [A: int,N2: nat,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.39 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_le_imp_le_base
% 5.15/5.39 thf(fact_2710_div__add__self2,axiom,
% 5.15/5.39 ! [B: nat,A: nat] :
% 5.15/5.39 ( ( B != zero_zero_nat )
% 5.15/5.39 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.15/5.39 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_add_self2
% 5.15/5.39 thf(fact_2711_div__add__self2,axiom,
% 5.15/5.39 ! [B: int,A: int] :
% 5.15/5.39 ( ( B != zero_zero_int )
% 5.15/5.39 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.15/5.39 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_add_self2
% 5.15/5.39 thf(fact_2712_div__add__self1,axiom,
% 5.15/5.39 ! [B: nat,A: nat] :
% 5.15/5.39 ( ( B != zero_zero_nat )
% 5.15/5.39 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.15/5.39 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_add_self1
% 5.15/5.39 thf(fact_2713_div__add__self1,axiom,
% 5.15/5.39 ! [B: int,A: int] :
% 5.15/5.39 ( ( B != zero_zero_int )
% 5.15/5.39 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.15/5.39 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_add_self1
% 5.15/5.39 thf(fact_2714_add__divide__eq__if__simps_I4_J,axiom,
% 5.15/5.39 ! [Z: complex,A: complex,B: complex] :
% 5.15/5.39 ( ( ( Z = zero_zero_complex )
% 5.15/5.39 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.15/5.39 = A ) )
% 5.15/5.39 & ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(4)
% 5.15/5.39 thf(fact_2715_add__divide__eq__if__simps_I4_J,axiom,
% 5.15/5.39 ! [Z: real,A: real,B: real] :
% 5.15/5.39 ( ( ( Z = zero_zero_real )
% 5.15/5.39 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.15/5.39 = A ) )
% 5.15/5.39 & ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.15/5.39 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(4)
% 5.15/5.39 thf(fact_2716_add__divide__eq__if__simps_I4_J,axiom,
% 5.15/5.39 ! [Z: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ( Z = zero_zero_rat )
% 5.15/5.39 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.15/5.39 = A ) )
% 5.15/5.39 & ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.15/5.39 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_divide_eq_if_simps(4)
% 5.15/5.39 thf(fact_2717_diff__frac__eq,axiom,
% 5.15/5.39 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.15/5.39 ( ( Y != zero_zero_complex )
% 5.15/5.39 => ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % diff_frac_eq
% 5.15/5.39 thf(fact_2718_diff__frac__eq,axiom,
% 5.15/5.39 ! [Y: real,Z: real,X: real,W: real] :
% 5.15/5.39 ( ( Y != zero_zero_real )
% 5.15/5.39 => ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.15/5.39 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % diff_frac_eq
% 5.15/5.39 thf(fact_2719_diff__frac__eq,axiom,
% 5.15/5.39 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.15/5.39 ( ( Y != zero_zero_rat )
% 5.15/5.39 => ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.15/5.39 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % diff_frac_eq
% 5.15/5.39 thf(fact_2720_diff__divide__eq__iff,axiom,
% 5.15/5.39 ! [Z: complex,X: complex,Y: complex] :
% 5.15/5.39 ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % diff_divide_eq_iff
% 5.15/5.39 thf(fact_2721_diff__divide__eq__iff,axiom,
% 5.15/5.39 ! [Z: real,X: real,Y: real] :
% 5.15/5.39 ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 5.15/5.39 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % diff_divide_eq_iff
% 5.15/5.39 thf(fact_2722_diff__divide__eq__iff,axiom,
% 5.15/5.39 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.39 ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 5.15/5.39 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % diff_divide_eq_iff
% 5.15/5.39 thf(fact_2723_divide__diff__eq__iff,axiom,
% 5.15/5.39 ! [Z: complex,X: complex,Y: complex] :
% 5.15/5.39 ( ( Z != zero_zero_complex )
% 5.15/5.39 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_diff_eq_iff
% 5.15/5.39 thf(fact_2724_divide__diff__eq__iff,axiom,
% 5.15/5.39 ! [Z: real,X: real,Y: real] :
% 5.15/5.39 ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 5.15/5.39 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_diff_eq_iff
% 5.15/5.39 thf(fact_2725_divide__diff__eq__iff,axiom,
% 5.15/5.39 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.39 ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 5.15/5.39 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_diff_eq_iff
% 5.15/5.39 thf(fact_2726_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.15/5.39 ! [A: code_integer,B: code_integer] :
% 5.15/5.39 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.39 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.15/5.39 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.15/5.39 = A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.mod_less
% 5.15/5.39 thf(fact_2727_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.15/5.39 ! [A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ A @ B )
% 5.15/5.39 => ( ( modulo_modulo_nat @ A @ B )
% 5.15/5.39 = A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.mod_less
% 5.15/5.39 thf(fact_2728_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.15/5.39 ! [A: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_int @ A @ B )
% 5.15/5.39 => ( ( modulo_modulo_int @ A @ B )
% 5.15/5.39 = A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.mod_less
% 5.15/5.39 thf(fact_2729_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.15/5.39 ! [B: code_integer,A: code_integer] :
% 5.15/5.39 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.39 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.15/5.39 thf(fact_2730_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.15/5.39 ! [B: nat,A: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.39 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.15/5.39 thf(fact_2731_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.15/5.39 ! [B: int,A: int] :
% 5.15/5.39 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.39 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.15/5.39 thf(fact_2732_cong__exp__iff__simps_I2_J,axiom,
% 5.15/5.39 ! [N2: num,Q3: num] :
% 5.15/5.39 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = zero_zero_nat )
% 5.15/5.39 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.15/5.39 = zero_zero_nat ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(2)
% 5.15/5.39 thf(fact_2733_cong__exp__iff__simps_I2_J,axiom,
% 5.15/5.39 ! [N2: num,Q3: num] :
% 5.15/5.39 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = zero_zero_int )
% 5.15/5.39 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 5.15/5.39 = zero_zero_int ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(2)
% 5.15/5.39 thf(fact_2734_cong__exp__iff__simps_I2_J,axiom,
% 5.15/5.39 ! [N2: num,Q3: num] :
% 5.15/5.39 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = zero_z3403309356797280102nteger )
% 5.15/5.39 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.15/5.39 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(2)
% 5.15/5.39 thf(fact_2735_cong__exp__iff__simps_I1_J,axiom,
% 5.15/5.39 ! [N2: num] :
% 5.15/5.39 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 5.15/5.39 = zero_zero_nat ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(1)
% 5.15/5.39 thf(fact_2736_cong__exp__iff__simps_I1_J,axiom,
% 5.15/5.39 ! [N2: num] :
% 5.15/5.39 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 5.15/5.39 = zero_zero_int ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(1)
% 5.15/5.39 thf(fact_2737_cong__exp__iff__simps_I1_J,axiom,
% 5.15/5.39 ! [N2: num] :
% 5.15/5.39 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) )
% 5.15/5.39 = zero_z3403309356797280102nteger ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(1)
% 5.15/5.39 thf(fact_2738_numeral__1__eq__Suc__0,axiom,
% 5.15/5.39 ( ( numeral_numeral_nat @ one )
% 5.15/5.39 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.39
% 5.15/5.39 % numeral_1_eq_Suc_0
% 5.15/5.39 thf(fact_2739_num_Osize_I5_J,axiom,
% 5.15/5.39 ! [X22: num] :
% 5.15/5.39 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.15/5.39 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % num.size(5)
% 5.15/5.39 thf(fact_2740_ex__least__nat__less,axiom,
% 5.15/5.39 ! [P: nat > $o,N2: nat] :
% 5.15/5.39 ( ( P @ N2 )
% 5.15/5.39 => ( ~ ( P @ zero_zero_nat )
% 5.15/5.39 => ? [K3: nat] :
% 5.15/5.39 ( ( ord_less_nat @ K3 @ N2 )
% 5.15/5.39 & ! [I4: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ I4 @ K3 )
% 5.15/5.39 => ~ ( P @ I4 ) )
% 5.15/5.39 & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % ex_least_nat_less
% 5.15/5.39 thf(fact_2741_nat__induct__non__zero,axiom,
% 5.15/5.39 ! [N2: nat,P: nat > $o] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ( P @ one_one_nat )
% 5.15/5.39 => ( ! [N: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.15/5.39 => ( ( P @ N )
% 5.15/5.39 => ( P @ ( suc @ N ) ) ) )
% 5.15/5.39 => ( P @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % nat_induct_non_zero
% 5.15/5.39 thf(fact_2742_diff__Suc__less,axiom,
% 5.15/5.39 ! [N2: nat,I: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) @ N2 ) ) ).
% 5.15/5.39
% 5.15/5.39 % diff_Suc_less
% 5.15/5.39 thf(fact_2743_num_Osize_I6_J,axiom,
% 5.15/5.39 ! [X33: num] :
% 5.15/5.39 ( ( size_size_num @ ( bit1 @ X33 ) )
% 5.15/5.39 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % num.size(6)
% 5.15/5.39 thf(fact_2744_one__less__mult,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.39 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.15/5.39 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % one_less_mult
% 5.15/5.39 thf(fact_2745_n__less__m__mult__n,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.15/5.39 => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % n_less_m_mult_n
% 5.15/5.39 thf(fact_2746_n__less__n__mult__m,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.15/5.39 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % n_less_n_mult_m
% 5.15/5.39 thf(fact_2747_length__pos__if__in__set,axiom,
% 5.15/5.39 ! [X: complex,Xs2: list_complex] :
% 5.15/5.39 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % length_pos_if_in_set
% 5.15/5.39 thf(fact_2748_length__pos__if__in__set,axiom,
% 5.15/5.39 ! [X: real,Xs2: list_real] :
% 5.15/5.39 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % length_pos_if_in_set
% 5.15/5.39 thf(fact_2749_length__pos__if__in__set,axiom,
% 5.15/5.39 ! [X: set_nat,Xs2: list_set_nat] :
% 5.15/5.39 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % length_pos_if_in_set
% 5.15/5.39 thf(fact_2750_length__pos__if__in__set,axiom,
% 5.15/5.39 ! [X: nat,Xs2: list_nat] :
% 5.15/5.39 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % length_pos_if_in_set
% 5.15/5.39 thf(fact_2751_length__pos__if__in__set,axiom,
% 5.15/5.39 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.15/5.39 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % length_pos_if_in_set
% 5.15/5.39 thf(fact_2752_length__pos__if__in__set,axiom,
% 5.15/5.39 ! [X: $o,Xs2: list_o] :
% 5.15/5.39 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % length_pos_if_in_set
% 5.15/5.39 thf(fact_2753_length__pos__if__in__set,axiom,
% 5.15/5.39 ! [X: int,Xs2: list_int] :
% 5.15/5.39 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.15/5.39 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % length_pos_if_in_set
% 5.15/5.39 thf(fact_2754_nat__mult__le__cancel1,axiom,
% 5.15/5.39 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.39 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.39 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % nat_mult_le_cancel1
% 5.15/5.39 thf(fact_2755_power__gt__expt,axiom,
% 5.15/5.39 ! [N2: nat,K: nat] :
% 5.15/5.39 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.39 => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_gt_expt
% 5.15/5.39 thf(fact_2756_nat__diff__split__asm,axiom,
% 5.15/5.39 ! [P: nat > $o,A: nat,B: nat] :
% 5.15/5.39 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.15/5.39 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.15/5.39 & ~ ( P @ zero_zero_nat ) )
% 5.15/5.39 | ? [D2: nat] :
% 5.15/5.39 ( ( A
% 5.15/5.39 = ( plus_plus_nat @ B @ D2 ) )
% 5.15/5.39 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % nat_diff_split_asm
% 5.15/5.39 thf(fact_2757_nat__diff__split,axiom,
% 5.15/5.39 ! [P: nat > $o,A: nat,B: nat] :
% 5.15/5.39 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.15/5.39 = ( ( ( ord_less_nat @ A @ B )
% 5.15/5.39 => ( P @ zero_zero_nat ) )
% 5.15/5.39 & ! [D2: nat] :
% 5.15/5.39 ( ( A
% 5.15/5.39 = ( plus_plus_nat @ B @ D2 ) )
% 5.15/5.39 => ( P @ D2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % nat_diff_split
% 5.15/5.39 thf(fact_2758_div__greater__zero__iff,axiom,
% 5.15/5.39 ! [M: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.15/5.39 = ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.39 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_greater_zero_iff
% 5.15/5.39 thf(fact_2759_div__le__mono2,axiom,
% 5.15/5.39 ! [M: nat,N2: nat,K: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.39 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.39 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_le_mono2
% 5.15/5.39 thf(fact_2760_nat__one__le__power,axiom,
% 5.15/5.39 ! [I: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.15/5.39 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % nat_one_le_power
% 5.15/5.39 thf(fact_2761_div__eq__dividend__iff,axiom,
% 5.15/5.39 ! [M: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.39 => ( ( ( divide_divide_nat @ M @ N2 )
% 5.15/5.39 = M )
% 5.15/5.39 = ( N2 = one_one_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_eq_dividend_iff
% 5.15/5.39 thf(fact_2762_div__less__dividend,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.39 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_less_dividend
% 5.15/5.39 thf(fact_2763_div__less__iff__less__mult,axiom,
% 5.15/5.39 ! [Q3: nat,M: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.15/5.39 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N2 )
% 5.15/5.39 = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q3 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_less_iff_less_mult
% 5.15/5.39 thf(fact_2764_nat__mult__div__cancel1,axiom,
% 5.15/5.39 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.39 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.39 = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % nat_mult_div_cancel1
% 5.15/5.39 thf(fact_2765_mod__le__divisor,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.15/5.39
% 5.15/5.39 % mod_le_divisor
% 5.15/5.39 thf(fact_2766_vebt__insert_Osimps_I3_J,axiom,
% 5.15/5.39 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.15/5.39 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 5.15/5.39 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 5.15/5.39
% 5.15/5.39 % vebt_insert.simps(3)
% 5.15/5.39 thf(fact_2767_vebt__member_Osimps_I3_J,axiom,
% 5.15/5.39 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.15/5.39 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 5.15/5.39
% 5.15/5.39 % vebt_member.simps(3)
% 5.15/5.39 thf(fact_2768_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.15/5.39 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.15/5.39 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 5.15/5.39 = one_one_nat ) ).
% 5.15/5.39
% 5.15/5.39 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(2)
% 5.15/5.39 thf(fact_2769_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.15/5.39 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.15/5.39 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.15/5.39
% 5.15/5.39 % VEBT_internal.membermima.simps(2)
% 5.15/5.39 thf(fact_2770_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 5.15/5.39 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.15/5.39 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 5.15/5.39 = one_one_nat ) ).
% 5.15/5.39
% 5.15/5.39 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(2)
% 5.15/5.39 thf(fact_2771_field__le__mult__one__interval,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ! [Z2: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.15/5.39 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X ) @ Y ) ) )
% 5.15/5.39 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.15/5.39
% 5.15/5.39 % field_le_mult_one_interval
% 5.15/5.39 thf(fact_2772_field__le__mult__one__interval,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ! [Z2: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.15/5.39 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ Y ) ) )
% 5.15/5.39 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.15/5.39
% 5.15/5.39 % field_le_mult_one_interval
% 5.15/5.39 thf(fact_2773_mult__less__cancel__right2,axiom,
% 5.15/5.39 ! [A: real,C: real] :
% 5.15/5.39 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.15/5.39 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ A @ one_one_real ) )
% 5.15/5.39 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right2
% 5.15/5.39 thf(fact_2774_mult__less__cancel__right2,axiom,
% 5.15/5.39 ! [A: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.15/5.39 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.15/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right2
% 5.15/5.39 thf(fact_2775_mult__less__cancel__right2,axiom,
% 5.15/5.39 ! [A: int,C: int] :
% 5.15/5.39 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.15/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ A @ one_one_int ) )
% 5.15/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right2
% 5.15/5.39 thf(fact_2776_mult__less__cancel__right1,axiom,
% 5.15/5.39 ! [C: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ one_one_real @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right1
% 5.15/5.39 thf(fact_2777_mult__less__cancel__right1,axiom,
% 5.15/5.39 ! [C: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right1
% 5.15/5.39 thf(fact_2778_mult__less__cancel__right1,axiom,
% 5.15/5.39 ! [C: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ one_one_int @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_right1
% 5.15/5.39 thf(fact_2779_mult__less__cancel__left2,axiom,
% 5.15/5.39 ! [C: real,A: real] :
% 5.15/5.39 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.15/5.39 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ A @ one_one_real ) )
% 5.15/5.39 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_left2
% 5.15/5.39 thf(fact_2780_mult__less__cancel__left2,axiom,
% 5.15/5.39 ! [C: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.15/5.39 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.15/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_left2
% 5.15/5.39 thf(fact_2781_mult__less__cancel__left2,axiom,
% 5.15/5.39 ! [C: int,A: int] :
% 5.15/5.39 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.15/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ A @ one_one_int ) )
% 5.15/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_left2
% 5.15/5.39 thf(fact_2782_mult__less__cancel__left1,axiom,
% 5.15/5.39 ! [C: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.15/5.39 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ one_one_real @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_left1
% 5.15/5.39 thf(fact_2783_mult__less__cancel__left1,axiom,
% 5.15/5.39 ! [C: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.15/5.39 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_left1
% 5.15/5.39 thf(fact_2784_mult__less__cancel__left1,axiom,
% 5.15/5.39 ! [C: int,B: int] :
% 5.15/5.39 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.15/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_int @ one_one_int @ B ) )
% 5.15/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_less_cancel_left1
% 5.15/5.39 thf(fact_2785_mult__le__cancel__right2,axiom,
% 5.15/5.39 ! [A: real,C: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.15/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_right2
% 5.15/5.39 thf(fact_2786_mult__le__cancel__right2,axiom,
% 5.15/5.39 ! [A: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.15/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_right2
% 5.15/5.39 thf(fact_2787_mult__le__cancel__right2,axiom,
% 5.15/5.39 ! [A: int,C: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.15/5.39 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.15/5.39 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_right2
% 5.15/5.39 thf(fact_2788_mult__le__cancel__right1,axiom,
% 5.15/5.39 ! [C: real,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.15/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_right1
% 5.15/5.39 thf(fact_2789_mult__le__cancel__right1,axiom,
% 5.15/5.39 ! [C: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.15/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_right1
% 5.15/5.39 thf(fact_2790_mult__le__cancel__right1,axiom,
% 5.15/5.39 ! [C: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.15/5.39 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_right1
% 5.15/5.39 thf(fact_2791_mult__le__cancel__left2,axiom,
% 5.15/5.39 ! [C: real,A: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.15/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left2
% 5.15/5.39 thf(fact_2792_mult__le__cancel__left2,axiom,
% 5.15/5.39 ! [C: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.15/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left2
% 5.15/5.39 thf(fact_2793_mult__le__cancel__left2,axiom,
% 5.15/5.39 ! [C: int,A: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.15/5.39 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.15/5.39 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left2
% 5.15/5.39 thf(fact_2794_mult__le__cancel__left1,axiom,
% 5.15/5.39 ! [C: real,B: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.15/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left1
% 5.15/5.39 thf(fact_2795_mult__le__cancel__left1,axiom,
% 5.15/5.39 ! [C: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.15/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left1
% 5.15/5.39 thf(fact_2796_mult__le__cancel__left1,axiom,
% 5.15/5.39 ! [C: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.15/5.39 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.15/5.39 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.15/5.39 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_le_cancel_left1
% 5.15/5.39 thf(fact_2797_divide__left__mono__neg,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.39 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.15/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_left_mono_neg
% 5.15/5.39 thf(fact_2798_divide__left__mono__neg,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.39 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_left_mono_neg
% 5.15/5.39 thf(fact_2799_mult__imp__le__div__pos,axiom,
% 5.15/5.39 ! [Y: real,Z: real,X: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X )
% 5.15/5.39 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_imp_le_div_pos
% 5.15/5.39 thf(fact_2800_mult__imp__le__div__pos,axiom,
% 5.15/5.39 ! [Y: rat,Z: rat,X: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 5.15/5.39 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_imp_le_div_pos
% 5.15/5.39 thf(fact_2801_mult__imp__div__pos__le,axiom,
% 5.15/5.39 ! [Y: real,X: real,Z: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y ) )
% 5.15/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_imp_div_pos_le
% 5.15/5.39 thf(fact_2802_mult__imp__div__pos__le,axiom,
% 5.15/5.39 ! [Y: rat,X: rat,Z: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 5.15/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_imp_div_pos_le
% 5.15/5.39 thf(fact_2803_pos__le__divide__eq,axiom,
% 5.15/5.39 ! [C: real,A: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos_le_divide_eq
% 5.15/5.39 thf(fact_2804_pos__le__divide__eq,axiom,
% 5.15/5.39 ! [C: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos_le_divide_eq
% 5.15/5.39 thf(fact_2805_pos__divide__le__eq,axiom,
% 5.15/5.39 ! [C: real,B: real,A: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.15/5.39 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos_divide_le_eq
% 5.15/5.39 thf(fact_2806_pos__divide__le__eq,axiom,
% 5.15/5.39 ! [C: rat,B: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.15/5.39 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos_divide_le_eq
% 5.15/5.39 thf(fact_2807_neg__le__divide__eq,axiom,
% 5.15/5.39 ! [C: real,A: real,B: real] :
% 5.15/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % neg_le_divide_eq
% 5.15/5.39 thf(fact_2808_neg__le__divide__eq,axiom,
% 5.15/5.39 ! [C: rat,A: rat,B: rat] :
% 5.15/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % neg_le_divide_eq
% 5.15/5.39 thf(fact_2809_neg__divide__le__eq,axiom,
% 5.15/5.39 ! [C: real,B: real,A: real] :
% 5.15/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.15/5.39 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % neg_divide_le_eq
% 5.15/5.39 thf(fact_2810_neg__divide__le__eq,axiom,
% 5.15/5.39 ! [C: rat,B: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.15/5.39 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % neg_divide_le_eq
% 5.15/5.39 thf(fact_2811_divide__left__mono,axiom,
% 5.15/5.39 ! [B: real,A: real,C: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ B @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.15/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_left_mono
% 5.15/5.39 thf(fact_2812_divide__left__mono,axiom,
% 5.15/5.39 ! [B: rat,A: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_left_mono
% 5.15/5.39 thf(fact_2813_le__divide__eq,axiom,
% 5.15/5.39 ! [A: real,B: real,C: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % le_divide_eq
% 5.15/5.39 thf(fact_2814_le__divide__eq,axiom,
% 5.15/5.39 ! [A: rat,B: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % le_divide_eq
% 5.15/5.39 thf(fact_2815_divide__le__eq,axiom,
% 5.15/5.39 ! [B: real,C: real,A: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_le_eq
% 5.15/5.39 thf(fact_2816_divide__le__eq,axiom,
% 5.15/5.39 ! [B: rat,C: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_le_eq
% 5.15/5.39 thf(fact_2817_le__divide__eq__1,axiom,
% 5.15/5.39 ! [B: real,A: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 & ( ord_less_eq_real @ A @ B ) )
% 5.15/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.39 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % le_divide_eq_1
% 5.15/5.39 thf(fact_2818_le__divide__eq__1,axiom,
% 5.15/5.39 ! [B: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 & ( ord_less_eq_rat @ A @ B ) )
% 5.15/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.39 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % le_divide_eq_1
% 5.15/5.39 thf(fact_2819_divide__le__eq__1,axiom,
% 5.15/5.39 ! [B: real,A: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 & ( ord_less_eq_real @ B @ A ) )
% 5.15/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.39 & ( ord_less_eq_real @ A @ B ) )
% 5.15/5.39 | ( A = zero_zero_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_le_eq_1
% 5.15/5.39 thf(fact_2820_divide__le__eq__1,axiom,
% 5.15/5.39 ! [B: rat,A: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 & ( ord_less_eq_rat @ B @ A ) )
% 5.15/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.39 & ( ord_less_eq_rat @ A @ B ) )
% 5.15/5.39 | ( A = zero_zero_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_le_eq_1
% 5.15/5.39 thf(fact_2821_convex__bound__le,axiom,
% 5.15/5.39 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ X @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ Y @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.15/5.39 => ( ( ( plus_plus_real @ U @ V )
% 5.15/5.39 = one_one_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % convex_bound_le
% 5.15/5.39 thf(fact_2822_convex__bound__le,axiom,
% 5.15/5.39 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ X @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ Y @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.15/5.39 => ( ( ( plus_plus_rat @ U @ V )
% 5.15/5.39 = one_one_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % convex_bound_le
% 5.15/5.39 thf(fact_2823_convex__bound__le,axiom,
% 5.15/5.39 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ X @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ Y @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.15/5.39 => ( ( ( plus_plus_int @ U @ V )
% 5.15/5.39 = one_one_int )
% 5.15/5.39 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % convex_bound_le
% 5.15/5.39 thf(fact_2824_less__divide__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [W: num,B: real,C: real] :
% 5.15/5.39 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % less_divide_eq_numeral(1)
% 5.15/5.39 thf(fact_2825_less__divide__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [W: num,B: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % less_divide_eq_numeral(1)
% 5.15/5.39 thf(fact_2826_divide__less__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [B: real,C: real,W: num] :
% 5.15/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_less_eq_numeral(1)
% 5.15/5.39 thf(fact_2827_divide__less__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [B: rat,C: rat,W: num] :
% 5.15/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_less_eq_numeral(1)
% 5.15/5.39 thf(fact_2828_frac__le__eq,axiom,
% 5.15/5.39 ! [Y: real,Z: real,X: real,W: real] :
% 5.15/5.39 ( ( Y != zero_zero_real )
% 5.15/5.39 => ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.15/5.39 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_le_eq
% 5.15/5.39 thf(fact_2829_frac__le__eq,axiom,
% 5.15/5.39 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.15/5.39 ( ( Y != zero_zero_rat )
% 5.15/5.39 => ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.15/5.39 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_le_eq
% 5.15/5.39 thf(fact_2830_power__Suc__less,axiom,
% 5.15/5.39 ! [A: real,N2: nat] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_real @ A @ one_one_real )
% 5.15/5.39 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_less
% 5.15/5.39 thf(fact_2831_power__Suc__less,axiom,
% 5.15/5.39 ! [A: rat,N2: nat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.15/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_less
% 5.15/5.39 thf(fact_2832_power__Suc__less,axiom,
% 5.15/5.39 ! [A: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.15/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_less
% 5.15/5.39 thf(fact_2833_power__Suc__less,axiom,
% 5.15/5.39 ! [A: int,N2: nat] :
% 5.15/5.39 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_int @ A @ one_one_int )
% 5.15/5.39 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_less
% 5.15/5.39 thf(fact_2834_frac__less__eq,axiom,
% 5.15/5.39 ! [Y: real,Z: real,X: real,W: real] :
% 5.15/5.39 ( ( Y != zero_zero_real )
% 5.15/5.39 => ( ( Z != zero_zero_real )
% 5.15/5.39 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.15/5.39 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_less_eq
% 5.15/5.39 thf(fact_2835_frac__less__eq,axiom,
% 5.15/5.39 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.15/5.39 ( ( Y != zero_zero_rat )
% 5.15/5.39 => ( ( Z != zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.15/5.39 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % frac_less_eq
% 5.15/5.39 thf(fact_2836_power__Suc__le__self,axiom,
% 5.15/5.39 ! [A: real,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_le_self
% 5.15/5.39 thf(fact_2837_power__Suc__le__self,axiom,
% 5.15/5.39 ! [A: rat,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_le_self
% 5.15/5.39 thf(fact_2838_power__Suc__le__self,axiom,
% 5.15/5.39 ! [A: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.15/5.39 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_le_self
% 5.15/5.39 thf(fact_2839_power__Suc__le__self,axiom,
% 5.15/5.39 ! [A: int,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.15/5.39 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_le_self
% 5.15/5.39 thf(fact_2840_power__Suc__less__one,axiom,
% 5.15/5.39 ! [A: real,N2: nat] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_real @ A @ one_one_real )
% 5.15/5.39 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_less_one
% 5.15/5.39 thf(fact_2841_power__Suc__less__one,axiom,
% 5.15/5.39 ! [A: rat,N2: nat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.15/5.39 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_less_one
% 5.15/5.39 thf(fact_2842_power__Suc__less__one,axiom,
% 5.15/5.39 ! [A: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.15/5.39 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_less_one
% 5.15/5.39 thf(fact_2843_power__Suc__less__one,axiom,
% 5.15/5.39 ! [A: int,N2: nat] :
% 5.15/5.39 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_int @ A @ one_one_int )
% 5.15/5.39 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_Suc_less_one
% 5.15/5.39 thf(fact_2844_power__strict__decreasing,axiom,
% 5.15/5.39 ! [N2: nat,N5: nat,A: real] :
% 5.15/5.39 ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.39 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_real @ A @ one_one_real )
% 5.15/5.39 => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_strict_decreasing
% 5.15/5.39 thf(fact_2845_power__strict__decreasing,axiom,
% 5.15/5.39 ! [N2: nat,N5: nat,A: rat] :
% 5.15/5.39 ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.39 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.15/5.39 => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_strict_decreasing
% 5.15/5.39 thf(fact_2846_power__strict__decreasing,axiom,
% 5.15/5.39 ! [N2: nat,N5: nat,A: nat] :
% 5.15/5.39 ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.15/5.39 => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_strict_decreasing
% 5.15/5.39 thf(fact_2847_power__strict__decreasing,axiom,
% 5.15/5.39 ! [N2: nat,N5: nat,A: int] :
% 5.15/5.39 ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.39 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_int @ A @ one_one_int )
% 5.15/5.39 => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_strict_decreasing
% 5.15/5.39 thf(fact_2848_power__decreasing,axiom,
% 5.15/5.39 ! [N2: nat,N5: nat,A: real] :
% 5.15/5.39 ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_decreasing
% 5.15/5.39 thf(fact_2849_power__decreasing,axiom,
% 5.15/5.39 ! [N2: nat,N5: nat,A: rat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_decreasing
% 5.15/5.39 thf(fact_2850_power__decreasing,axiom,
% 5.15/5.39 ! [N2: nat,N5: nat,A: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.39 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.15/5.39 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_decreasing
% 5.15/5.39 thf(fact_2851_power__decreasing,axiom,
% 5.15/5.39 ! [N2: nat,N5: nat,A: int] :
% 5.15/5.39 ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.15/5.39 => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_decreasing
% 5.15/5.39 thf(fact_2852_zero__power2,axiom,
% 5.15/5.39 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = zero_zero_rat ) ).
% 5.15/5.39
% 5.15/5.39 % zero_power2
% 5.15/5.39 thf(fact_2853_zero__power2,axiom,
% 5.15/5.39 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = zero_zero_nat ) ).
% 5.15/5.39
% 5.15/5.39 % zero_power2
% 5.15/5.39 thf(fact_2854_zero__power2,axiom,
% 5.15/5.39 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = zero_zero_real ) ).
% 5.15/5.39
% 5.15/5.39 % zero_power2
% 5.15/5.39 thf(fact_2855_zero__power2,axiom,
% 5.15/5.39 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = zero_zero_complex ) ).
% 5.15/5.39
% 5.15/5.39 % zero_power2
% 5.15/5.39 thf(fact_2856_zero__power2,axiom,
% 5.15/5.39 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = zero_zero_int ) ).
% 5.15/5.39
% 5.15/5.39 % zero_power2
% 5.15/5.39 thf(fact_2857_self__le__power,axiom,
% 5.15/5.39 ! [A: real,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % self_le_power
% 5.15/5.39 thf(fact_2858_self__le__power,axiom,
% 5.15/5.39 ! [A: rat,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % self_le_power
% 5.15/5.39 thf(fact_2859_self__le__power,axiom,
% 5.15/5.39 ! [A: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % self_le_power
% 5.15/5.39 thf(fact_2860_self__le__power,axiom,
% 5.15/5.39 ! [A: int,N2: nat] :
% 5.15/5.39 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % self_le_power
% 5.15/5.39 thf(fact_2861_cong__exp__iff__simps_I3_J,axiom,
% 5.15/5.39 ! [N2: num,Q3: num] :
% 5.15/5.39 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 != zero_zero_nat ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(3)
% 5.15/5.39 thf(fact_2862_cong__exp__iff__simps_I3_J,axiom,
% 5.15/5.39 ! [N2: num,Q3: num] :
% 5.15/5.39 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 != zero_zero_int ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(3)
% 5.15/5.39 thf(fact_2863_cong__exp__iff__simps_I3_J,axiom,
% 5.15/5.39 ! [N2: num,Q3: num] :
% 5.15/5.39 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 != zero_z3403309356797280102nteger ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(3)
% 5.15/5.39 thf(fact_2864_one__less__power,axiom,
% 5.15/5.39 ! [A: real,N2: nat] :
% 5.15/5.39 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % one_less_power
% 5.15/5.39 thf(fact_2865_one__less__power,axiom,
% 5.15/5.39 ! [A: rat,N2: nat] :
% 5.15/5.39 ( ( ord_less_rat @ one_one_rat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % one_less_power
% 5.15/5.39 thf(fact_2866_one__less__power,axiom,
% 5.15/5.39 ! [A: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ one_one_nat @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % one_less_power
% 5.15/5.39 thf(fact_2867_one__less__power,axiom,
% 5.15/5.39 ! [A: int,N2: nat] :
% 5.15/5.39 ( ( ord_less_int @ one_one_int @ A )
% 5.15/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % one_less_power
% 5.15/5.39 thf(fact_2868_numeral__2__eq__2,axiom,
% 5.15/5.39 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.15/5.39 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % numeral_2_eq_2
% 5.15/5.39 thf(fact_2869_pos2,axiom,
% 5.15/5.39 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.15/5.39
% 5.15/5.39 % pos2
% 5.15/5.39 thf(fact_2870_power__diff,axiom,
% 5.15/5.39 ! [A: complex,N2: nat,M: nat] :
% 5.15/5.39 ( ( A != zero_zero_complex )
% 5.15/5.39 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.39 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.39 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_diff
% 5.15/5.39 thf(fact_2871_power__diff,axiom,
% 5.15/5.39 ! [A: real,N2: nat,M: nat] :
% 5.15/5.39 ( ( A != zero_zero_real )
% 5.15/5.39 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.39 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.39 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_diff
% 5.15/5.39 thf(fact_2872_power__diff,axiom,
% 5.15/5.39 ! [A: rat,N2: nat,M: nat] :
% 5.15/5.39 ( ( A != zero_zero_rat )
% 5.15/5.39 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.39 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.39 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_diff
% 5.15/5.39 thf(fact_2873_power__diff,axiom,
% 5.15/5.39 ! [A: nat,N2: nat,M: nat] :
% 5.15/5.39 ( ( A != zero_zero_nat )
% 5.15/5.39 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.39 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.39 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_diff
% 5.15/5.39 thf(fact_2874_power__diff,axiom,
% 5.15/5.39 ! [A: int,N2: nat,M: nat] :
% 5.15/5.39 ( ( A != zero_zero_int )
% 5.15/5.39 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.39 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.39 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power_diff
% 5.15/5.39 thf(fact_2875_numeral__3__eq__3,axiom,
% 5.15/5.39 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.15/5.39 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % numeral_3_eq_3
% 5.15/5.39 thf(fact_2876_Suc__diff__eq__diff__pred,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.15/5.39 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % Suc_diff_eq_diff_pred
% 5.15/5.39 thf(fact_2877_Suc__pred_H,axiom,
% 5.15/5.39 ! [N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( N2
% 5.15/5.39 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % Suc_pred'
% 5.15/5.39 thf(fact_2878_div__if,axiom,
% 5.15/5.39 ( divide_divide_nat
% 5.15/5.39 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.39 ( if_nat
% 5.15/5.39 @ ( ( ord_less_nat @ M5 @ N3 )
% 5.15/5.39 | ( N3 = zero_zero_nat ) )
% 5.15/5.39 @ zero_zero_nat
% 5.15/5.39 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M5 @ N3 ) @ N3 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_if
% 5.15/5.39 thf(fact_2879_div__geq,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.15/5.39 => ( ( divide_divide_nat @ M @ N2 )
% 5.15/5.39 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % div_geq
% 5.15/5.39 thf(fact_2880_add__eq__if,axiom,
% 5.15/5.39 ( plus_plus_nat
% 5.15/5.39 = ( ^ [M5: nat,N3: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % add_eq_if
% 5.15/5.39 thf(fact_2881_less__eq__div__iff__mult__less__eq,axiom,
% 5.15/5.39 ! [Q3: nat,M: nat,N2: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.15/5.39 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q3 ) )
% 5.15/5.39 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N2 ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % less_eq_div_iff_mult_less_eq
% 5.15/5.39 thf(fact_2882_dividend__less__times__div,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % dividend_less_times_div
% 5.15/5.39 thf(fact_2883_dividend__less__div__times,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.39 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % dividend_less_div_times
% 5.15/5.39 thf(fact_2884_split__div,axiom,
% 5.15/5.39 ! [P: nat > $o,M: nat,N2: nat] :
% 5.15/5.39 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.15/5.39 = ( ( ( N2 = zero_zero_nat )
% 5.15/5.39 => ( P @ zero_zero_nat ) )
% 5.15/5.39 & ( ( N2 != zero_zero_nat )
% 5.15/5.39 => ! [I3: nat,J3: nat] :
% 5.15/5.39 ( ( ord_less_nat @ J3 @ N2 )
% 5.15/5.39 => ( ( M
% 5.15/5.39 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J3 ) )
% 5.15/5.39 => ( P @ I3 ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % split_div
% 5.15/5.39 thf(fact_2885_mult__eq__if,axiom,
% 5.15/5.39 ( times_times_nat
% 5.15/5.39 = ( ^ [M5: nat,N3: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % mult_eq_if
% 5.15/5.39 thf(fact_2886_split__mod,axiom,
% 5.15/5.39 ! [P: nat > $o,M: nat,N2: nat] :
% 5.15/5.39 ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.15/5.39 = ( ( ( N2 = zero_zero_nat )
% 5.15/5.39 => ( P @ M ) )
% 5.15/5.39 & ( ( N2 != zero_zero_nat )
% 5.15/5.39 => ! [I3: nat,J3: nat] :
% 5.15/5.39 ( ( ord_less_nat @ J3 @ N2 )
% 5.15/5.39 => ( ( M
% 5.15/5.39 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J3 ) )
% 5.15/5.39 => ( P @ J3 ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % split_mod
% 5.15/5.39 thf(fact_2887_vebt__member_Osimps_I4_J,axiom,
% 5.15/5.39 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.15/5.39 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 5.15/5.39
% 5.15/5.39 % vebt_member.simps(4)
% 5.15/5.39 thf(fact_2888_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.15/5.39 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.15/5.39 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 5.15/5.39 = one_one_nat ) ).
% 5.15/5.39
% 5.15/5.39 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(3)
% 5.15/5.39 thf(fact_2889_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 5.15/5.39 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.15/5.39 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 5.15/5.39 = one_one_nat ) ).
% 5.15/5.39
% 5.15/5.39 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(3)
% 5.15/5.39 thf(fact_2890_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.15/5.39 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.15/5.39 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 5.15/5.39 = ( ( X = Mi )
% 5.15/5.39 | ( X = Ma ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % VEBT_internal.membermima.simps(3)
% 5.15/5.39 thf(fact_2891_vebt__succ_Osimps_I4_J,axiom,
% 5.15/5.39 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 5.15/5.39 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 5.15/5.39 = none_nat ) ).
% 5.15/5.39
% 5.15/5.39 % vebt_succ.simps(4)
% 5.15/5.39 thf(fact_2892_vebt__pred_Osimps_I5_J,axiom,
% 5.15/5.39 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.15/5.39 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 5.15/5.39 = none_nat ) ).
% 5.15/5.39
% 5.15/5.39 % vebt_pred.simps(5)
% 5.15/5.39 thf(fact_2893_convex__bound__lt,axiom,
% 5.15/5.39 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.15/5.39 ( ( ord_less_real @ X @ A )
% 5.15/5.39 => ( ( ord_less_real @ Y @ A )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.15/5.39 => ( ( ( plus_plus_real @ U @ V )
% 5.15/5.39 = one_one_real )
% 5.15/5.39 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % convex_bound_lt
% 5.15/5.39 thf(fact_2894_convex__bound__lt,axiom,
% 5.15/5.39 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.15/5.39 ( ( ord_less_rat @ X @ A )
% 5.15/5.39 => ( ( ord_less_rat @ Y @ A )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.15/5.39 => ( ( ( plus_plus_rat @ U @ V )
% 5.15/5.39 = one_one_rat )
% 5.15/5.39 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % convex_bound_lt
% 5.15/5.39 thf(fact_2895_convex__bound__lt,axiom,
% 5.15/5.39 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.15/5.39 ( ( ord_less_int @ X @ A )
% 5.15/5.39 => ( ( ord_less_int @ Y @ A )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.15/5.39 => ( ( ( plus_plus_int @ U @ V )
% 5.15/5.39 = one_one_int )
% 5.15/5.39 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % convex_bound_lt
% 5.15/5.39 thf(fact_2896_le__divide__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [W: num,B: real,C: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % le_divide_eq_numeral(1)
% 5.15/5.39 thf(fact_2897_le__divide__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [W: num,B: rat,C: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % le_divide_eq_numeral(1)
% 5.15/5.39 thf(fact_2898_divide__le__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [B: real,C: real,W: num] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.15/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_le_eq_numeral(1)
% 5.15/5.39 thf(fact_2899_divide__le__eq__numeral_I1_J,axiom,
% 5.15/5.39 ! [B: rat,C: rat,W: num] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.15/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.15/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % divide_le_eq_numeral(1)
% 5.15/5.39 thf(fact_2900_half__gt__zero__iff,axiom,
% 5.15/5.39 ! [A: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.39 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.15/5.39
% 5.15/5.39 % half_gt_zero_iff
% 5.15/5.39 thf(fact_2901_half__gt__zero__iff,axiom,
% 5.15/5.39 ! [A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.39
% 5.15/5.39 % half_gt_zero_iff
% 5.15/5.39 thf(fact_2902_half__gt__zero,axiom,
% 5.15/5.39 ! [A: real] :
% 5.15/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.39 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % half_gt_zero
% 5.15/5.39 thf(fact_2903_half__gt__zero,axiom,
% 5.15/5.39 ! [A: rat] :
% 5.15/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.39 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % half_gt_zero
% 5.15/5.39 thf(fact_2904_scaling__mono,axiom,
% 5.15/5.39 ! [U: real,V: real,R2: real,S: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ U @ V )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.15/5.39 => ( ( ord_less_eq_real @ R2 @ S )
% 5.15/5.39 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % scaling_mono
% 5.15/5.39 thf(fact_2905_scaling__mono,axiom,
% 5.15/5.39 ! [U: rat,V: rat,R2: rat,S: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ U @ V )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.15/5.39 => ( ( ord_less_eq_rat @ R2 @ S )
% 5.15/5.39 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % scaling_mono
% 5.15/5.39 thf(fact_2906_power2__le__imp__le,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power2_le_imp_le
% 5.15/5.39 thf(fact_2907_power2__le__imp__le,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power2_le_imp_le
% 5.15/5.39 thf(fact_2908_power2__le__imp__le,axiom,
% 5.15/5.39 ! [X: nat,Y: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.15/5.39 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power2_le_imp_le
% 5.15/5.39 thf(fact_2909_power2__le__imp__le,axiom,
% 5.15/5.39 ! [X: int,Y: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.39 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power2_le_imp_le
% 5.15/5.39 thf(fact_2910_power2__eq__imp__eq,axiom,
% 5.15/5.39 ! [X: real,Y: real] :
% 5.15/5.39 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.39 => ( X = Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power2_eq_imp_eq
% 5.15/5.39 thf(fact_2911_power2__eq__imp__eq,axiom,
% 5.15/5.39 ! [X: rat,Y: rat] :
% 5.15/5.39 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.39 => ( X = Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power2_eq_imp_eq
% 5.15/5.39 thf(fact_2912_power2__eq__imp__eq,axiom,
% 5.15/5.39 ! [X: nat,Y: nat] :
% 5.15/5.39 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.15/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.15/5.39 => ( X = Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power2_eq_imp_eq
% 5.15/5.39 thf(fact_2913_power2__eq__imp__eq,axiom,
% 5.15/5.39 ! [X: int,Y: int] :
% 5.15/5.39 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.39 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.39 => ( X = Y ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % power2_eq_imp_eq
% 5.15/5.39 thf(fact_2914_zero__le__power2,axiom,
% 5.15/5.39 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % zero_le_power2
% 5.15/5.39 thf(fact_2915_zero__le__power2,axiom,
% 5.15/5.39 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % zero_le_power2
% 5.15/5.39 thf(fact_2916_zero__le__power2,axiom,
% 5.15/5.39 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % zero_le_power2
% 5.15/5.39 thf(fact_2917_power2__less__0,axiom,
% 5.15/5.39 ! [A: real] :
% 5.15/5.39 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.15/5.39
% 5.15/5.39 % power2_less_0
% 5.15/5.39 thf(fact_2918_power2__less__0,axiom,
% 5.15/5.39 ! [A: rat] :
% 5.15/5.39 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.15/5.39
% 5.15/5.39 % power2_less_0
% 5.15/5.39 thf(fact_2919_power2__less__0,axiom,
% 5.15/5.39 ! [A: int] :
% 5.15/5.39 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.15/5.39
% 5.15/5.39 % power2_less_0
% 5.15/5.39 thf(fact_2920_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.15/5.39 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.39 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.15/5.39 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.15/5.39 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.15/5.39 thf(fact_2921_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.15/5.39 ! [C: nat,A: nat,B: nat] :
% 5.15/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.15/5.39 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.15/5.39 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.15/5.39 thf(fact_2922_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.15/5.39 ! [C: int,A: int,B: int] :
% 5.15/5.39 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.39 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.39 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.15/5.39
% 5.15/5.39 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.15/5.39 thf(fact_2923_exp__add__not__zero__imp__right,axiom,
% 5.15/5.39 ! [M: nat,N2: nat] :
% 5.15/5.39 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.39 != zero_zero_nat )
% 5.15/5.39 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.39 != zero_zero_nat ) ) ).
% 5.15/5.39
% 5.15/5.39 % exp_add_not_zero_imp_right
% 5.15/5.39 thf(fact_2924_exp__add__not__zero__imp__right,axiom,
% 5.15/5.39 ! [M: nat,N2: nat] :
% 5.15/5.39 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.39 != zero_zero_int )
% 5.15/5.39 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.39 != zero_zero_int ) ) ).
% 5.15/5.39
% 5.15/5.39 % exp_add_not_zero_imp_right
% 5.15/5.39 thf(fact_2925_exp__add__not__zero__imp__left,axiom,
% 5.15/5.39 ! [M: nat,N2: nat] :
% 5.15/5.39 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.39 != zero_zero_nat )
% 5.15/5.39 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.15/5.39 != zero_zero_nat ) ) ).
% 5.15/5.39
% 5.15/5.39 % exp_add_not_zero_imp_left
% 5.15/5.39 thf(fact_2926_exp__add__not__zero__imp__left,axiom,
% 5.15/5.39 ! [M: nat,N2: nat] :
% 5.15/5.39 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.39 != zero_zero_int )
% 5.15/5.39 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.15/5.39 != zero_zero_int ) ) ).
% 5.15/5.39
% 5.15/5.39 % exp_add_not_zero_imp_left
% 5.15/5.39 thf(fact_2927_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.39 != zero_zero_nat )
% 5.15/5.39 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.15/5.39 != zero_zero_nat ) ) ).
% 5.15/5.39
% 5.15/5.39 % exp_not_zero_imp_exp_diff_not_zero
% 5.15/5.39 thf(fact_2928_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.15/5.39 ! [N2: nat,M: nat] :
% 5.15/5.39 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.39 != zero_zero_int )
% 5.15/5.39 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.15/5.39 != zero_zero_int ) ) ).
% 5.15/5.39
% 5.15/5.39 % exp_not_zero_imp_exp_diff_not_zero
% 5.15/5.39 thf(fact_2929_cong__exp__iff__simps_I7_J,axiom,
% 5.15/5.39 ! [Q3: num,N2: num] :
% 5.15/5.39 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.39 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.15/5.39 = zero_zero_nat ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(7)
% 5.15/5.39 thf(fact_2930_cong__exp__iff__simps_I7_J,axiom,
% 5.15/5.39 ! [Q3: num,N2: num] :
% 5.15/5.39 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.39 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 5.15/5.39 = zero_zero_int ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(7)
% 5.15/5.39 thf(fact_2931_cong__exp__iff__simps_I7_J,axiom,
% 5.15/5.39 ! [Q3: num,N2: num] :
% 5.15/5.39 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.39 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.15/5.39 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(7)
% 5.15/5.39 thf(fact_2932_cong__exp__iff__simps_I11_J,axiom,
% 5.15/5.39 ! [M: num,Q3: num] :
% 5.15/5.39 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.39 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.15/5.39 = zero_zero_nat ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(11)
% 5.15/5.39 thf(fact_2933_cong__exp__iff__simps_I11_J,axiom,
% 5.15/5.39 ! [M: num,Q3: num] :
% 5.15/5.39 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.39 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.15/5.39 = zero_zero_int ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(11)
% 5.15/5.39 thf(fact_2934_cong__exp__iff__simps_I11_J,axiom,
% 5.15/5.39 ! [M: num,Q3: num] :
% 5.15/5.39 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.15/5.39 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.15/5.39 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.15/5.39 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.39
% 5.15/5.39 % cong_exp_iff_simps(11)
% 5.15/5.39 thf(fact_2935_power__diff__power__eq,axiom,
% 5.15/5.39 ! [A: nat,N2: nat,M: nat] :
% 5.15/5.39 ( ( A != zero_zero_nat )
% 5.15/5.39 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.39 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.15/5.39 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.15/5.39 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.39 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.15/5.40 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_diff_power_eq
% 5.15/5.40 thf(fact_2936_power__diff__power__eq,axiom,
% 5.15/5.40 ! [A: int,N2: nat,M: nat] :
% 5.15/5.40 ( ( A != zero_zero_int )
% 5.15/5.40 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.40 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.15/5.40 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.15/5.40 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.40 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.15/5.40 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_diff_power_eq
% 5.15/5.40 thf(fact_2937_less__2__cases__iff,axiom,
% 5.15/5.40 ! [N2: nat] :
% 5.15/5.40 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.40 = ( ( N2 = zero_zero_nat )
% 5.15/5.40 | ( N2
% 5.15/5.40 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % less_2_cases_iff
% 5.15/5.40 thf(fact_2938_less__2__cases,axiom,
% 5.15/5.40 ! [N2: nat] :
% 5.15/5.40 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.40 => ( ( N2 = zero_zero_nat )
% 5.15/5.40 | ( N2
% 5.15/5.40 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % less_2_cases
% 5.15/5.40 thf(fact_2939_nat__induct2,axiom,
% 5.15/5.40 ! [P: nat > $o,N2: nat] :
% 5.15/5.40 ( ( P @ zero_zero_nat )
% 5.15/5.40 => ( ( P @ one_one_nat )
% 5.15/5.40 => ( ! [N: nat] :
% 5.15/5.40 ( ( P @ N )
% 5.15/5.40 => ( P @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 => ( P @ N2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % nat_induct2
% 5.15/5.40 thf(fact_2940_power__eq__if,axiom,
% 5.15/5.40 ( power_power_complex
% 5.15/5.40 = ( ^ [P5: complex,M5: nat] : ( if_complex @ ( M5 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_eq_if
% 5.15/5.40 thf(fact_2941_power__eq__if,axiom,
% 5.15/5.40 ( power_power_real
% 5.15/5.40 = ( ^ [P5: real,M5: nat] : ( if_real @ ( M5 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_eq_if
% 5.15/5.40 thf(fact_2942_power__eq__if,axiom,
% 5.15/5.40 ( power_power_rat
% 5.15/5.40 = ( ^ [P5: rat,M5: nat] : ( if_rat @ ( M5 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_eq_if
% 5.15/5.40 thf(fact_2943_power__eq__if,axiom,
% 5.15/5.40 ( power_power_nat
% 5.15/5.40 = ( ^ [P5: nat,M5: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_eq_if
% 5.15/5.40 thf(fact_2944_power__eq__if,axiom,
% 5.15/5.40 ( power_power_int
% 5.15/5.40 = ( ^ [P5: int,M5: nat] : ( if_int @ ( M5 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_eq_if
% 5.15/5.40 thf(fact_2945_power__minus__mult,axiom,
% 5.15/5.40 ! [N2: nat,A: complex] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.15/5.40 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_minus_mult
% 5.15/5.40 thf(fact_2946_power__minus__mult,axiom,
% 5.15/5.40 ! [N2: nat,A: real] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.15/5.40 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_minus_mult
% 5.15/5.40 thf(fact_2947_power__minus__mult,axiom,
% 5.15/5.40 ! [N2: nat,A: rat] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.15/5.40 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_minus_mult
% 5.15/5.40 thf(fact_2948_power__minus__mult,axiom,
% 5.15/5.40 ! [N2: nat,A: nat] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.15/5.40 = ( power_power_nat @ A @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_minus_mult
% 5.15/5.40 thf(fact_2949_power__minus__mult,axiom,
% 5.15/5.40 ! [N2: nat,A: int] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.15/5.40 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power_minus_mult
% 5.15/5.40 thf(fact_2950_le__div__geq,axiom,
% 5.15/5.40 ! [N2: nat,M: nat] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.40 => ( ( divide_divide_nat @ M @ N2 )
% 5.15/5.40 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % le_div_geq
% 5.15/5.40 thf(fact_2951_split__div_H,axiom,
% 5.15/5.40 ! [P: nat > $o,M: nat,N2: nat] :
% 5.15/5.40 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.15/5.40 = ( ( ( N2 = zero_zero_nat )
% 5.15/5.40 & ( P @ zero_zero_nat ) )
% 5.15/5.40 | ? [Q4: nat] :
% 5.15/5.40 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q4 ) @ M )
% 5.15/5.40 & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q4 ) ) )
% 5.15/5.40 & ( P @ Q4 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % split_div'
% 5.15/5.40 thf(fact_2952_Suc__times__mod__eq,axiom,
% 5.15/5.40 ! [M: nat,N2: nat] :
% 5.15/5.40 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.15/5.40 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 5.15/5.40 = one_one_nat ) ) ).
% 5.15/5.40
% 5.15/5.40 % Suc_times_mod_eq
% 5.15/5.40 thf(fact_2953_vebt__succ_Osimps_I5_J,axiom,
% 5.15/5.40 ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.15/5.40 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 5.15/5.40 = none_nat ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_succ.simps(5)
% 5.15/5.40 thf(fact_2954_vebt__pred_Osimps_I6_J,axiom,
% 5.15/5.40 ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.15/5.40 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 5.15/5.40 = none_nat ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_pred.simps(6)
% 5.15/5.40 thf(fact_2955_power2__less__imp__less,axiom,
% 5.15/5.40 ! [X: real,Y: real] :
% 5.15/5.40 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.40 => ( ord_less_real @ X @ Y ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power2_less_imp_less
% 5.15/5.40 thf(fact_2956_power2__less__imp__less,axiom,
% 5.15/5.40 ! [X: rat,Y: rat] :
% 5.15/5.40 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.40 => ( ord_less_rat @ X @ Y ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power2_less_imp_less
% 5.15/5.40 thf(fact_2957_power2__less__imp__less,axiom,
% 5.15/5.40 ! [X: nat,Y: nat] :
% 5.15/5.40 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.15/5.40 => ( ord_less_nat @ X @ Y ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power2_less_imp_less
% 5.15/5.40 thf(fact_2958_power2__less__imp__less,axiom,
% 5.15/5.40 ! [X: int,Y: int] :
% 5.15/5.40 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.40 => ( ord_less_int @ X @ Y ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % power2_less_imp_less
% 5.15/5.40 thf(fact_2959_sum__power2__le__zero__iff,axiom,
% 5.15/5.40 ! [X: real,Y: real] :
% 5.15/5.40 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.15/5.40 = ( ( X = zero_zero_real )
% 5.15/5.40 & ( Y = zero_zero_real ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_le_zero_iff
% 5.15/5.40 thf(fact_2960_sum__power2__le__zero__iff,axiom,
% 5.15/5.40 ! [X: rat,Y: rat] :
% 5.15/5.40 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.15/5.40 = ( ( X = zero_zero_rat )
% 5.15/5.40 & ( Y = zero_zero_rat ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_le_zero_iff
% 5.15/5.40 thf(fact_2961_sum__power2__le__zero__iff,axiom,
% 5.15/5.40 ! [X: int,Y: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.15/5.40 = ( ( X = zero_zero_int )
% 5.15/5.40 & ( Y = zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_le_zero_iff
% 5.15/5.40 thf(fact_2962_sum__power2__ge__zero,axiom,
% 5.15/5.40 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_ge_zero
% 5.15/5.40 thf(fact_2963_sum__power2__ge__zero,axiom,
% 5.15/5.40 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_ge_zero
% 5.15/5.40 thf(fact_2964_sum__power2__ge__zero,axiom,
% 5.15/5.40 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_ge_zero
% 5.15/5.40 thf(fact_2965_sum__power2__gt__zero__iff,axiom,
% 5.15/5.40 ! [X: real,Y: real] :
% 5.15/5.40 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 = ( ( X != zero_zero_real )
% 5.15/5.40 | ( Y != zero_zero_real ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_gt_zero_iff
% 5.15/5.40 thf(fact_2966_sum__power2__gt__zero__iff,axiom,
% 5.15/5.40 ! [X: rat,Y: rat] :
% 5.15/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 = ( ( X != zero_zero_rat )
% 5.15/5.40 | ( Y != zero_zero_rat ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_gt_zero_iff
% 5.15/5.40 thf(fact_2967_sum__power2__gt__zero__iff,axiom,
% 5.15/5.40 ! [X: int,Y: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 = ( ( X != zero_zero_int )
% 5.15/5.40 | ( Y != zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % sum_power2_gt_zero_iff
% 5.15/5.40 thf(fact_2968_not__sum__power2__lt__zero,axiom,
% 5.15/5.40 ! [X: real,Y: real] :
% 5.15/5.40 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.15/5.40
% 5.15/5.40 % not_sum_power2_lt_zero
% 5.15/5.40 thf(fact_2969_not__sum__power2__lt__zero,axiom,
% 5.15/5.40 ! [X: rat,Y: rat] :
% 5.15/5.40 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.15/5.40
% 5.15/5.40 % not_sum_power2_lt_zero
% 5.15/5.40 thf(fact_2970_not__sum__power2__lt__zero,axiom,
% 5.15/5.40 ! [X: int,Y: int] :
% 5.15/5.40 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.15/5.40
% 5.15/5.40 % not_sum_power2_lt_zero
% 5.15/5.40 thf(fact_2971_divmod__digit__0_I2_J,axiom,
% 5.15/5.40 ! [B: nat,A: nat] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.40 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.15/5.40 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_0(2)
% 5.15/5.40 thf(fact_2972_divmod__digit__0_I2_J,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.15/5.40 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_0(2)
% 5.15/5.40 thf(fact_2973_divmod__digit__0_I2_J,axiom,
% 5.15/5.40 ! [B: code_integer,A: code_integer] :
% 5.15/5.40 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.40 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.15/5.40 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_0(2)
% 5.15/5.40 thf(fact_2974_bits__stable__imp__add__self,axiom,
% 5.15/5.40 ! [A: nat] :
% 5.15/5.40 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.40 = A )
% 5.15/5.40 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 = zero_zero_nat ) ) ).
% 5.15/5.40
% 5.15/5.40 % bits_stable_imp_add_self
% 5.15/5.40 thf(fact_2975_bits__stable__imp__add__self,axiom,
% 5.15/5.40 ! [A: int] :
% 5.15/5.40 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.40 = A )
% 5.15/5.40 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.15/5.40 = zero_zero_int ) ) ).
% 5.15/5.40
% 5.15/5.40 % bits_stable_imp_add_self
% 5.15/5.40 thf(fact_2976_bits__stable__imp__add__self,axiom,
% 5.15/5.40 ! [A: code_integer] :
% 5.15/5.40 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.40 = A )
% 5.15/5.40 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.15/5.40 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.40
% 5.15/5.40 % bits_stable_imp_add_self
% 5.15/5.40 thf(fact_2977_zero__le__even__power_H,axiom,
% 5.15/5.40 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zero_le_even_power'
% 5.15/5.40 thf(fact_2978_zero__le__even__power_H,axiom,
% 5.15/5.40 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zero_le_even_power'
% 5.15/5.40 thf(fact_2979_zero__le__even__power_H,axiom,
% 5.15/5.40 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zero_le_even_power'
% 5.15/5.40 thf(fact_2980_nat__bit__induct,axiom,
% 5.15/5.40 ! [P: nat > $o,N2: nat] :
% 5.15/5.40 ( ( P @ zero_zero_nat )
% 5.15/5.40 => ( ! [N: nat] :
% 5.15/5.40 ( ( P @ N )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.15/5.40 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.15/5.40 => ( ! [N: nat] :
% 5.15/5.40 ( ( P @ N )
% 5.15/5.40 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.15/5.40 => ( P @ N2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % nat_bit_induct
% 5.15/5.40 thf(fact_2981_Suc__n__div__2__gt__zero,axiom,
% 5.15/5.40 ! [N2: nat] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % Suc_n_div_2_gt_zero
% 5.15/5.40 thf(fact_2982_div__2__gt__zero,axiom,
% 5.15/5.40 ! [N2: nat] :
% 5.15/5.40 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.40 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_2_gt_zero
% 5.15/5.40 thf(fact_2983_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.15/5.40 ! [X: produc5542196010084753463at_nat] :
% 5.15/5.40 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.15/5.40 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.15/5.40 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B6: product_prod_nat_nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B6 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.option_shift.cases
% 5.15/5.40 thf(fact_2984_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.15/5.40 ! [X: produc8306885398267862888on_nat] :
% 5.15/5.40 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.15/5.40 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.15/5.40 => ~ ! [F2: nat > nat > nat,A5: nat,B6: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B6 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.option_shift.cases
% 5.15/5.40 thf(fact_2985_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.15/5.40 ! [X: produc1193250871479095198on_num] :
% 5.15/5.40 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.15/5.40 => ( ! [Uw2: num > num > num,V2: num] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.15/5.40 => ~ ! [F2: num > num > num,A5: num,B6: num] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B6 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.option_shift.cases
% 5.15/5.40 thf(fact_2986_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.15/5.40 ! [X: produc5491161045314408544at_nat] :
% 5.15/5.40 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.15/5.40 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.15/5.40 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.option_comp_shift.cases
% 5.15/5.40 thf(fact_2987_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.15/5.40 ! [X: produc2233624965454879586on_nat] :
% 5.15/5.40 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.15/5.40 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.15/5.40 => ~ ! [F2: nat > nat > $o,X3: nat,Y3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.option_comp_shift.cases
% 5.15/5.40 thf(fact_2988_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.15/5.40 ! [X: produc7036089656553540234on_num] :
% 5.15/5.40 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.15/5.40 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.15/5.40 => ~ ! [F2: num > num > $o,X3: num,Y3: num] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.option_comp_shift.cases
% 5.15/5.40 thf(fact_2989_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 5.15/5.40 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.15/5.40 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X )
% 5.15/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 5.15/5.40 thf(fact_2990_divmod__digit__0_I1_J,axiom,
% 5.15/5.40 ! [B: nat,A: nat] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.40 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_0(1)
% 5.15/5.40 thf(fact_2991_divmod__digit__0_I1_J,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_0(1)
% 5.15/5.40 thf(fact_2992_divmod__digit__0_I1_J,axiom,
% 5.15/5.40 ! [B: code_integer,A: code_integer] :
% 5.15/5.40 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.40 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_0(1)
% 5.15/5.40 thf(fact_2993_odd__0__le__power__imp__0__le,axiom,
% 5.15/5.40 ! [A: real,N2: nat] :
% 5.15/5.40 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.15/5.40 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.15/5.40
% 5.15/5.40 % odd_0_le_power_imp_0_le
% 5.15/5.40 thf(fact_2994_odd__0__le__power__imp__0__le,axiom,
% 5.15/5.40 ! [A: rat,N2: nat] :
% 5.15/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.15/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.40
% 5.15/5.40 % odd_0_le_power_imp_0_le
% 5.15/5.40 thf(fact_2995_odd__0__le__power__imp__0__le,axiom,
% 5.15/5.40 ! [A: int,N2: nat] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.15/5.40 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.15/5.40
% 5.15/5.40 % odd_0_le_power_imp_0_le
% 5.15/5.40 thf(fact_2996_odd__power__less__zero,axiom,
% 5.15/5.40 ! [A: real,N2: nat] :
% 5.15/5.40 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.40 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 5.15/5.40
% 5.15/5.40 % odd_power_less_zero
% 5.15/5.40 thf(fact_2997_odd__power__less__zero,axiom,
% 5.15/5.40 ! [A: rat,N2: nat] :
% 5.15/5.40 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.40 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 5.15/5.40
% 5.15/5.40 % odd_power_less_zero
% 5.15/5.40 thf(fact_2998_odd__power__less__zero,axiom,
% 5.15/5.40 ! [A: int,N2: nat] :
% 5.15/5.40 ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.40 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 5.15/5.40
% 5.15/5.40 % odd_power_less_zero
% 5.15/5.40 thf(fact_2999_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.15/5.40 ! [X: nat,N2: nat,M: nat] :
% 5.15/5.40 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.40 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.exp_split_high_low(1)
% 5.15/5.40 thf(fact_3000_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.15/5.40 ! [X: nat,N2: nat,M: nat] :
% 5.15/5.40 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.40 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.exp_split_high_low(2)
% 5.15/5.40 thf(fact_3001_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 5.15/5.40 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.15/5.40 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 5.15/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 5.15/5.40 thf(fact_3002_mod__double__modulus,axiom,
% 5.15/5.40 ! [M: code_integer,X: code_integer] :
% 5.15/5.40 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.15/5.40 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.15/5.40 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.40 = ( modulo364778990260209775nteger @ X @ M ) )
% 5.15/5.40 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.40 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % mod_double_modulus
% 5.15/5.40 thf(fact_3003_mod__double__modulus,axiom,
% 5.15/5.40 ! [M: nat,X: nat] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.15/5.40 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.40 = ( modulo_modulo_nat @ X @ M ) )
% 5.15/5.40 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.40 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % mod_double_modulus
% 5.15/5.40 thf(fact_3004_mod__double__modulus,axiom,
% 5.15/5.40 ! [M: int,X: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ M )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.40 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.40 = ( modulo_modulo_int @ X @ M ) )
% 5.15/5.40 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.15/5.40 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % mod_double_modulus
% 5.15/5.40 thf(fact_3005_divmod__digit__1_I2_J,axiom,
% 5.15/5.40 ! [A: code_integer,B: code_integer] :
% 5.15/5.40 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.40 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.40 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_1(2)
% 5.15/5.40 thf(fact_3006_divmod__digit__1_I2_J,axiom,
% 5.15/5.40 ! [A: nat,B: nat] :
% 5.15/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.40 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_1(2)
% 5.15/5.40 thf(fact_3007_divmod__digit__1_I2_J,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.15/5.40 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_1(2)
% 5.15/5.40 thf(fact_3008_arith__geo__mean,axiom,
% 5.15/5.40 ! [U: real,X: real,Y: real] :
% 5.15/5.40 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.40 = ( times_times_real @ X @ Y ) )
% 5.15/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.40 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % arith_geo_mean
% 5.15/5.40 thf(fact_3009_arith__geo__mean,axiom,
% 5.15/5.40 ! [U: rat,X: rat,Y: rat] :
% 5.15/5.40 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.40 = ( times_times_rat @ X @ Y ) )
% 5.15/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.40 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % arith_geo_mean
% 5.15/5.40 thf(fact_3010_divmod__digit__1_I1_J,axiom,
% 5.15/5.40 ! [A: code_integer,B: code_integer] :
% 5.15/5.40 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.40 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.40 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.15/5.40 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_1(1)
% 5.15/5.40 thf(fact_3011_divmod__digit__1_I1_J,axiom,
% 5.15/5.40 ! [A: nat,B: nat] :
% 5.15/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.15/5.40 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 5.15/5.40 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_1(1)
% 5.15/5.40 thf(fact_3012_divmod__digit__1_I1_J,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.15/5.40 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 5.15/5.40 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % divmod_digit_1(1)
% 5.15/5.40 thf(fact_3013_vebt__succ_Osimps_I6_J,axiom,
% 5.15/5.40 ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.40 ( ( ( ord_less_nat @ X @ Mi )
% 5.15/5.40 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.40 = ( some_nat @ Mi ) ) )
% 5.15/5.40 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.15/5.40 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.40 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.40 @ ( if_option_nat
% 5.15/5.40 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 != none_nat )
% 5.15/5.40 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.40 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 @ ( if_option_nat
% 5.15/5.40 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 = none_nat )
% 5.15/5.40 @ none_nat
% 5.15/5.40 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.40 @ none_nat ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_succ.simps(6)
% 5.15/5.40 thf(fact_3014_vebt__pred_Osimps_I7_J,axiom,
% 5.15/5.40 ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.40 ( ( ( ord_less_nat @ Ma @ X )
% 5.15/5.40 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.40 = ( some_nat @ Ma ) ) )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.15/5.40 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.40 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.40 @ ( if_option_nat
% 5.15/5.40 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 != none_nat )
% 5.15/5.40 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.40 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 @ ( if_option_nat
% 5.15/5.40 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 = none_nat )
% 5.15/5.40 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.15/5.40 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.40 @ none_nat ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_pred.simps(7)
% 5.15/5.40 thf(fact_3015_vebt__mint_Osimps_I2_J,axiom,
% 5.15/5.40 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.15/5.40 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.15/5.40 = none_nat ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_mint.simps(2)
% 5.15/5.40 thf(fact_3016_vebt__maxt_Osimps_I2_J,axiom,
% 5.15/5.40 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.15/5.40 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.15/5.40 = none_nat ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_maxt.simps(2)
% 5.15/5.40 thf(fact_3017_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 5.15/5.40 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.40 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.40 = ( plus_plus_nat @ one_one_nat
% 5.15/5.40 @ ( if_nat @ ( X = Mi ) @ zero_zero_nat
% 5.15/5.40 @ ( if_nat @ ( X = Ma ) @ zero_zero_nat
% 5.15/5.40 @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ zero_zero_nat
% 5.15/5.40 @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ zero_zero_nat
% 5.15/5.40 @ ( if_nat
% 5.15/5.40 @ ( ( ord_less_nat @ Mi @ X )
% 5.15/5.40 & ( ord_less_nat @ X @ Ma ) )
% 5.15/5.40 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.15/5.40 @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 5.15/5.40 thf(fact_3018_vebt__succ_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.15/5.40 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ! [Uu2: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ Uu2 @ B6 ) )
% 5.15/5.40 => ( ( Xa2 = zero_zero_nat )
% 5.15/5.40 => ~ ( ( B6
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.40 & ( ~ B6
% 5.15/5.40 => ( Y = none_nat ) ) ) ) )
% 5.15/5.40 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ( ? [N: nat] :
% 5.15/5.40 ( Xa2
% 5.15/5.40 = ( suc @ N ) )
% 5.15/5.40 => ( Y != none_nat ) ) )
% 5.15/5.40 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.40 => ( Y != none_nat ) )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.15/5.40 => ( Y != none_nat ) )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 5.15/5.40 => ( Y != none_nat ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ Mi2 ) ) )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 @ ( if_option_nat
% 5.15/5.40 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 != none_nat )
% 5.15/5.40 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.40 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 @ ( if_option_nat
% 5.15/5.40 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 = none_nat )
% 5.15/5.40 @ none_nat
% 5.15/5.40 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.40 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_succ.elims
% 5.15/5.40 thf(fact_3019_vebt__pred_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.15/5.40 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.40 => ( ( Xa2 = zero_zero_nat )
% 5.15/5.40 => ( Y != none_nat ) ) )
% 5.15/5.40 => ( ! [A5: $o] :
% 5.15/5.40 ( ? [Uw2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 5.15/5.40 => ( ( Xa2
% 5.15/5.40 = ( suc @ zero_zero_nat ) )
% 5.15/5.40 => ~ ( ( A5
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.40 & ( ~ A5
% 5.15/5.40 => ( Y = none_nat ) ) ) ) )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( ? [Va3: nat] :
% 5.15/5.40 ( Xa2
% 5.15/5.40 = ( suc @ ( suc @ Va3 ) ) )
% 5.15/5.40 => ~ ( ( B6
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.40 & ( ~ B6
% 5.15/5.40 => ( ( A5
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.40 & ( ~ A5
% 5.15/5.40 => ( Y = none_nat ) ) ) ) ) ) )
% 5.15/5.40 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.15/5.40 => ( Y != none_nat ) )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.15/5.40 => ( Y != none_nat ) )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 5.15/5.40 => ( Y != none_nat ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ Ma2 ) ) )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 @ ( if_option_nat
% 5.15/5.40 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 != none_nat )
% 5.15/5.40 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.40 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 @ ( if_option_nat
% 5.15/5.40 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 = none_nat )
% 5.15/5.40 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.15/5.40 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.40 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_pred.elims
% 5.15/5.40 thf(fact_3020_verit__le__mono__div,axiom,
% 5.15/5.40 ! [A2: nat,B3: nat,N2: nat] :
% 5.15/5.40 ( ( ord_less_nat @ A2 @ B3 )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ord_less_eq_nat
% 5.15/5.40 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 5.15/5.40 @ ( if_nat
% 5.15/5.40 @ ( ( modulo_modulo_nat @ B3 @ N2 )
% 5.15/5.40 = zero_zero_nat )
% 5.15/5.40 @ one_one_nat
% 5.15/5.40 @ zero_zero_nat ) )
% 5.15/5.40 @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_le_mono_div
% 5.15/5.40 thf(fact_3021_mod__exhaust__less__4,axiom,
% 5.15/5.40 ! [M: nat] :
% 5.15/5.40 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.40 = zero_zero_nat )
% 5.15/5.40 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.40 = one_one_nat )
% 5.15/5.40 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.40 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.40 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % mod_exhaust_less_4
% 5.15/5.40 thf(fact_3022_arcosh__1,axiom,
% 5.15/5.40 ( ( arcosh_real @ one_one_real )
% 5.15/5.40 = zero_zero_real ) ).
% 5.15/5.40
% 5.15/5.40 % arcosh_1
% 5.15/5.40 thf(fact_3023_inrange,axiom,
% 5.15/5.40 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.40 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.40 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % inrange
% 5.15/5.40 thf(fact_3024_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 5.15/5.40 ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( ? [A5: $o,B6: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.15/5.40 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.40 @ ( if_nat
% 5.15/5.40 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 & ~ ( ( Xa2 = Mi2 )
% 5.15/5.40 | ( Xa2 = Ma2 ) ) )
% 5.15/5.40 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.15/5.40 @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.elims
% 5.15/5.40 thf(fact_3025_finite__nth__roots,axiom,
% 5.15/5.40 ! [N2: nat,C: complex] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( finite3207457112153483333omplex
% 5.15/5.40 @ ( collect_complex
% 5.15/5.40 @ ^ [Z3: complex] :
% 5.15/5.40 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.40 = C ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % finite_nth_roots
% 5.15/5.40 thf(fact_3026_set__bit__0,axiom,
% 5.15/5.40 ! [A: int] :
% 5.15/5.40 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.15/5.40 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % set_bit_0
% 5.15/5.40 thf(fact_3027_set__bit__0,axiom,
% 5.15/5.40 ! [A: nat] :
% 5.15/5.40 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.15/5.40 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % set_bit_0
% 5.15/5.40 thf(fact_3028_Leaf__0__not,axiom,
% 5.15/5.40 ! [A: $o,B: $o] :
% 5.15/5.40 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.15/5.40
% 5.15/5.40 % Leaf_0_not
% 5.15/5.40 thf(fact_3029_deg1Leaf,axiom,
% 5.15/5.40 ! [T: vEBT_VEBT] :
% 5.15/5.40 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.15/5.40 = ( ? [A3: $o,B2: $o] :
% 5.15/5.40 ( T
% 5.15/5.40 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % deg1Leaf
% 5.15/5.40 thf(fact_3030_deg__1__Leaf,axiom,
% 5.15/5.40 ! [T: vEBT_VEBT] :
% 5.15/5.40 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.15/5.40 => ? [A5: $o,B6: $o] :
% 5.15/5.40 ( T
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % deg_1_Leaf
% 5.15/5.40 thf(fact_3031_deg__1__Leafy,axiom,
% 5.15/5.40 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.40 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.40 => ( ( N2 = one_one_nat )
% 5.15/5.40 => ? [A5: $o,B6: $o] :
% 5.15/5.40 ( T
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % deg_1_Leafy
% 5.15/5.40 thf(fact_3032_verit__eq__simplify_I8_J,axiom,
% 5.15/5.40 ! [X22: num,Y22: num] :
% 5.15/5.40 ( ( ( bit0 @ X22 )
% 5.15/5.40 = ( bit0 @ Y22 ) )
% 5.15/5.40 = ( X22 = Y22 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_eq_simplify(8)
% 5.15/5.40 thf(fact_3033_verit__eq__simplify_I9_J,axiom,
% 5.15/5.40 ! [X33: num,Y32: num] :
% 5.15/5.40 ( ( ( bit1 @ X33 )
% 5.15/5.40 = ( bit1 @ Y32 ) )
% 5.15/5.40 = ( X33 = Y32 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_eq_simplify(9)
% 5.15/5.40 thf(fact_3034_set__bit__nonnegative__int__iff,axiom,
% 5.15/5.40 ! [N2: nat,K: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) )
% 5.15/5.40 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.15/5.40
% 5.15/5.40 % set_bit_nonnegative_int_iff
% 5.15/5.40 thf(fact_3035_VEBT_Oinject_I2_J,axiom,
% 5.15/5.40 ! [X21: $o,X222: $o,Y21: $o,Y222: $o] :
% 5.15/5.40 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 5.15/5.40 = ( vEBT_Leaf @ Y21 @ Y222 ) )
% 5.15/5.40 = ( ( X21 = Y21 )
% 5.15/5.40 & ( X222 = Y222 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT.inject(2)
% 5.15/5.40 thf(fact_3036_i0__less,axiom,
% 5.15/5.40 ! [N2: extended_enat] :
% 5.15/5.40 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.15/5.40 = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 5.15/5.40
% 5.15/5.40 % i0_less
% 5.15/5.40 thf(fact_3037_idiff__0,axiom,
% 5.15/5.40 ! [N2: extended_enat] :
% 5.15/5.40 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.15/5.40 = zero_z5237406670263579293d_enat ) ).
% 5.15/5.40
% 5.15/5.40 % idiff_0
% 5.15/5.40 thf(fact_3038_idiff__0__right,axiom,
% 5.15/5.40 ! [N2: extended_enat] :
% 5.15/5.40 ( ( minus_3235023915231533773d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.15/5.40 = N2 ) ).
% 5.15/5.40
% 5.15/5.40 % idiff_0_right
% 5.15/5.40 thf(fact_3039_not__real__square__gt__zero,axiom,
% 5.15/5.40 ! [X: real] :
% 5.15/5.40 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 5.15/5.40 = ( X = zero_zero_real ) ) ).
% 5.15/5.40
% 5.15/5.40 % not_real_square_gt_zero
% 5.15/5.40 thf(fact_3040_div__neg__neg__trivial,axiom,
% 5.15/5.40 ! [K: int,L: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ L @ K )
% 5.15/5.40 => ( ( divide_divide_int @ K @ L )
% 5.15/5.40 = zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_neg_neg_trivial
% 5.15/5.40 thf(fact_3041_div__pos__pos__trivial,axiom,
% 5.15/5.40 ! [K: int,L: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.40 => ( ( ord_less_int @ K @ L )
% 5.15/5.40 => ( ( divide_divide_int @ K @ L )
% 5.15/5.40 = zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_pos_pos_trivial
% 5.15/5.40 thf(fact_3042_mod__pos__pos__trivial,axiom,
% 5.15/5.40 ! [K: int,L: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.40 => ( ( ord_less_int @ K @ L )
% 5.15/5.40 => ( ( modulo_modulo_int @ K @ L )
% 5.15/5.40 = K ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % mod_pos_pos_trivial
% 5.15/5.40 thf(fact_3043_mod__neg__neg__trivial,axiom,
% 5.15/5.40 ! [K: int,L: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ L @ K )
% 5.15/5.40 => ( ( modulo_modulo_int @ K @ L )
% 5.15/5.40 = K ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % mod_neg_neg_trivial
% 5.15/5.40 thf(fact_3044_half__negative__int__iff,axiom,
% 5.15/5.40 ! [K: int] :
% 5.15/5.40 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.15/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.15/5.40
% 5.15/5.40 % half_negative_int_iff
% 5.15/5.40 thf(fact_3045_half__nonnegative__int__iff,axiom,
% 5.15/5.40 ! [K: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.15/5.40 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.15/5.40
% 5.15/5.40 % half_nonnegative_int_iff
% 5.15/5.40 thf(fact_3046_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 5.15/5.40 ! [A: $o,B: $o,X: nat] :
% 5.15/5.40 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = one_one_nat ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(1)
% 5.15/5.40 thf(fact_3047_VEBT_Osize_I4_J,axiom,
% 5.15/5.40 ! [X21: $o,X222: $o] :
% 5.15/5.40 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.15/5.40 = zero_zero_nat ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT.size(4)
% 5.15/5.40 thf(fact_3048_VEBT_Odistinct_I1_J,axiom,
% 5.15/5.40 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.15/5.40 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.15/5.40 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT.distinct(1)
% 5.15/5.40 thf(fact_3049_VEBT_Oexhaust,axiom,
% 5.15/5.40 ! [Y: vEBT_VEBT] :
% 5.15/5.40 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.15/5.40 ( Y
% 5.15/5.40 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.15/5.40 => ~ ! [X212: $o,X223: $o] :
% 5.15/5.40 ( Y
% 5.15/5.40 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT.exhaust
% 5.15/5.40 thf(fact_3050_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.15/5.40 ! [X: produc9072475918466114483BT_nat] :
% 5.15/5.40 ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 5.15/5.40 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.valid'.cases
% 5.15/5.40 thf(fact_3051_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.15/5.40 ! [Uu: $o] :
% 5.15/5.40 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.minNull.simps(3)
% 5.15/5.40 thf(fact_3052_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.15/5.40 ! [Uv: $o] :
% 5.15/5.40 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.minNull.simps(2)
% 5.15/5.40 thf(fact_3053_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.15/5.40 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.minNull.simps(1)
% 5.15/5.40 thf(fact_3054_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.15/5.40 ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.15/5.40 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.membermima.simps(1)
% 5.15/5.40 thf(fact_3055_div__neg__pos__less0,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_neg_pos_less0
% 5.15/5.40 thf(fact_3056_neg__imp__zdiv__neg__iff,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.15/5.40 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % neg_imp_zdiv_neg_iff
% 5.15/5.40 thf(fact_3057_pos__imp__zdiv__neg__iff,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.15/5.40 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % pos_imp_zdiv_neg_iff
% 5.15/5.40 thf(fact_3058_Euclidean__Division_Opos__mod__bound,axiom,
% 5.15/5.40 ! [L: int,K: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ L )
% 5.15/5.40 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.15/5.40
% 5.15/5.40 % Euclidean_Division.pos_mod_bound
% 5.15/5.40 thf(fact_3059_neg__mod__bound,axiom,
% 5.15/5.40 ! [L: int,K: int] :
% 5.15/5.40 ( ( ord_less_int @ L @ zero_zero_int )
% 5.15/5.40 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % neg_mod_bound
% 5.15/5.40 thf(fact_3060_enat__0__less__mult__iff,axiom,
% 5.15/5.40 ! [M: extended_enat,N2: extended_enat] :
% 5.15/5.40 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 5.15/5.40 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.15/5.40 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % enat_0_less_mult_iff
% 5.15/5.40 thf(fact_3061_not__iless0,axiom,
% 5.15/5.40 ! [N2: extended_enat] :
% 5.15/5.40 ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 5.15/5.40
% 5.15/5.40 % not_iless0
% 5.15/5.40 thf(fact_3062_iadd__is__0,axiom,
% 5.15/5.40 ! [M: extended_enat,N2: extended_enat] :
% 5.15/5.40 ( ( ( plus_p3455044024723400733d_enat @ M @ N2 )
% 5.15/5.40 = zero_z5237406670263579293d_enat )
% 5.15/5.40 = ( ( M = zero_z5237406670263579293d_enat )
% 5.15/5.40 & ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % iadd_is_0
% 5.15/5.40 thf(fact_3063_ile0__eq,axiom,
% 5.15/5.40 ! [N2: extended_enat] :
% 5.15/5.40 ( ( ord_le2932123472753598470d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.15/5.40 = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 5.15/5.40
% 5.15/5.40 % ile0_eq
% 5.15/5.40 thf(fact_3064_i0__lb,axiom,
% 5.15/5.40 ! [N2: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N2 ) ).
% 5.15/5.40
% 5.15/5.40 % i0_lb
% 5.15/5.40 thf(fact_3065_zdiv__mono__strict,axiom,
% 5.15/5.40 ! [A2: int,B3: int,N2: int] :
% 5.15/5.40 ( ( ord_less_int @ A2 @ B3 )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.15/5.40 => ( ( ( modulo_modulo_int @ A2 @ N2 )
% 5.15/5.40 = zero_zero_int )
% 5.15/5.40 => ( ( ( modulo_modulo_int @ B3 @ N2 )
% 5.15/5.40 = zero_zero_int )
% 5.15/5.40 => ( ord_less_int @ ( divide_divide_int @ A2 @ N2 ) @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_mono_strict
% 5.15/5.40 thf(fact_3066_set__bit__greater__eq,axiom,
% 5.15/5.40 ! [K: int,N2: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N2 @ K ) ) ).
% 5.15/5.40
% 5.15/5.40 % set_bit_greater_eq
% 5.15/5.40 thf(fact_3067_all__nat__less,axiom,
% 5.15/5.40 ! [N2: nat,P: nat > $o] :
% 5.15/5.40 ( ( ! [M5: nat] :
% 5.15/5.40 ( ( ord_less_eq_nat @ M5 @ N2 )
% 5.15/5.40 => ( P @ M5 ) ) )
% 5.15/5.40 = ( ! [X2: nat] :
% 5.15/5.40 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.40 => ( P @ X2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % all_nat_less
% 5.15/5.40 thf(fact_3068_ex__nat__less,axiom,
% 5.15/5.40 ! [N2: nat,P: nat > $o] :
% 5.15/5.40 ( ( ? [M5: nat] :
% 5.15/5.40 ( ( ord_less_eq_nat @ M5 @ N2 )
% 5.15/5.40 & ( P @ M5 ) ) )
% 5.15/5.40 = ( ? [X2: nat] :
% 5.15/5.40 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.40 & ( P @ X2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % ex_nat_less
% 5.15/5.40 thf(fact_3069_vebt__buildup_Osimps_I1_J,axiom,
% 5.15/5.40 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.15/5.40 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_buildup.simps(1)
% 5.15/5.40 thf(fact_3070_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J,axiom,
% 5.15/5.40 ! [A: $o,B: $o,X: nat] :
% 5.15/5.40 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = one_one_nat ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(1)
% 5.15/5.40 thf(fact_3071_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J,axiom,
% 5.15/5.40 ! [Uu: $o] :
% 5.15/5.40 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu @ $true ) )
% 5.15/5.40 = one_one_nat ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(3)
% 5.15/5.40 thf(fact_3072_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J,axiom,
% 5.15/5.40 ! [Uv: $o] :
% 5.15/5.40 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv ) )
% 5.15/5.40 = one_one_nat ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(2)
% 5.15/5.40 thf(fact_3073_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J,axiom,
% 5.15/5.40 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.40 = one_one_nat ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(1)
% 5.15/5.40 thf(fact_3074_zdiv__mono1,axiom,
% 5.15/5.40 ! [A: int,A4: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ A @ A4 )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_mono1
% 5.15/5.40 thf(fact_3075_zdiv__mono2,axiom,
% 5.15/5.40 ! [A: int,B4: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.15/5.40 => ( ( ord_less_eq_int @ B4 @ B )
% 5.15/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_mono2
% 5.15/5.40 thf(fact_3076_zdiv__eq__0__iff,axiom,
% 5.15/5.40 ! [I: int,K: int] :
% 5.15/5.40 ( ( ( divide_divide_int @ I @ K )
% 5.15/5.40 = zero_zero_int )
% 5.15/5.40 = ( ( K = zero_zero_int )
% 5.15/5.40 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.15/5.40 & ( ord_less_int @ I @ K ) )
% 5.15/5.40 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.15/5.40 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_eq_0_iff
% 5.15/5.40 thf(fact_3077_zdiv__mono1__neg,axiom,
% 5.15/5.40 ! [A: int,A4: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ A @ A4 )
% 5.15/5.40 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_mono1_neg
% 5.15/5.40 thf(fact_3078_zdiv__mono2__neg,axiom,
% 5.15/5.40 ! [A: int,B4: int,B: int] :
% 5.15/5.40 ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.15/5.40 => ( ( ord_less_eq_int @ B4 @ B )
% 5.15/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_mono2_neg
% 5.15/5.40 thf(fact_3079_div__int__pos__iff,axiom,
% 5.15/5.40 ! [K: int,L: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.15/5.40 = ( ( K = zero_zero_int )
% 5.15/5.40 | ( L = zero_zero_int )
% 5.15/5.40 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.40 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.15/5.40 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.40 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_int_pos_iff
% 5.15/5.40 thf(fact_3080_div__positive__int,axiom,
% 5.15/5.40 ! [L: int,K: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ L @ K )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.15/5.40 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_positive_int
% 5.15/5.40 thf(fact_3081_div__nonneg__neg__le0,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.40 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_nonneg_neg_le0
% 5.15/5.40 thf(fact_3082_div__nonpos__pos__le0,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_nonpos_pos_le0
% 5.15/5.40 thf(fact_3083_pos__imp__zdiv__pos__iff,axiom,
% 5.15/5.40 ! [K: int,I: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.15/5.40 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % pos_imp_zdiv_pos_iff
% 5.15/5.40 thf(fact_3084_neg__imp__zdiv__nonneg__iff,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.15/5.40 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % neg_imp_zdiv_nonneg_iff
% 5.15/5.40 thf(fact_3085_pos__imp__zdiv__nonneg__iff,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.15/5.40 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % pos_imp_zdiv_nonneg_iff
% 5.15/5.40 thf(fact_3086_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.15/5.40 = ( ( ord_less_eq_int @ B @ A )
% 5.15/5.40 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % nonneg1_imp_zdiv_pos_iff
% 5.15/5.40 thf(fact_3087_int__div__less__self,axiom,
% 5.15/5.40 ! [X: int,K: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ X )
% 5.15/5.40 => ( ( ord_less_int @ one_one_int @ K )
% 5.15/5.40 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % int_div_less_self
% 5.15/5.40 thf(fact_3088_Euclidean__Division_Opos__mod__sign,axiom,
% 5.15/5.40 ! [L: int,K: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ L )
% 5.15/5.40 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % Euclidean_Division.pos_mod_sign
% 5.15/5.40 thf(fact_3089_neg__mod__sign,axiom,
% 5.15/5.40 ! [L: int,K: int] :
% 5.15/5.40 ( ( ord_less_int @ L @ zero_zero_int )
% 5.15/5.40 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.15/5.40
% 5.15/5.40 % neg_mod_sign
% 5.15/5.40 thf(fact_3090_zmod__le__nonneg__dividend,axiom,
% 5.15/5.40 ! [M: int,K: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.15/5.40 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.15/5.40
% 5.15/5.40 % zmod_le_nonneg_dividend
% 5.15/5.40 thf(fact_3091_zmod__trivial__iff,axiom,
% 5.15/5.40 ! [I: int,K: int] :
% 5.15/5.40 ( ( ( modulo_modulo_int @ I @ K )
% 5.15/5.40 = I )
% 5.15/5.40 = ( ( K = zero_zero_int )
% 5.15/5.40 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.15/5.40 & ( ord_less_int @ I @ K ) )
% 5.15/5.40 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.15/5.40 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zmod_trivial_iff
% 5.15/5.40 thf(fact_3092_pos__mod__conj,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.15/5.40 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % pos_mod_conj
% 5.15/5.40 thf(fact_3093_neg__mod__conj,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ B @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.15/5.40 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % neg_mod_conj
% 5.15/5.40 thf(fact_3094_mod__pos__geq,axiom,
% 5.15/5.40 ! [L: int,K: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ L )
% 5.15/5.40 => ( ( ord_less_eq_int @ L @ K )
% 5.15/5.40 => ( ( modulo_modulo_int @ K @ L )
% 5.15/5.40 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % mod_pos_geq
% 5.15/5.40 thf(fact_3095_zmod__eq__0D,axiom,
% 5.15/5.40 ! [M: int,D: int] :
% 5.15/5.40 ( ( ( modulo_modulo_int @ M @ D )
% 5.15/5.40 = zero_zero_int )
% 5.15/5.40 => ? [Q2: int] :
% 5.15/5.40 ( M
% 5.15/5.40 = ( times_times_int @ D @ Q2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zmod_eq_0D
% 5.15/5.40 thf(fact_3096_zmod__eq__0__iff,axiom,
% 5.15/5.40 ! [M: int,D: int] :
% 5.15/5.40 ( ( ( modulo_modulo_int @ M @ D )
% 5.15/5.40 = zero_zero_int )
% 5.15/5.40 = ( ? [Q4: int] :
% 5.15/5.40 ( M
% 5.15/5.40 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zmod_eq_0_iff
% 5.15/5.40 thf(fact_3097_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.15/5.40 ! [X: produc9072475918466114483BT_nat] :
% 5.15/5.40 ( ! [A5: $o,B6: $o,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ X3 ) )
% 5.15/5.40 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.15/5.40 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ X3 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.naive_member.cases
% 5.15/5.40 thf(fact_3098_invar__vebt_Ointros_I1_J,axiom,
% 5.15/5.40 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.15/5.40
% 5.15/5.40 % invar_vebt.intros(1)
% 5.15/5.40 thf(fact_3099_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT] :
% 5.15/5.40 ( ( X
% 5.15/5.40 != ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.40 => ( ! [Uv2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.15/5.40 => ( ! [Uu2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.15/5.40 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.15/5.40 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.cases
% 5.15/5.40 thf(fact_3100_vebt__member_Osimps_I1_J,axiom,
% 5.15/5.40 ! [A: $o,B: $o,X: nat] :
% 5.15/5.40 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = ( ( ( X = zero_zero_nat )
% 5.15/5.40 => A )
% 5.15/5.40 & ( ( X != zero_zero_nat )
% 5.15/5.40 => ( ( ( X = one_one_nat )
% 5.15/5.40 => B )
% 5.15/5.40 & ( X = one_one_nat ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_member.simps(1)
% 5.15/5.40 thf(fact_3101_vebt__buildup_Osimps_I2_J,axiom,
% 5.15/5.40 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.15/5.40 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_buildup.simps(2)
% 5.15/5.40 thf(fact_3102_verit__la__disequality,axiom,
% 5.15/5.40 ! [A: rat,B: rat] :
% 5.15/5.40 ( ( A = B )
% 5.15/5.40 | ~ ( ord_less_eq_rat @ A @ B )
% 5.15/5.40 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_la_disequality
% 5.15/5.40 thf(fact_3103_verit__la__disequality,axiom,
% 5.15/5.40 ! [A: num,B: num] :
% 5.15/5.40 ( ( A = B )
% 5.15/5.40 | ~ ( ord_less_eq_num @ A @ B )
% 5.15/5.40 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_la_disequality
% 5.15/5.40 thf(fact_3104_verit__la__disequality,axiom,
% 5.15/5.40 ! [A: nat,B: nat] :
% 5.15/5.40 ( ( A = B )
% 5.15/5.40 | ~ ( ord_less_eq_nat @ A @ B )
% 5.15/5.40 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_la_disequality
% 5.15/5.40 thf(fact_3105_verit__la__disequality,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( A = B )
% 5.15/5.40 | ~ ( ord_less_eq_int @ A @ B )
% 5.15/5.40 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_la_disequality
% 5.15/5.40 thf(fact_3106_verit__comp__simplify1_I2_J,axiom,
% 5.15/5.40 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(2)
% 5.15/5.40 thf(fact_3107_verit__comp__simplify1_I2_J,axiom,
% 5.15/5.40 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(2)
% 5.15/5.40 thf(fact_3108_verit__comp__simplify1_I2_J,axiom,
% 5.15/5.40 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(2)
% 5.15/5.40 thf(fact_3109_verit__comp__simplify1_I2_J,axiom,
% 5.15/5.40 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(2)
% 5.15/5.40 thf(fact_3110_verit__comp__simplify1_I2_J,axiom,
% 5.15/5.40 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(2)
% 5.15/5.40 thf(fact_3111_vebt__insert_Osimps_I1_J,axiom,
% 5.15/5.40 ! [X: nat,A: $o,B: $o] :
% 5.15/5.40 ( ( ( X = zero_zero_nat )
% 5.15/5.40 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.15/5.40 & ( ( X != zero_zero_nat )
% 5.15/5.40 => ( ( ( X = one_one_nat )
% 5.15/5.40 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.15/5.40 & ( ( X != one_one_nat )
% 5.15/5.40 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_insert.simps(1)
% 5.15/5.40 thf(fact_3112_verit__comp__simplify1_I1_J,axiom,
% 5.15/5.40 ! [A: real] :
% 5.15/5.40 ~ ( ord_less_real @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(1)
% 5.15/5.40 thf(fact_3113_verit__comp__simplify1_I1_J,axiom,
% 5.15/5.40 ! [A: rat] :
% 5.15/5.40 ~ ( ord_less_rat @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(1)
% 5.15/5.40 thf(fact_3114_verit__comp__simplify1_I1_J,axiom,
% 5.15/5.40 ! [A: num] :
% 5.15/5.40 ~ ( ord_less_num @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(1)
% 5.15/5.40 thf(fact_3115_verit__comp__simplify1_I1_J,axiom,
% 5.15/5.40 ! [A: nat] :
% 5.15/5.40 ~ ( ord_less_nat @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(1)
% 5.15/5.40 thf(fact_3116_verit__comp__simplify1_I1_J,axiom,
% 5.15/5.40 ! [A: int] :
% 5.15/5.40 ~ ( ord_less_int @ A @ A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(1)
% 5.15/5.40 thf(fact_3117_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.15/5.40 ! [A: $o,B: $o,X: nat] :
% 5.15/5.40 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = ( ( ( X = zero_zero_nat )
% 5.15/5.40 => A )
% 5.15/5.40 & ( ( X != zero_zero_nat )
% 5.15/5.40 => ( ( ( X = one_one_nat )
% 5.15/5.40 => B )
% 5.15/5.40 & ( X = one_one_nat ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.naive_member.simps(1)
% 5.15/5.40 thf(fact_3118_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT] :
% 5.15/5.40 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.15/5.40 => ( ! [Uv2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.15/5.40 => ( ! [Uu2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.15/5.40 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.minNull.elims(3)
% 5.15/5.40 thf(fact_3119_vebt__succ_Osimps_I2_J,axiom,
% 5.15/5.40 ! [Uv: $o,Uw: $o,N2: nat] :
% 5.15/5.40 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) )
% 5.15/5.40 = none_nat ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_succ.simps(2)
% 5.15/5.40 thf(fact_3120_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT] :
% 5.15/5.40 ( ( vEBT_VEBT_minNull @ X )
% 5.15/5.40 => ( ( X
% 5.15/5.40 != ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.40 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.minNull.elims(2)
% 5.15/5.40 thf(fact_3121_realpow__pos__nth2,axiom,
% 5.15/5.40 ! [A: real,N2: nat] :
% 5.15/5.40 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.40 => ? [R3: real] :
% 5.15/5.40 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.15/5.40 & ( ( power_power_real @ R3 @ ( suc @ N2 ) )
% 5.15/5.40 = A ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % realpow_pos_nth2
% 5.15/5.40 thf(fact_3122_real__arch__pow__inv,axiom,
% 5.15/5.40 ! [Y: real,X: real] :
% 5.15/5.40 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.40 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.40 => ? [N: nat] : ( ord_less_real @ ( power_power_real @ X @ N ) @ Y ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % real_arch_pow_inv
% 5.15/5.40 thf(fact_3123_unique__quotient__lemma__neg,axiom,
% 5.15/5.40 ! [B: int,Q5: int,R4: int,Q3: int,R2: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.15/5.40 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ B @ R2 )
% 5.15/5.40 => ( ( ord_less_int @ B @ R4 )
% 5.15/5.40 => ( ord_less_eq_int @ Q3 @ Q5 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % unique_quotient_lemma_neg
% 5.15/5.40 thf(fact_3124_unique__quotient__lemma,axiom,
% 5.15/5.40 ! [B: int,Q5: int,R4: int,Q3: int,R2: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.15/5.40 => ( ( ord_less_int @ R4 @ B )
% 5.15/5.40 => ( ( ord_less_int @ R2 @ B )
% 5.15/5.40 => ( ord_less_eq_int @ Q5 @ Q3 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % unique_quotient_lemma
% 5.15/5.40 thf(fact_3125_zdiv__mono2__neg__lemma,axiom,
% 5.15/5.40 ! [B: int,Q3: int,R2: int,B4: int,Q5: int,R4: int] :
% 5.15/5.40 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.15/5.40 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ R2 @ B )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.15/5.40 => ( ( ord_less_eq_int @ B4 @ B )
% 5.15/5.40 => ( ord_less_eq_int @ Q5 @ Q3 ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_mono2_neg_lemma
% 5.15/5.40 thf(fact_3126_zdiv__mono2__lemma,axiom,
% 5.15/5.40 ! [B: int,Q3: int,R2: int,B4: int,Q5: int,R4: int] :
% 5.15/5.40 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.15/5.40 => ( ( ord_less_int @ R4 @ B4 )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.15/5.40 => ( ( ord_less_eq_int @ B4 @ B )
% 5.15/5.40 => ( ord_less_eq_int @ Q3 @ Q5 ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_mono2_lemma
% 5.15/5.40 thf(fact_3127_q__pos__lemma,axiom,
% 5.15/5.40 ! [B4: int,Q5: int,R4: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q5 ) @ R4 ) )
% 5.15/5.40 => ( ( ord_less_int @ R4 @ B4 )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.15/5.40 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % q_pos_lemma
% 5.15/5.40 thf(fact_3128_zdiv__zmult2__eq,axiom,
% 5.15/5.40 ! [C: int,A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.40 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.40 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zdiv_zmult2_eq
% 5.15/5.40 thf(fact_3129_mod__pos__neg__trivial,axiom,
% 5.15/5.40 ! [K: int,L: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.40 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.15/5.40 => ( ( modulo_modulo_int @ K @ L )
% 5.15/5.40 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % mod_pos_neg_trivial
% 5.15/5.40 thf(fact_3130_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT] :
% 5.15/5.40 ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.cases
% 5.15/5.40 thf(fact_3131_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.15/5.40 ! [A: $o,B: $o,X: nat] :
% 5.15/5.40 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(1)
% 5.15/5.40 thf(fact_3132_verit__le__mono__div__int,axiom,
% 5.15/5.40 ! [A2: int,B3: int,N2: int] :
% 5.15/5.40 ( ( ord_less_int @ A2 @ B3 )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.15/5.40 => ( ord_less_eq_int
% 5.15/5.40 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 5.15/5.40 @ ( if_int
% 5.15/5.40 @ ( ( modulo_modulo_int @ B3 @ N2 )
% 5.15/5.40 = zero_zero_int )
% 5.15/5.40 @ one_one_int
% 5.15/5.40 @ zero_zero_int ) )
% 5.15/5.40 @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_le_mono_div_int
% 5.15/5.40 thf(fact_3133_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Y: $o] :
% 5.15/5.40 ( ( ( vEBT_VEBT_minNull @ X )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.40 => ~ Y )
% 5.15/5.40 => ( ( ? [Uv2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.15/5.40 => Y )
% 5.15/5.40 => ( ( ? [Uu2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.15/5.40 => Y )
% 5.15/5.40 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.15/5.40 => ~ Y )
% 5.15/5.40 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.15/5.40 => Y ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.minNull.elims(1)
% 5.15/5.40 thf(fact_3134_not__exp__less__eq__0__int,axiom,
% 5.15/5.40 ! [N2: nat] :
% 5.15/5.40 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 5.15/5.40
% 5.15/5.40 % not_exp_less_eq_0_int
% 5.15/5.40 thf(fact_3135_realpow__pos__nth__unique,axiom,
% 5.15/5.40 ! [N2: nat,A: real] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.40 => ? [X3: real] :
% 5.15/5.40 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.15/5.40 & ( ( power_power_real @ X3 @ N2 )
% 5.15/5.40 = A )
% 5.15/5.40 & ! [Y4: real] :
% 5.15/5.40 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.15/5.40 & ( ( power_power_real @ Y4 @ N2 )
% 5.15/5.40 = A ) )
% 5.15/5.40 => ( Y4 = X3 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % realpow_pos_nth_unique
% 5.15/5.40 thf(fact_3136_realpow__pos__nth,axiom,
% 5.15/5.40 ! [N2: nat,A: real] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.40 => ? [R3: real] :
% 5.15/5.40 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.15/5.40 & ( ( power_power_real @ R3 @ N2 )
% 5.15/5.40 = A ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % realpow_pos_nth
% 5.15/5.40 thf(fact_3137_div__pos__geq,axiom,
% 5.15/5.40 ! [L: int,K: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ L )
% 5.15/5.40 => ( ( ord_less_eq_int @ L @ K )
% 5.15/5.40 => ( ( divide_divide_int @ K @ L )
% 5.15/5.40 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_pos_geq
% 5.15/5.40 thf(fact_3138_split__zdiv,axiom,
% 5.15/5.40 ! [P: int > $o,N2: int,K: int] :
% 5.15/5.40 ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 5.15/5.40 = ( ( ( K = zero_zero_int )
% 5.15/5.40 => ( P @ zero_zero_int ) )
% 5.15/5.40 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.40 => ! [I3: int,J3: int] :
% 5.15/5.40 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.15/5.40 & ( ord_less_int @ J3 @ K )
% 5.15/5.40 & ( N2
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.15/5.40 => ( P @ I3 ) ) )
% 5.15/5.40 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.40 => ! [I3: int,J3: int] :
% 5.15/5.40 ( ( ( ord_less_int @ K @ J3 )
% 5.15/5.40 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.15/5.40 & ( N2
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.15/5.40 => ( P @ I3 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % split_zdiv
% 5.15/5.40 thf(fact_3139_int__div__neg__eq,axiom,
% 5.15/5.40 ! [A: int,B: int,Q3: int,R2: int] :
% 5.15/5.40 ( ( A
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.15/5.40 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ B @ R2 )
% 5.15/5.40 => ( ( divide_divide_int @ A @ B )
% 5.15/5.40 = Q3 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % int_div_neg_eq
% 5.15/5.40 thf(fact_3140_int__div__pos__eq,axiom,
% 5.15/5.40 ! [A: int,B: int,Q3: int,R2: int] :
% 5.15/5.40 ( ( A
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.15/5.40 => ( ( ord_less_int @ R2 @ B )
% 5.15/5.40 => ( ( divide_divide_int @ A @ B )
% 5.15/5.40 = Q3 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % int_div_pos_eq
% 5.15/5.40 thf(fact_3141_split__zmod,axiom,
% 5.15/5.40 ! [P: int > $o,N2: int,K: int] :
% 5.15/5.40 ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 5.15/5.40 = ( ( ( K = zero_zero_int )
% 5.15/5.40 => ( P @ N2 ) )
% 5.15/5.40 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.40 => ! [I3: int,J3: int] :
% 5.15/5.40 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.15/5.40 & ( ord_less_int @ J3 @ K )
% 5.15/5.40 & ( N2
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.15/5.40 => ( P @ J3 ) ) )
% 5.15/5.40 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.40 => ! [I3: int,J3: int] :
% 5.15/5.40 ( ( ( ord_less_int @ K @ J3 )
% 5.15/5.40 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.15/5.40 & ( N2
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.15/5.40 => ( P @ J3 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % split_zmod
% 5.15/5.40 thf(fact_3142_int__mod__neg__eq,axiom,
% 5.15/5.40 ! [A: int,B: int,Q3: int,R2: int] :
% 5.15/5.40 ( ( A
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.15/5.40 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.15/5.40 => ( ( ord_less_int @ B @ R2 )
% 5.15/5.40 => ( ( modulo_modulo_int @ A @ B )
% 5.15/5.40 = R2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % int_mod_neg_eq
% 5.15/5.40 thf(fact_3143_int__mod__pos__eq,axiom,
% 5.15/5.40 ! [A: int,B: int,Q3: int,R2: int] :
% 5.15/5.40 ( ( A
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.15/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.15/5.40 => ( ( ord_less_int @ R2 @ B )
% 5.15/5.40 => ( ( modulo_modulo_int @ A @ B )
% 5.15/5.40 = R2 ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % int_mod_pos_eq
% 5.15/5.40 thf(fact_3144_vebt__pred_Osimps_I2_J,axiom,
% 5.15/5.40 ! [A: $o,Uw: $o] :
% 5.15/5.40 ( ( A
% 5.15/5.40 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.40 & ( ~ A
% 5.15/5.40 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.40 = none_nat ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_pred.simps(2)
% 5.15/5.40 thf(fact_3145_vebt__mint_Osimps_I1_J,axiom,
% 5.15/5.40 ! [A: $o,B: $o] :
% 5.15/5.40 ( ( A
% 5.15/5.40 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.40 & ( ~ A
% 5.15/5.40 => ( ( B
% 5.15/5.40 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.40 & ( ~ B
% 5.15/5.40 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.40 = none_nat ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_mint.simps(1)
% 5.15/5.40 thf(fact_3146_vebt__succ_Osimps_I1_J,axiom,
% 5.15/5.40 ! [B: $o,Uu: $o] :
% 5.15/5.40 ( ( B
% 5.15/5.40 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.15/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.40 & ( ~ B
% 5.15/5.40 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.15/5.40 = none_nat ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_succ.simps(1)
% 5.15/5.40 thf(fact_3147_vebt__maxt_Osimps_I1_J,axiom,
% 5.15/5.40 ! [B: $o,A: $o] :
% 5.15/5.40 ( ( B
% 5.15/5.40 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.40 & ( ~ B
% 5.15/5.40 => ( ( A
% 5.15/5.40 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.40 & ( ~ A
% 5.15/5.40 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.40 = none_nat ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_maxt.simps(1)
% 5.15/5.40 thf(fact_3148_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Y: nat] :
% 5.15/5.40 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [Uv2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [Uu2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.elims
% 5.15/5.40 thf(fact_3149_int__power__div__base,axiom,
% 5.15/5.40 ! [M: nat,K: int] :
% 5.15/5.40 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.40 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.40 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.15/5.40 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % int_power_div_base
% 5.15/5.40 thf(fact_3150_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 5.15/5.40 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.15/5.40 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X )
% 5.15/5.40 = one_one_nat ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(2)
% 5.15/5.40 thf(fact_3151_split__neg__lemma,axiom,
% 5.15/5.40 ! [K: int,P: int > int > $o,N2: int] :
% 5.15/5.40 ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.40 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 5.15/5.40 = ( ! [I3: int,J3: int] :
% 5.15/5.40 ( ( ( ord_less_int @ K @ J3 )
% 5.15/5.40 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.15/5.40 & ( N2
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.15/5.40 => ( P @ I3 @ J3 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % split_neg_lemma
% 5.15/5.40 thf(fact_3152_split__pos__lemma,axiom,
% 5.15/5.40 ! [K: int,P: int > int > $o,N2: int] :
% 5.15/5.40 ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.40 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 5.15/5.40 = ( ! [I3: int,J3: int] :
% 5.15/5.40 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.15/5.40 & ( ord_less_int @ J3 @ K )
% 5.15/5.40 & ( N2
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.15/5.40 => ( P @ I3 @ J3 ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % split_pos_lemma
% 5.15/5.40 thf(fact_3153_zmod__zmult2__eq,axiom,
% 5.15/5.40 ! [C: int,A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.15/5.40 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % zmod_zmult2_eq
% 5.15/5.40 thf(fact_3154_vebt__pred_Ocases,axiom,
% 5.15/5.40 ! [X: produc9072475918466114483BT_nat] :
% 5.15/5.40 ( ! [Uu2: $o,Uv2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.15/5.40 => ( ! [A5: $o,Uw2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.15/5.40 => ( ! [A5: $o,B6: $o,Va3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ ( suc @ ( suc @ Va3 ) ) ) )
% 5.15/5.40 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Vb2 ) )
% 5.15/5.40 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 5.15/5.40 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_pred.cases
% 5.15/5.40 thf(fact_3155_vebt__succ_Ocases,axiom,
% 5.15/5.40 ! [X: produc9072475918466114483BT_nat] :
% 5.15/5.40 ( ! [Uu2: $o,B6: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B6 ) @ zero_zero_nat ) )
% 5.15/5.40 => ( ! [Uv2: $o,Uw2: $o,N: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) ) )
% 5.15/5.40 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va2 ) )
% 5.15/5.40 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 5.15/5.40 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_succ.cases
% 5.15/5.40 thf(fact_3156_VEBT__internal_Omembermima_Ocases,axiom,
% 5.15/5.40 ! [X: produc9072475918466114483BT_nat] :
% 5.15/5.40 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.15/5.40 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.15/5.40 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 ) )
% 5.15/5.40 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X3 ) )
% 5.15/5.40 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.membermima.cases
% 5.15/5.40 thf(fact_3157_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 5.15/5.40 ! [X: produc9072475918466114483BT_nat] :
% 5.15/5.40 ( ! [A5: $o,B6: $o,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ X3 ) )
% 5.15/5.40 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X3 ) )
% 5.15/5.40 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X3 ) )
% 5.15/5.40 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.cases
% 5.15/5.40 thf(fact_3158_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 5.15/5.40 ! [X: produc9072475918466114483BT_nat] :
% 5.15/5.40 ( ! [A5: $o,B6: $o,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ X3 ) )
% 5.15/5.40 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 ) )
% 5.15/5.40 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X3 ) )
% 5.15/5.40 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 5.15/5.40 thf(fact_3159_vebt__pred_Osimps_I3_J,axiom,
% 5.15/5.40 ! [B: $o,A: $o,Va: nat] :
% 5.15/5.40 ( ( B
% 5.15/5.40 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.15/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.40 & ( ~ B
% 5.15/5.40 => ( ( A
% 5.15/5.40 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.15/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.40 & ( ~ A
% 5.15/5.40 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.15/5.40 = none_nat ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_pred.simps(3)
% 5.15/5.40 thf(fact_3160_verit__comp__simplify1_I3_J,axiom,
% 5.15/5.40 ! [B4: real,A4: real] :
% 5.15/5.40 ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 5.15/5.40 = ( ord_less_real @ A4 @ B4 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(3)
% 5.15/5.40 thf(fact_3161_verit__comp__simplify1_I3_J,axiom,
% 5.15/5.40 ! [B4: rat,A4: rat] :
% 5.15/5.40 ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 5.15/5.40 = ( ord_less_rat @ A4 @ B4 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(3)
% 5.15/5.40 thf(fact_3162_verit__comp__simplify1_I3_J,axiom,
% 5.15/5.40 ! [B4: num,A4: num] :
% 5.15/5.40 ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 5.15/5.40 = ( ord_less_num @ A4 @ B4 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(3)
% 5.15/5.40 thf(fact_3163_verit__comp__simplify1_I3_J,axiom,
% 5.15/5.40 ! [B4: nat,A4: nat] :
% 5.15/5.40 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 5.15/5.40 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(3)
% 5.15/5.40 thf(fact_3164_verit__comp__simplify1_I3_J,axiom,
% 5.15/5.40 ! [B4: int,A4: int] :
% 5.15/5.40 ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 5.15/5.40 = ( ord_less_int @ A4 @ B4 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_comp_simplify1(3)
% 5.15/5.40 thf(fact_3165_verit__sum__simplify,axiom,
% 5.15/5.40 ! [A: complex] :
% 5.15/5.40 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.15/5.40 = A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_sum_simplify
% 5.15/5.40 thf(fact_3166_verit__sum__simplify,axiom,
% 5.15/5.40 ! [A: real] :
% 5.15/5.40 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.15/5.40 = A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_sum_simplify
% 5.15/5.40 thf(fact_3167_verit__sum__simplify,axiom,
% 5.15/5.40 ! [A: rat] :
% 5.15/5.40 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.15/5.40 = A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_sum_simplify
% 5.15/5.40 thf(fact_3168_verit__sum__simplify,axiom,
% 5.15/5.40 ! [A: nat] :
% 5.15/5.40 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.15/5.40 = A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_sum_simplify
% 5.15/5.40 thf(fact_3169_verit__sum__simplify,axiom,
% 5.15/5.40 ! [A: int] :
% 5.15/5.40 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.15/5.40 = A ) ).
% 5.15/5.40
% 5.15/5.40 % verit_sum_simplify
% 5.15/5.40 thf(fact_3170_verit__eq__simplify_I10_J,axiom,
% 5.15/5.40 ! [X22: num] :
% 5.15/5.40 ( one
% 5.15/5.40 != ( bit0 @ X22 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_eq_simplify(10)
% 5.15/5.40 thf(fact_3171_verit__eq__simplify_I14_J,axiom,
% 5.15/5.40 ! [X22: num,X33: num] :
% 5.15/5.40 ( ( bit0 @ X22 )
% 5.15/5.40 != ( bit1 @ X33 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_eq_simplify(14)
% 5.15/5.40 thf(fact_3172_verit__eq__simplify_I12_J,axiom,
% 5.15/5.40 ! [X33: num] :
% 5.15/5.40 ( one
% 5.15/5.40 != ( bit1 @ X33 ) ) ).
% 5.15/5.40
% 5.15/5.40 % verit_eq_simplify(12)
% 5.15/5.40 thf(fact_3173_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 5.15/5.40 ! [A: $o,B: $o,X: nat] :
% 5.15/5.40 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.15/5.40 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 5.15/5.40 thf(fact_3174_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 5.15/5.40 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.15/5.40 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X )
% 5.15/5.40 = one_one_nat ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 5.15/5.40 thf(fact_3175_eq__diff__eq_H,axiom,
% 5.15/5.40 ! [X: real,Y: real,Z: real] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( minus_minus_real @ Y @ Z ) )
% 5.15/5.40 = ( Y
% 5.15/5.40 = ( plus_plus_real @ X @ Z ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % eq_diff_eq'
% 5.15/5.40 thf(fact_3176_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 5.15/5.40 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.15/5.40 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 5.15/5.40 = one_one_nat ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 5.15/5.40 thf(fact_3177_pos__zdiv__mult__2,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.40 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.40 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % pos_zdiv_mult_2
% 5.15/5.40 thf(fact_3178_neg__zdiv__mult__2,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.40 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.40 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % neg_zdiv_mult_2
% 5.15/5.40 thf(fact_3179_neg__zmod__mult__2,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.40 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.40 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % neg_zmod_mult_2
% 5.15/5.40 thf(fact_3180_pos__zmod__mult__2,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.40 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.40 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % pos_zmod_mult_2
% 5.15/5.40 thf(fact_3181_vebt__mint_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.15/5.40 ( ( ( vEBT_vebt_mint @ X )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ~ ( ( A5
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.40 & ( ~ A5
% 5.15/5.40 => ( ( B6
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.40 & ( ~ B6
% 5.15/5.40 => ( Y = none_nat ) ) ) ) ) )
% 5.15/5.40 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ( Y != none_nat ) )
% 5.15/5.40 => ~ ! [Mi2: nat] :
% 5.15/5.40 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_mint.elims
% 5.15/5.40 thf(fact_3182_vebt__maxt_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.15/5.40 ( ( ( vEBT_vebt_maxt @ X )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ~ ( ( B6
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.40 & ( ~ B6
% 5.15/5.40 => ( ( A5
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.40 & ( ~ A5
% 5.15/5.40 => ( Y = none_nat ) ) ) ) ) )
% 5.15/5.40 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ( Y != none_nat ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.15/5.40 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_maxt.elims
% 5.15/5.40 thf(fact_3183_member__bound__height_H,axiom,
% 5.15/5.40 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.15/5.40 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.40 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % member_bound_height'
% 5.15/5.40 thf(fact_3184_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 5.15/5.40 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( ? [A5: $o,B6: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Summary2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( plus_plus_nat @ one_one_nat
% 5.15/5.40 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 5.15/5.40 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 5.15/5.40 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 5.15/5.40 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 5.15/5.40 @ ( if_nat
% 5.15/5.40 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 5.15/5.40 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 5.15/5.40 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.15/5.40 @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 5.15/5.40 thf(fact_3185_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.40 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.40 => A5 )
% 5.15/5.40 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.40 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.40 => B6 )
% 5.15/5.40 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.15/5.40 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [S2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.15/5.40 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.naive_member.elims(3)
% 5.15/5.40 thf(fact_3186_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.40 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.40 => A5 )
% 5.15/5.40 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.40 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.40 => B6 )
% 5.15/5.40 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.15/5.40 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [S2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.15/5.40 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.naive_member.elims(2)
% 5.15/5.40 thf(fact_3187_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.15/5.40 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.40 => A5 )
% 5.15/5.40 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.40 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.40 => B6 )
% 5.15/5.40 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.15/5.40 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.15/5.40 => Y )
% 5.15/5.40 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [S2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.naive_member.elims(1)
% 5.15/5.40 thf(fact_3188_div__less__mono,axiom,
% 5.15/5.40 ! [A2: nat,B3: nat,N2: nat] :
% 5.15/5.40 ( ( ord_less_nat @ A2 @ B3 )
% 5.15/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.40 => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 5.15/5.40 = zero_zero_nat )
% 5.15/5.40 => ( ( ( modulo_modulo_nat @ B3 @ N2 )
% 5.15/5.40 = zero_zero_nat )
% 5.15/5.40 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_less_mono
% 5.15/5.40 thf(fact_3189_set__bit__Suc,axiom,
% 5.15/5.40 ! [N2: nat,A: code_integer] :
% 5.15/5.40 ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 5.15/5.40 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % set_bit_Suc
% 5.15/5.40 thf(fact_3190_set__bit__Suc,axiom,
% 5.15/5.40 ! [N2: nat,A: int] :
% 5.15/5.40 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 5.15/5.40 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % set_bit_Suc
% 5.15/5.40 thf(fact_3191_set__bit__Suc,axiom,
% 5.15/5.40 ! [N2: nat,A: nat] :
% 5.15/5.40 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 5.15/5.40 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % set_bit_Suc
% 5.15/5.40 thf(fact_3192_div__mod__decomp,axiom,
% 5.15/5.40 ! [A2: nat,N2: nat] :
% 5.15/5.40 ( A2
% 5.15/5.40 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_mod_decomp
% 5.15/5.40 thf(fact_3193_div__mod__decomp__int,axiom,
% 5.15/5.40 ! [A2: int,N2: int] :
% 5.15/5.40 ( A2
% 5.15/5.40 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % div_mod_decomp_int
% 5.15/5.40 thf(fact_3194_vebt__member_Oelims_I2_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.40 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.40 => A5 )
% 5.15/5.40 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.40 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.40 => B6 )
% 5.15/5.40 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Summary2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ~ ( ( Xa2 != Mi2 )
% 5.15/5.40 => ( ( Xa2 != Ma2 )
% 5.15/5.40 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.40 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.40 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_member.elims(2)
% 5.15/5.40 thf(fact_3195_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.40 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.15/5.40 => ( ! [Uu2: $o,Uv2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.40 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.15/5.40 => ( ! [Mi2: nat,Ma2: nat] :
% 5.15/5.40 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.15/5.40 => ( ( Xa2 = Mi2 )
% 5.15/5.40 | ( Xa2 = Ma2 ) ) )
% 5.15/5.40 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.15/5.40 => ( ( Xa2 = Mi2 )
% 5.15/5.40 | ( Xa2 = Ma2 )
% 5.15/5.40 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.15/5.40 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Vd2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.15/5.40 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.membermima.elims(3)
% 5.15/5.40 thf(fact_3196_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.15/5.40 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.40 => Y )
% 5.15/5.40 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.15/5.40 => Y )
% 5.15/5.40 => ( ! [Mi2: nat,Ma2: nat] :
% 5.15/5.40 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( ~ ( ( Xa2 = Mi2 )
% 5.15/5.40 | ( Xa2 = Ma2 ) ) ) ) )
% 5.15/5.40 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( ~ ( ( Xa2 = Mi2 )
% 5.15/5.40 | ( Xa2 = Ma2 )
% 5.15/5.40 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.15/5.40 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Vd2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % VEBT_internal.membermima.elims(1)
% 5.15/5.40 thf(fact_3197_vebt__member_Oelims_I3_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.40 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.40 => A5 )
% 5.15/5.40 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.40 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.40 => B6 )
% 5.15/5.40 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.15/5.40 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.15/5.40 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Summary2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( ( Xa2 != Mi2 )
% 5.15/5.40 => ( ( Xa2 != Ma2 )
% 5.15/5.40 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.40 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.40 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_member.elims(3)
% 5.15/5.40 thf(fact_3198_vebt__member_Oelims_I1_J,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.15/5.40 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ! [A5: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.40 => A5 )
% 5.15/5.40 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.40 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.40 => B6 )
% 5.15/5.40 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.15/5.40 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.40 => Y )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.15/5.40 => Y )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.15/5.40 => Y )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Summary2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 = ( ~ ( ( Xa2 != Mi2 )
% 5.15/5.40 => ( ( Xa2 != Ma2 )
% 5.15/5.40 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.40 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.40 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.40 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.40 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % vebt_member.elims(1)
% 5.15/5.40 thf(fact_3199_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 5.15/5.40 ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( ? [A5: $o,B6: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.15/5.40 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT] :
% 5.15/5.40 ( ? [Summary2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 5.15/5.40 thf(fact_3200_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 5.15/5.40 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( ? [A5: $o,B6: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ( ( ? [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.40 ( ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( if_nat
% 5.15/5.40 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.40 & ~ ( ( Xa2 = Mi2 )
% 5.15/5.40 | ( Xa2 = Ma2 ) ) )
% 5.15/5.40 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.15/5.40 @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.elims
% 5.15/5.40 thf(fact_3201_invar__vebt_Ocases,axiom,
% 5.15/5.40 ! [A1: vEBT_VEBT,A22: nat] :
% 5.15/5.40 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 5.15/5.40 => ( ( ? [A5: $o,B6: $o] :
% 5.15/5.40 ( A1
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( A22
% 5.15/5.40 != ( suc @ zero_zero_nat ) ) )
% 5.15/5.40 => ( ! [TreeList3: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 5.15/5.40 ( ( A1
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( ( A22 = Deg2 )
% 5.15/5.40 => ( ! [X5: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.15/5.40 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 5.15/5.40 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.15/5.40 => ( ( M3 = N )
% 5.15/5.40 => ( ( Deg2
% 5.15/5.40 = ( plus_plus_nat @ N @ M3 ) )
% 5.15/5.40 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.15/5.40 => ~ ! [X5: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.40 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.15/5.40 => ( ! [TreeList3: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 5.15/5.40 ( ( A1
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( ( A22 = Deg2 )
% 5.15/5.40 => ( ! [X5: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.15/5.40 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 5.15/5.40 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.15/5.40 => ( ( M3
% 5.15/5.40 = ( suc @ N ) )
% 5.15/5.40 => ( ( Deg2
% 5.15/5.40 = ( plus_plus_nat @ N @ M3 ) )
% 5.15/5.40 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.15/5.40 => ~ ! [X5: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.40 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.15/5.40 => ( ! [TreeList3: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.15/5.40 ( ( A1
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( ( A22 = Deg2 )
% 5.15/5.40 => ( ! [X5: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.15/5.40 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 5.15/5.40 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.15/5.40 => ( ( M3 = N )
% 5.15/5.40 => ( ( Deg2
% 5.15/5.40 = ( plus_plus_nat @ N @ M3 ) )
% 5.15/5.40 => ( ! [I4: nat] :
% 5.15/5.40 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.15/5.40 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X4 ) )
% 5.15/5.40 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.15/5.40 => ( ( ( Mi2 = Ma2 )
% 5.15/5.40 => ! [X5: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.40 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.15/5.40 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.15/5.40 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.40 => ~ ( ( Mi2 != Ma2 )
% 5.15/5.40 => ! [I4: nat] :
% 5.15/5.40 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.15/5.40 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 5.15/5.40 = I4 )
% 5.15/5.40 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 5.15/5.40 & ! [X5: nat] :
% 5.15/5.40 ( ( ( ( vEBT_VEBT_high @ X5 @ N )
% 5.15/5.40 = I4 )
% 5.15/5.40 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N ) ) )
% 5.15/5.40 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.15/5.40 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.40 => ~ ! [TreeList3: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.15/5.40 ( ( A1
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.40 => ( ( A22 = Deg2 )
% 5.15/5.40 => ( ! [X5: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.40 => ( vEBT_invar_vebt @ X5 @ N ) )
% 5.15/5.40 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 5.15/5.40 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.15/5.40 => ( ( M3
% 5.15/5.40 = ( suc @ N ) )
% 5.15/5.40 => ( ( Deg2
% 5.15/5.40 = ( plus_plus_nat @ N @ M3 ) )
% 5.15/5.40 => ( ! [I4: nat] :
% 5.15/5.40 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.15/5.40 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X4 ) )
% 5.15/5.40 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.15/5.40 => ( ( ( Mi2 = Ma2 )
% 5.15/5.40 => ! [X5: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.40 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.15/5.40 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.15/5.40 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.40 => ~ ( ( Mi2 != Ma2 )
% 5.15/5.40 => ! [I4: nat] :
% 5.15/5.40 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.15/5.40 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 5.15/5.40 = I4 )
% 5.15/5.40 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 5.15/5.40 & ! [X5: nat] :
% 5.15/5.40 ( ( ( ( vEBT_VEBT_high @ X5 @ N )
% 5.15/5.40 = I4 )
% 5.15/5.40 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N ) ) )
% 5.15/5.40 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.15/5.40 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % invar_vebt.cases
% 5.15/5.40 thf(fact_3202_invar__vebt_Osimps,axiom,
% 5.15/5.40 ( vEBT_invar_vebt
% 5.15/5.40 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 5.15/5.40 ( ( ? [A3: $o,B2: $o] :
% 5.15/5.40 ( A12
% 5.15/5.40 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.15/5.40 & ( A23
% 5.15/5.40 = ( suc @ zero_zero_nat ) ) )
% 5.15/5.40 | ? [TreeList2: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 5.15/5.40 ( ( A12
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList2 @ Summary3 ) )
% 5.15/5.40 & ! [X2: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.15/5.40 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 5.15/5.40 & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 5.15/5.40 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.15/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 5.15/5.40 & ( A23
% 5.15/5.40 = ( plus_plus_nat @ N3 @ N3 ) )
% 5.15/5.40 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 5.15/5.40 & ! [X2: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.15/5.40 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.40 | ? [TreeList2: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 5.15/5.40 ( ( A12
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList2 @ Summary3 ) )
% 5.15/5.40 & ! [X2: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.15/5.40 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 5.15/5.40 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 5.15/5.40 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.15/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 5.15/5.40 & ( A23
% 5.15/5.40 = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 5.15/5.40 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 5.15/5.40 & ! [X2: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.15/5.40 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.40 | ? [TreeList2: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.15/5.40 ( ( A12
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList2 @ Summary3 ) )
% 5.15/5.40 & ! [X2: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.15/5.40 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 5.15/5.40 & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 5.15/5.40 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.15/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 5.15/5.40 & ( A23
% 5.15/5.40 = ( plus_plus_nat @ N3 @ N3 ) )
% 5.15/5.40 & ! [I3: nat] :
% 5.15/5.40 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 5.15/5.40 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 5.15/5.40 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.15/5.40 & ( ( Mi3 = Ma3 )
% 5.15/5.40 => ! [X2: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.15/5.40 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.40 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.40 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.15/5.40 & ( ( Mi3 != Ma3 )
% 5.15/5.40 => ! [I3: nat] :
% 5.15/5.40 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 5.15/5.40 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 5.15/5.40 = I3 )
% 5.15/5.40 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 5.15/5.40 & ! [X2: nat] :
% 5.15/5.40 ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 5.15/5.40 = I3 )
% 5.15/5.40 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 5.15/5.40 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.40 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 5.15/5.40 | ? [TreeList2: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.15/5.40 ( ( A12
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList2 @ Summary3 ) )
% 5.15/5.40 & ! [X2: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.15/5.40 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 5.15/5.40 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 5.15/5.40 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.15/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 5.15/5.40 & ( A23
% 5.15/5.40 = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 5.15/5.40 & ! [I3: nat] :
% 5.15/5.40 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 5.15/5.40 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X4 ) )
% 5.15/5.40 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.15/5.40 & ( ( Mi3 = Ma3 )
% 5.15/5.40 => ! [X2: vEBT_VEBT] :
% 5.15/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.15/5.40 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.40 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.40 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.15/5.40 & ( ( Mi3 != Ma3 )
% 5.15/5.40 => ! [I3: nat] :
% 5.15/5.40 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 5.15/5.40 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 5.15/5.40 = I3 )
% 5.15/5.40 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 5.15/5.40 & ! [X2: nat] :
% 5.15/5.40 ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 5.15/5.40 = I3 )
% 5.15/5.40 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 5.15/5.40 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.40 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % invar_vebt.simps
% 5.15/5.40 thf(fact_3203_infinite__Icc__iff,axiom,
% 5.15/5.40 ! [A: rat,B: rat] :
% 5.15/5.40 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.15/5.40 = ( ord_less_rat @ A @ B ) ) ).
% 5.15/5.40
% 5.15/5.40 % infinite_Icc_iff
% 5.15/5.40 thf(fact_3204_infinite__Icc__iff,axiom,
% 5.15/5.40 ! [A: real,B: real] :
% 5.15/5.40 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.15/5.40 = ( ord_less_real @ A @ B ) ) ).
% 5.15/5.40
% 5.15/5.40 % infinite_Icc_iff
% 5.15/5.40 thf(fact_3205_atLeastatMost__empty,axiom,
% 5.15/5.40 ! [B: rat,A: rat] :
% 5.15/5.40 ( ( ord_less_rat @ B @ A )
% 5.15/5.40 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.15/5.40 = bot_bot_set_rat ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty
% 5.15/5.40 thf(fact_3206_atLeastatMost__empty,axiom,
% 5.15/5.40 ! [B: num,A: num] :
% 5.15/5.40 ( ( ord_less_num @ B @ A )
% 5.15/5.40 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.15/5.40 = bot_bot_set_num ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty
% 5.15/5.40 thf(fact_3207_atLeastatMost__empty,axiom,
% 5.15/5.40 ! [B: nat,A: nat] :
% 5.15/5.40 ( ( ord_less_nat @ B @ A )
% 5.15/5.40 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.15/5.40 = bot_bot_set_nat ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty
% 5.15/5.40 thf(fact_3208_atLeastatMost__empty,axiom,
% 5.15/5.40 ! [B: int,A: int] :
% 5.15/5.40 ( ( ord_less_int @ B @ A )
% 5.15/5.40 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.15/5.40 = bot_bot_set_int ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty
% 5.15/5.40 thf(fact_3209_atLeastatMost__empty,axiom,
% 5.15/5.40 ! [B: real,A: real] :
% 5.15/5.40 ( ( ord_less_real @ B @ A )
% 5.15/5.40 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.15/5.40 = bot_bot_set_real ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty
% 5.15/5.40 thf(fact_3210_atLeastatMost__subset__iff,axiom,
% 5.15/5.40 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.15/5.40 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.15/5.40 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.15/5.40 & ( ord_less_eq_set_nat @ B @ D ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_subset_iff
% 5.15/5.40 thf(fact_3211_atLeastatMost__subset__iff,axiom,
% 5.15/5.40 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.40 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.15/5.40 | ( ( ord_less_eq_rat @ C @ A )
% 5.15/5.40 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_subset_iff
% 5.15/5.40 thf(fact_3212_atLeastatMost__subset__iff,axiom,
% 5.15/5.40 ! [A: num,B: num,C: num,D: num] :
% 5.15/5.40 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.15/5.40 | ( ( ord_less_eq_num @ C @ A )
% 5.15/5.40 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_subset_iff
% 5.15/5.40 thf(fact_3213_atLeastatMost__subset__iff,axiom,
% 5.15/5.40 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.40 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.15/5.40 | ( ( ord_less_eq_nat @ C @ A )
% 5.15/5.40 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_subset_iff
% 5.15/5.40 thf(fact_3214_atLeastatMost__subset__iff,axiom,
% 5.15/5.40 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.40 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.15/5.40 | ( ( ord_less_eq_int @ C @ A )
% 5.15/5.40 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_subset_iff
% 5.15/5.40 thf(fact_3215_atLeastatMost__subset__iff,axiom,
% 5.15/5.40 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.40 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.15/5.40 | ( ( ord_less_eq_real @ C @ A )
% 5.15/5.40 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_subset_iff
% 5.15/5.40 thf(fact_3216_atLeastatMost__empty__iff2,axiom,
% 5.15/5.40 ! [A: set_nat,B: set_nat] :
% 5.15/5.40 ( ( bot_bot_set_set_nat
% 5.15/5.40 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff2
% 5.15/5.40 thf(fact_3217_atLeastatMost__empty__iff2,axiom,
% 5.15/5.40 ! [A: rat,B: rat] :
% 5.15/5.40 ( ( bot_bot_set_rat
% 5.15/5.40 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff2
% 5.15/5.40 thf(fact_3218_atLeastatMost__empty__iff2,axiom,
% 5.15/5.40 ! [A: num,B: num] :
% 5.15/5.40 ( ( bot_bot_set_num
% 5.15/5.40 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff2
% 5.15/5.40 thf(fact_3219_atLeastatMost__empty__iff2,axiom,
% 5.15/5.40 ! [A: nat,B: nat] :
% 5.15/5.40 ( ( bot_bot_set_nat
% 5.15/5.40 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff2
% 5.15/5.40 thf(fact_3220_atLeastatMost__empty__iff2,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( bot_bot_set_int
% 5.15/5.40 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff2
% 5.15/5.40 thf(fact_3221_atLeastatMost__empty__iff2,axiom,
% 5.15/5.40 ! [A: real,B: real] :
% 5.15/5.40 ( ( bot_bot_set_real
% 5.15/5.40 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.15/5.40 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff2
% 5.15/5.40 thf(fact_3222_atLeastatMost__empty__iff,axiom,
% 5.15/5.40 ! [A: set_nat,B: set_nat] :
% 5.15/5.40 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 5.15/5.40 = bot_bot_set_set_nat )
% 5.15/5.40 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff
% 5.15/5.40 thf(fact_3223_atLeastatMost__empty__iff,axiom,
% 5.15/5.40 ! [A: rat,B: rat] :
% 5.15/5.40 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.15/5.40 = bot_bot_set_rat )
% 5.15/5.40 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff
% 5.15/5.40 thf(fact_3224_atLeastatMost__empty__iff,axiom,
% 5.15/5.40 ! [A: num,B: num] :
% 5.15/5.40 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.15/5.40 = bot_bot_set_num )
% 5.15/5.40 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff
% 5.15/5.40 thf(fact_3225_atLeastatMost__empty__iff,axiom,
% 5.15/5.40 ! [A: nat,B: nat] :
% 5.15/5.40 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.15/5.40 = bot_bot_set_nat )
% 5.15/5.40 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff
% 5.15/5.40 thf(fact_3226_atLeastatMost__empty__iff,axiom,
% 5.15/5.40 ! [A: int,B: int] :
% 5.15/5.40 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.15/5.40 = bot_bot_set_int )
% 5.15/5.40 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff
% 5.15/5.40 thf(fact_3227_atLeastatMost__empty__iff,axiom,
% 5.15/5.40 ! [A: real,B: real] :
% 5.15/5.40 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.15/5.40 = bot_bot_set_real )
% 5.15/5.40 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % atLeastatMost_empty_iff
% 5.15/5.40 thf(fact_3228_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Y: nat] :
% 5.15/5.40 ( ( ( vEBT_T_m_i_n_t @ X )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ! [A5: $o] :
% 5.15/5.40 ( ? [B6: $o] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.40 => ( Y
% 5.15/5.40 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.15/5.40 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) )
% 5.15/5.40 => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.40 ( X
% 5.15/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.40 => ( Y != one_one_nat ) ) ) ) ) ).
% 5.15/5.40
% 5.15/5.40 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.elims
% 5.15/5.40 thf(fact_3229_vebt__succ_Opelims,axiom,
% 5.15/5.40 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.15/5.40 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.15/5.40 = Y )
% 5.15/5.40 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.40 => ( ! [Uu2: $o,B6: $o] :
% 5.15/5.40 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ Uu2 @ B6 ) )
% 5.15/5.41 => ( ( Xa2 = zero_zero_nat )
% 5.15/5.41 => ( ( ( B6
% 5.15/5.41 => ( Y
% 5.15/5.41 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.41 & ( ~ B6
% 5.15/5.41 => ( Y = none_nat ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B6 ) @ zero_zero_nat ) ) ) ) )
% 5.15/5.41 => ( ! [Uv2: $o,Uw2: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.15/5.41 => ! [N: nat] :
% 5.15/5.41 ( ( Xa2
% 5.15/5.41 = ( suc @ N ) )
% 5.15/5.41 => ( ( Y = none_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) ) ) ) ) )
% 5.15/5.41 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.41 => ( ( Y = none_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.15/5.41 => ( ( Y = none_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 5.15/5.41 => ( ( Y = none_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.41 => ( Y
% 5.15/5.41 = ( some_nat @ Mi2 ) ) )
% 5.15/5.41 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.41 => ( Y
% 5.15/5.41 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 @ ( if_option_nat
% 5.15/5.41 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 != none_nat )
% 5.15/5.41 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.41 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 @ ( if_option_nat
% 5.15/5.41 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.41 = none_nat )
% 5.15/5.41 @ none_nat
% 5.15/5.41 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.41 @ none_nat ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % vebt_succ.pelims
% 5.15/5.41 thf(fact_3230_vebt__pred_Opelims,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.15/5.41 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [Uu2: $o,Uv2: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.41 => ( ( Xa2 = zero_zero_nat )
% 5.15/5.41 => ( ( Y = none_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.15/5.41 => ( ! [A5: $o,Uw2: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 5.15/5.41 => ( ( Xa2
% 5.15/5.41 = ( suc @ zero_zero_nat ) )
% 5.15/5.41 => ( ( ( A5
% 5.15/5.41 => ( Y
% 5.15/5.41 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.41 & ( ~ A5
% 5.15/5.41 => ( Y = none_nat ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ! [Va3: nat] :
% 5.15/5.41 ( ( Xa2
% 5.15/5.41 = ( suc @ ( suc @ Va3 ) ) )
% 5.15/5.41 => ( ( ( B6
% 5.15/5.41 => ( Y
% 5.15/5.41 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.41 & ( ~ B6
% 5.15/5.41 => ( ( A5
% 5.15/5.41 => ( Y
% 5.15/5.41 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.41 & ( ~ A5
% 5.15/5.41 => ( Y = none_nat ) ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) )
% 5.15/5.41 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) )
% 5.15/5.41 => ( ( Y = none_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.15/5.41 => ( ( Y = none_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 5.15/5.41 => ( ( Y = none_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.41 => ( Y
% 5.15/5.41 = ( some_nat @ Ma2 ) ) )
% 5.15/5.41 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.41 => ( Y
% 5.15/5.41 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 @ ( if_option_nat
% 5.15/5.41 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 != none_nat )
% 5.15/5.41 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.15/5.41 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 @ ( if_option_nat
% 5.15/5.41 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.41 = none_nat )
% 5.15/5.41 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.15/5.41 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.41 @ none_nat ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % vebt_pred.pelims
% 5.15/5.41 thf(fact_3231_Icc__eq__Icc,axiom,
% 5.15/5.41 ! [L: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 5.15/5.41 ( ( ( set_or4548717258645045905et_nat @ L @ H2 )
% 5.15/5.41 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 5.15/5.41 = ( ( ( L = L3 )
% 5.15/5.41 & ( H2 = H3 ) )
% 5.15/5.41 | ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 5.15/5.41 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % Icc_eq_Icc
% 5.15/5.41 thf(fact_3232_Icc__eq__Icc,axiom,
% 5.15/5.41 ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 5.15/5.41 ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 5.15/5.41 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.15/5.41 = ( ( ( L = L3 )
% 5.15/5.41 & ( H2 = H3 ) )
% 5.15/5.41 | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.15/5.41 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % Icc_eq_Icc
% 5.15/5.41 thf(fact_3233_Icc__eq__Icc,axiom,
% 5.15/5.41 ! [L: num,H2: num,L3: num,H3: num] :
% 5.15/5.41 ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 5.15/5.41 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.15/5.41 = ( ( ( L = L3 )
% 5.15/5.41 & ( H2 = H3 ) )
% 5.15/5.41 | ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.15/5.41 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % Icc_eq_Icc
% 5.15/5.41 thf(fact_3234_Icc__eq__Icc,axiom,
% 5.15/5.41 ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 5.15/5.41 ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 5.15/5.41 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.15/5.41 = ( ( ( L = L3 )
% 5.15/5.41 & ( H2 = H3 ) )
% 5.15/5.41 | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.15/5.41 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % Icc_eq_Icc
% 5.15/5.41 thf(fact_3235_Icc__eq__Icc,axiom,
% 5.15/5.41 ! [L: int,H2: int,L3: int,H3: int] :
% 5.15/5.41 ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 5.15/5.41 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.15/5.41 = ( ( ( L = L3 )
% 5.15/5.41 & ( H2 = H3 ) )
% 5.15/5.41 | ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.15/5.41 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % Icc_eq_Icc
% 5.15/5.41 thf(fact_3236_Icc__eq__Icc,axiom,
% 5.15/5.41 ! [L: real,H2: real,L3: real,H3: real] :
% 5.15/5.41 ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 5.15/5.41 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.15/5.41 = ( ( ( L = L3 )
% 5.15/5.41 & ( H2 = H3 ) )
% 5.15/5.41 | ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.15/5.41 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % Icc_eq_Icc
% 5.15/5.41 thf(fact_3237_atLeastAtMost__iff,axiom,
% 5.15/5.41 ! [I: set_nat,L: set_nat,U: set_nat] :
% 5.15/5.41 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 5.15/5.41 = ( ( ord_less_eq_set_nat @ L @ I )
% 5.15/5.41 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastAtMost_iff
% 5.15/5.41 thf(fact_3238_atLeastAtMost__iff,axiom,
% 5.15/5.41 ! [I: rat,L: rat,U: rat] :
% 5.15/5.41 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.15/5.41 = ( ( ord_less_eq_rat @ L @ I )
% 5.15/5.41 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastAtMost_iff
% 5.15/5.41 thf(fact_3239_atLeastAtMost__iff,axiom,
% 5.15/5.41 ! [I: num,L: num,U: num] :
% 5.15/5.41 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.15/5.41 = ( ( ord_less_eq_num @ L @ I )
% 5.15/5.41 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastAtMost_iff
% 5.15/5.41 thf(fact_3240_atLeastAtMost__iff,axiom,
% 5.15/5.41 ! [I: nat,L: nat,U: nat] :
% 5.15/5.41 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.15/5.41 = ( ( ord_less_eq_nat @ L @ I )
% 5.15/5.41 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastAtMost_iff
% 5.15/5.41 thf(fact_3241_atLeastAtMost__iff,axiom,
% 5.15/5.41 ! [I: int,L: int,U: int] :
% 5.15/5.41 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.15/5.41 = ( ( ord_less_eq_int @ L @ I )
% 5.15/5.41 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastAtMost_iff
% 5.15/5.41 thf(fact_3242_atLeastAtMost__iff,axiom,
% 5.15/5.41 ! [I: real,L: real,U: real] :
% 5.15/5.41 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.15/5.41 = ( ( ord_less_eq_real @ L @ I )
% 5.15/5.41 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastAtMost_iff
% 5.15/5.41 thf(fact_3243_set__bit__negative__int__iff,axiom,
% 5.15/5.41 ! [N2: nat,K: int] :
% 5.15/5.41 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 5.15/5.41 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.15/5.41
% 5.15/5.41 % set_bit_negative_int_iff
% 5.15/5.41 thf(fact_3244_imult__is__0,axiom,
% 5.15/5.41 ! [M: extended_enat,N2: extended_enat] :
% 5.15/5.41 ( ( ( times_7803423173614009249d_enat @ M @ N2 )
% 5.15/5.41 = zero_z5237406670263579293d_enat )
% 5.15/5.41 = ( ( M = zero_z5237406670263579293d_enat )
% 5.15/5.41 | ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % imult_is_0
% 5.15/5.41 thf(fact_3245_zero__one__enat__neq_I1_J,axiom,
% 5.15/5.41 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.15/5.41
% 5.15/5.41 % zero_one_enat_neq(1)
% 5.15/5.41 thf(fact_3246_bounded__Max__nat,axiom,
% 5.15/5.41 ! [P: nat > $o,X: nat,M7: nat] :
% 5.15/5.41 ( ( P @ X )
% 5.15/5.41 => ( ! [X3: nat] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 => ( ord_less_eq_nat @ X3 @ M7 ) )
% 5.15/5.41 => ~ ! [M3: nat] :
% 5.15/5.41 ( ( P @ M3 )
% 5.15/5.41 => ~ ! [X5: nat] :
% 5.15/5.41 ( ( P @ X5 )
% 5.15/5.41 => ( ord_less_eq_nat @ X5 @ M3 ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % bounded_Max_nat
% 5.15/5.41 thf(fact_3247_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.15/5.41 ! [X: produc3368934014287244435at_num] :
% 5.15/5.41 ~ ! [F2: nat > num > num,A5: nat,B6: nat,Acc: num] :
% 5.15/5.41 ( X
% 5.15/5.41 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A5 @ ( product_Pair_nat_num @ B6 @ Acc ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % fold_atLeastAtMost_nat.cases
% 5.15/5.41 thf(fact_3248_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.15/5.41 ! [X: produc4471711990508489141at_nat] :
% 5.15/5.41 ~ ! [F2: nat > nat > nat,A5: nat,B6: nat,Acc: nat] :
% 5.15/5.41 ( X
% 5.15/5.41 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B6 @ Acc ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % fold_atLeastAtMost_nat.cases
% 5.15/5.41 thf(fact_3249_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.15/5.41 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.15/5.41 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.15/5.41 = one_one_nat ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(2)
% 5.15/5.41 thf(fact_3250_finite__nat__set__iff__bounded,axiom,
% 5.15/5.41 ( finite_finite_nat
% 5.15/5.41 = ( ^ [N6: set_nat] :
% 5.15/5.41 ? [M5: nat] :
% 5.15/5.41 ! [X2: nat] :
% 5.15/5.41 ( ( member_nat @ X2 @ N6 )
% 5.15/5.41 => ( ord_less_nat @ X2 @ M5 ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % finite_nat_set_iff_bounded
% 5.15/5.41 thf(fact_3251_bounded__nat__set__is__finite,axiom,
% 5.15/5.41 ! [N5: set_nat,N2: nat] :
% 5.15/5.41 ( ! [X3: nat] :
% 5.15/5.41 ( ( member_nat @ X3 @ N5 )
% 5.15/5.41 => ( ord_less_nat @ X3 @ N2 ) )
% 5.15/5.41 => ( finite_finite_nat @ N5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % bounded_nat_set_is_finite
% 5.15/5.41 thf(fact_3252_finite__nat__set__iff__bounded__le,axiom,
% 5.15/5.41 ( finite_finite_nat
% 5.15/5.41 = ( ^ [N6: set_nat] :
% 5.15/5.41 ? [M5: nat] :
% 5.15/5.41 ! [X2: nat] :
% 5.15/5.41 ( ( member_nat @ X2 @ N6 )
% 5.15/5.41 => ( ord_less_eq_nat @ X2 @ M5 ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % finite_nat_set_iff_bounded_le
% 5.15/5.41 thf(fact_3253_finite__M__bounded__by__nat,axiom,
% 5.15/5.41 ! [P: nat > $o,I: nat] :
% 5.15/5.41 ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [K2: nat] :
% 5.15/5.41 ( ( P @ K2 )
% 5.15/5.41 & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % finite_M_bounded_by_nat
% 5.15/5.41 thf(fact_3254_finite__less__ub,axiom,
% 5.15/5.41 ! [F: nat > nat,U: nat] :
% 5.15/5.41 ( ! [N: nat] : ( ord_less_eq_nat @ N @ ( F @ N ) )
% 5.15/5.41 => ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ U ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % finite_less_ub
% 5.15/5.41 thf(fact_3255_mint__bound,axiom,
% 5.15/5.41 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % mint_bound
% 5.15/5.41 thf(fact_3256_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.15/5.41 ! [A: $o,B: $o] :
% 5.15/5.41 ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.41 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(1)
% 5.15/5.41 thf(fact_3257_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.15/5.41 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.15/5.41 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.15/5.41 = one_one_nat ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(3)
% 5.15/5.41 thf(fact_3258_atLeastatMost__psubset__iff,axiom,
% 5.15/5.41 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.15/5.41 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.15/5.41 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.15/5.41 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.15/5.41 & ( ord_less_eq_set_nat @ B @ D )
% 5.15/5.41 & ( ( ord_less_set_nat @ C @ A )
% 5.15/5.41 | ( ord_less_set_nat @ B @ D ) ) ) )
% 5.15/5.41 & ( ord_less_eq_set_nat @ C @ D ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastatMost_psubset_iff
% 5.15/5.41 thf(fact_3259_atLeastatMost__psubset__iff,axiom,
% 5.15/5.41 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.41 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.15/5.41 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.15/5.41 | ( ( ord_less_eq_rat @ C @ A )
% 5.15/5.41 & ( ord_less_eq_rat @ B @ D )
% 5.15/5.41 & ( ( ord_less_rat @ C @ A )
% 5.15/5.41 | ( ord_less_rat @ B @ D ) ) ) )
% 5.15/5.41 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastatMost_psubset_iff
% 5.15/5.41 thf(fact_3260_atLeastatMost__psubset__iff,axiom,
% 5.15/5.41 ! [A: num,B: num,C: num,D: num] :
% 5.15/5.41 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.15/5.41 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.15/5.41 | ( ( ord_less_eq_num @ C @ A )
% 5.15/5.41 & ( ord_less_eq_num @ B @ D )
% 5.15/5.41 & ( ( ord_less_num @ C @ A )
% 5.15/5.41 | ( ord_less_num @ B @ D ) ) ) )
% 5.15/5.41 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastatMost_psubset_iff
% 5.15/5.41 thf(fact_3261_atLeastatMost__psubset__iff,axiom,
% 5.15/5.41 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.41 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.15/5.41 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.15/5.41 | ( ( ord_less_eq_nat @ C @ A )
% 5.15/5.41 & ( ord_less_eq_nat @ B @ D )
% 5.15/5.41 & ( ( ord_less_nat @ C @ A )
% 5.15/5.41 | ( ord_less_nat @ B @ D ) ) ) )
% 5.15/5.41 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastatMost_psubset_iff
% 5.15/5.41 thf(fact_3262_atLeastatMost__psubset__iff,axiom,
% 5.15/5.41 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.41 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.15/5.41 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.15/5.41 | ( ( ord_less_eq_int @ C @ A )
% 5.15/5.41 & ( ord_less_eq_int @ B @ D )
% 5.15/5.41 & ( ( ord_less_int @ C @ A )
% 5.15/5.41 | ( ord_less_int @ B @ D ) ) ) )
% 5.15/5.41 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastatMost_psubset_iff
% 5.15/5.41 thf(fact_3263_atLeastatMost__psubset__iff,axiom,
% 5.15/5.41 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.41 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.15/5.41 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.15/5.41 | ( ( ord_less_eq_real @ C @ A )
% 5.15/5.41 & ( ord_less_eq_real @ B @ D )
% 5.15/5.41 & ( ( ord_less_real @ C @ A )
% 5.15/5.41 | ( ord_less_real @ B @ D ) ) ) )
% 5.15/5.41 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % atLeastatMost_psubset_iff
% 5.15/5.41 thf(fact_3264_infinite__Icc,axiom,
% 5.15/5.41 ! [A: rat,B: rat] :
% 5.15/5.41 ( ( ord_less_rat @ A @ B )
% 5.15/5.41 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % infinite_Icc
% 5.15/5.41 thf(fact_3265_infinite__Icc,axiom,
% 5.15/5.41 ! [A: real,B: real] :
% 5.15/5.41 ( ( ord_less_real @ A @ B )
% 5.15/5.41 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % infinite_Icc
% 5.15/5.41 thf(fact_3266_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 5.15/5.41 ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.41 @ ( if_nat
% 5.15/5.41 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 & ~ ( ( Xa2 = Mi2 )
% 5.15/5.41 | ( Xa2 = Ma2 ) ) )
% 5.15/5.41 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.15/5.41 @ one_one_nat ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.pelims
% 5.15/5.41 thf(fact_3267_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 5.15/5.41 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( if_nat
% 5.15/5.41 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 & ~ ( ( Xa2 = Mi2 )
% 5.15/5.41 | ( Xa2 = Ma2 ) ) )
% 5.15/5.41 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 5.15/5.41 @ one_one_nat ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.pelims
% 5.15/5.41 thf(fact_3268_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 5.15/5.41 ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 5.15/5.41 thf(fact_3269_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 5.15/5.41 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.15/5.41 => ( ( Y = one_one_nat )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( plus_plus_nat @ one_one_nat
% 5.15/5.41 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 5.15/5.41 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 5.15/5.41 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 5.15/5.41 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 5.15/5.41 @ ( if_nat
% 5.15/5.41 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 5.15/5.41 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 5.15/5.41 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.15/5.41 @ zero_zero_nat ) ) ) ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 5.15/5.41 thf(fact_3270_vebt__member_Opelims_I1_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.15/5.41 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.41 => A5 )
% 5.15/5.41 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.41 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.41 => B6 )
% 5.15/5.41 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.41 => ( ~ Y
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.15/5.41 => ( ~ Y
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.15/5.41 => ( ~ Y
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( ( Xa2 != Mi2 )
% 5.15/5.41 => ( ( Xa2 != Ma2 )
% 5.15/5.41 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.41 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.41 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.41 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.41 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % vebt_member.pelims(1)
% 5.15/5.41 thf(fact_3271_vebt__member_Opelims_I3_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.41 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) )
% 5.15/5.41 => ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.41 => A5 )
% 5.15/5.41 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.41 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.41 => B6 )
% 5.15/5.41 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.15/5.41 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.15/5.41 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.15/5.41 => ( ( Xa2 != Mi2 )
% 5.15/5.41 => ( ( Xa2 != Ma2 )
% 5.15/5.41 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.41 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.41 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.41 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.41 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % vebt_member.pelims(3)
% 5.15/5.41 thf(fact_3272_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.15/5.41 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.41 => A5 )
% 5.15/5.41 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.41 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.41 => B6 )
% 5.15/5.41 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.15/5.41 => ( ~ Y
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % VEBT_internal.naive_member.pelims(1)
% 5.15/5.41 thf(fact_3273_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.41 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) )
% 5.15/5.41 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.41 => A5 )
% 5.15/5.41 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.41 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.41 => B6 )
% 5.15/5.41 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.15/5.41 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) )
% 5.15/5.41 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % VEBT_internal.naive_member.pelims(2)
% 5.15/5.41 thf(fact_3274_vebt__member_Opelims_I2_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.41 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) )
% 5.15/5.41 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.41 => A5 )
% 5.15/5.41 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.41 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.41 => B6 )
% 5.15/5.41 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.15/5.41 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.15/5.41 => ~ ( ( Xa2 != Mi2 )
% 5.15/5.41 => ( ( Xa2 != Ma2 )
% 5.15/5.41 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.41 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.15/5.41 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.41 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.15/5.41 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % vebt_member.pelims(2)
% 5.15/5.41 thf(fact_3275_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.41 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) )
% 5.15/5.41 => ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.41 => A5 )
% 5.15/5.41 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.41 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.41 => B6 )
% 5.15/5.41 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.15/5.41 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.15/5.41 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) )
% 5.15/5.41 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % VEBT_internal.naive_member.pelims(3)
% 5.15/5.41 thf(fact_3276_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.41 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [Uu2: $o,Uv2: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.15/5.41 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.15/5.41 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.15/5.41 => ( ( Xa2 = Mi2 )
% 5.15/5.41 | ( Xa2 = Ma2 ) ) ) )
% 5.15/5.41 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.15/5.41 => ( ( Xa2 = Mi2 )
% 5.15/5.41 | ( Xa2 = Ma2 )
% 5.15/5.41 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.15/5.41 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.15/5.41 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % VEBT_internal.membermima.pelims(3)
% 5.15/5.41 thf(fact_3277_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.15/5.41 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [Uu2: $o,Uv2: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.41 => ( ~ Y
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.15/5.41 => ( ~ Y
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( ( Xa2 = Mi2 )
% 5.15/5.41 | ( Xa2 = Ma2 ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( ( Xa2 = Mi2 )
% 5.15/5.41 | ( Xa2 = Ma2 )
% 5.15/5.41 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 5.15/5.41 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.15/5.41 => ( ( Y
% 5.15/5.41 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.15/5.41 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % VEBT_internal.membermima.pelims(1)
% 5.15/5.41 thf(fact_3278_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.41 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.41 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 5.15/5.41 => ~ ( ( Xa2 = Mi2 )
% 5.15/5.41 | ( Xa2 = Ma2 ) ) ) )
% 5.15/5.41 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.15/5.41 => ~ ( ( Xa2 = Mi2 )
% 5.15/5.41 | ( Xa2 = Ma2 )
% 5.15/5.41 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.15/5.41 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.15/5.41 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.15/5.41 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.41 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.41 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % VEBT_internal.membermima.pelims(2)
% 5.15/5.41 thf(fact_3279_cpmi,axiom,
% 5.15/5.41 ! [D4: int,P: int > $o,P6: int > $o,B3: set_int] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.15/5.41 => ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ! [X3: int] :
% 5.15/5.41 ( ! [Xa: int] :
% 5.15/5.41 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.15/5.41 => ! [Xb2: int] :
% 5.15/5.41 ( ( member_int @ Xb2 @ B3 )
% 5.15/5.41 => ( X3
% 5.15/5.41 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.15/5.41 => ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( P6 @ X3 )
% 5.15/5.41 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.15/5.41 = ( ? [X2: int] :
% 5.15/5.41 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.15/5.41 & ( P6 @ X2 ) )
% 5.15/5.41 | ? [X2: int] :
% 5.15/5.41 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.15/5.41 & ? [Y2: int] :
% 5.15/5.41 ( ( member_int @ Y2 @ B3 )
% 5.15/5.41 & ( P @ ( plus_plus_int @ Y2 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % cpmi
% 5.15/5.41 thf(fact_3280_cppi,axiom,
% 5.15/5.41 ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.15/5.41 => ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ! [X3: int] :
% 5.15/5.41 ( ! [Xa: int] :
% 5.15/5.41 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.15/5.41 => ! [Xb2: int] :
% 5.15/5.41 ( ( member_int @ Xb2 @ A2 )
% 5.15/5.41 => ( X3
% 5.15/5.41 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.15/5.41 => ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( P6 @ X3 )
% 5.15/5.41 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.15/5.41 = ( ? [X2: int] :
% 5.15/5.41 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.15/5.41 & ( P6 @ X2 ) )
% 5.15/5.41 | ? [X2: int] :
% 5.15/5.41 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.15/5.41 & ? [Y2: int] :
% 5.15/5.41 ( ( member_int @ Y2 @ A2 )
% 5.15/5.41 & ( P @ ( minus_minus_int @ Y2 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % cppi
% 5.15/5.41 thf(fact_3281_finite__interval__int3,axiom,
% 5.15/5.41 ! [A: int,B: int] :
% 5.15/5.41 ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( ord_less_int @ A @ I3 )
% 5.15/5.41 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % finite_interval_int3
% 5.15/5.41 thf(fact_3282_finite__interval__int2,axiom,
% 5.15/5.41 ! [A: int,B: int] :
% 5.15/5.41 ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( ord_less_eq_int @ A @ I3 )
% 5.15/5.41 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % finite_interval_int2
% 5.15/5.41 thf(fact_3283_periodic__finite__ex,axiom,
% 5.15/5.41 ! [D: int,P: int > $o] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ D )
% 5.15/5.41 => ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.15/5.41 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.15/5.41 = ( ? [X2: int] :
% 5.15/5.41 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.15/5.41 & ( P @ X2 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % periodic_finite_ex
% 5.15/5.41 thf(fact_3284_double__eq__0__iff,axiom,
% 5.15/5.41 ! [A: real] :
% 5.15/5.41 ( ( ( plus_plus_real @ A @ A )
% 5.15/5.41 = zero_zero_real )
% 5.15/5.41 = ( A = zero_zero_real ) ) ).
% 5.15/5.41
% 5.15/5.41 % double_eq_0_iff
% 5.15/5.41 thf(fact_3285_double__eq__0__iff,axiom,
% 5.15/5.41 ! [A: rat] :
% 5.15/5.41 ( ( ( plus_plus_rat @ A @ A )
% 5.15/5.41 = zero_zero_rat )
% 5.15/5.41 = ( A = zero_zero_rat ) ) ).
% 5.15/5.41
% 5.15/5.41 % double_eq_0_iff
% 5.15/5.41 thf(fact_3286_double__eq__0__iff,axiom,
% 5.15/5.41 ! [A: int] :
% 5.15/5.41 ( ( ( plus_plus_int @ A @ A )
% 5.15/5.41 = zero_zero_int )
% 5.15/5.41 = ( A = zero_zero_int ) ) ).
% 5.15/5.41
% 5.15/5.41 % double_eq_0_iff
% 5.15/5.41 thf(fact_3287_finite__interval__int1,axiom,
% 5.15/5.41 ! [A: int,B: int] :
% 5.15/5.41 ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( ord_less_eq_int @ A @ I3 )
% 5.15/5.41 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % finite_interval_int1
% 5.15/5.41 thf(fact_3288_finite__interval__int4,axiom,
% 5.15/5.41 ! [A: int,B: int] :
% 5.15/5.41 ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( ord_less_int @ A @ I3 )
% 5.15/5.41 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % finite_interval_int4
% 5.15/5.41 thf(fact_3289_pinf_I1_J,axiom,
% 5.15/5.41 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.15/5.41 ( ? [Z4: real] :
% 5.15/5.41 ! [X3: real] :
% 5.15/5.41 ( ( ord_less_real @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: real] :
% 5.15/5.41 ! [X3: real] :
% 5.15/5.41 ( ( ord_less_real @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(1)
% 5.15/5.41 thf(fact_3290_pinf_I1_J,axiom,
% 5.15/5.41 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.15/5.41 ( ? [Z4: rat] :
% 5.15/5.41 ! [X3: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: rat] :
% 5.15/5.41 ! [X3: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(1)
% 5.15/5.41 thf(fact_3291_pinf_I1_J,axiom,
% 5.15/5.41 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.15/5.41 ( ? [Z4: num] :
% 5.15/5.41 ! [X3: num] :
% 5.15/5.41 ( ( ord_less_num @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: num] :
% 5.15/5.41 ! [X3: num] :
% 5.15/5.41 ( ( ord_less_num @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(1)
% 5.15/5.41 thf(fact_3292_pinf_I1_J,axiom,
% 5.15/5.41 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.15/5.41 ( ? [Z4: nat] :
% 5.15/5.41 ! [X3: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: nat] :
% 5.15/5.41 ! [X3: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(1)
% 5.15/5.41 thf(fact_3293_pinf_I1_J,axiom,
% 5.15/5.41 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.15/5.41 ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(1)
% 5.15/5.41 thf(fact_3294_pinf_I2_J,axiom,
% 5.15/5.41 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.15/5.41 ( ? [Z4: real] :
% 5.15/5.41 ! [X3: real] :
% 5.15/5.41 ( ( ord_less_real @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: real] :
% 5.15/5.41 ! [X3: real] :
% 5.15/5.41 ( ( ord_less_real @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(2)
% 5.15/5.41 thf(fact_3295_pinf_I2_J,axiom,
% 5.15/5.41 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.15/5.41 ( ? [Z4: rat] :
% 5.15/5.41 ! [X3: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: rat] :
% 5.15/5.41 ! [X3: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(2)
% 5.15/5.41 thf(fact_3296_pinf_I2_J,axiom,
% 5.15/5.41 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.15/5.41 ( ? [Z4: num] :
% 5.15/5.41 ! [X3: num] :
% 5.15/5.41 ( ( ord_less_num @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: num] :
% 5.15/5.41 ! [X3: num] :
% 5.15/5.41 ( ( ord_less_num @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(2)
% 5.15/5.41 thf(fact_3297_pinf_I2_J,axiom,
% 5.15/5.41 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.15/5.41 ( ? [Z4: nat] :
% 5.15/5.41 ! [X3: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: nat] :
% 5.15/5.41 ! [X3: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(2)
% 5.15/5.41 thf(fact_3298_pinf_I2_J,axiom,
% 5.15/5.41 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.15/5.41 ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ Z4 @ X3 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(2)
% 5.15/5.41 thf(fact_3299_pinf_I3_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(3)
% 5.15/5.41 thf(fact_3300_pinf_I3_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(3)
% 5.15/5.41 thf(fact_3301_pinf_I3_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(3)
% 5.15/5.41 thf(fact_3302_pinf_I3_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(3)
% 5.15/5.41 thf(fact_3303_pinf_I3_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(3)
% 5.15/5.41 thf(fact_3304_pinf_I4_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(4)
% 5.15/5.41 thf(fact_3305_pinf_I4_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(4)
% 5.15/5.41 thf(fact_3306_pinf_I4_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(4)
% 5.15/5.41 thf(fact_3307_pinf_I4_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(4)
% 5.15/5.41 thf(fact_3308_pinf_I4_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(4)
% 5.15/5.41 thf(fact_3309_pinf_I5_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_real @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(5)
% 5.15/5.41 thf(fact_3310_pinf_I5_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(5)
% 5.15/5.41 thf(fact_3311_pinf_I5_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_num @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(5)
% 5.15/5.41 thf(fact_3312_pinf_I5_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(5)
% 5.15/5.41 thf(fact_3313_pinf_I5_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_int @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(5)
% 5.15/5.41 thf(fact_3314_pinf_I7_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_real @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(7)
% 5.15/5.41 thf(fact_3315_pinf_I7_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_rat @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(7)
% 5.15/5.41 thf(fact_3316_pinf_I7_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_num @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(7)
% 5.15/5.41 thf(fact_3317_pinf_I7_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_nat @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(7)
% 5.15/5.41 thf(fact_3318_pinf_I7_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_int @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(7)
% 5.15/5.41 thf(fact_3319_minf_I1_J,axiom,
% 5.15/5.41 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.15/5.41 ( ? [Z4: real] :
% 5.15/5.41 ! [X3: real] :
% 5.15/5.41 ( ( ord_less_real @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: real] :
% 5.15/5.41 ! [X3: real] :
% 5.15/5.41 ( ( ord_less_real @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(1)
% 5.15/5.41 thf(fact_3320_minf_I1_J,axiom,
% 5.15/5.41 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.15/5.41 ( ? [Z4: rat] :
% 5.15/5.41 ! [X3: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: rat] :
% 5.15/5.41 ! [X3: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(1)
% 5.15/5.41 thf(fact_3321_minf_I1_J,axiom,
% 5.15/5.41 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.15/5.41 ( ? [Z4: num] :
% 5.15/5.41 ! [X3: num] :
% 5.15/5.41 ( ( ord_less_num @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: num] :
% 5.15/5.41 ! [X3: num] :
% 5.15/5.41 ( ( ord_less_num @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(1)
% 5.15/5.41 thf(fact_3322_minf_I1_J,axiom,
% 5.15/5.41 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.15/5.41 ( ? [Z4: nat] :
% 5.15/5.41 ! [X3: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: nat] :
% 5.15/5.41 ! [X3: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(1)
% 5.15/5.41 thf(fact_3323_minf_I1_J,axiom,
% 5.15/5.41 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.15/5.41 ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(1)
% 5.15/5.41 thf(fact_3324_minf_I2_J,axiom,
% 5.15/5.41 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.15/5.41 ( ? [Z4: real] :
% 5.15/5.41 ! [X3: real] :
% 5.15/5.41 ( ( ord_less_real @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: real] :
% 5.15/5.41 ! [X3: real] :
% 5.15/5.41 ( ( ord_less_real @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(2)
% 5.15/5.41 thf(fact_3325_minf_I2_J,axiom,
% 5.15/5.41 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.15/5.41 ( ? [Z4: rat] :
% 5.15/5.41 ! [X3: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: rat] :
% 5.15/5.41 ! [X3: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(2)
% 5.15/5.41 thf(fact_3326_minf_I2_J,axiom,
% 5.15/5.41 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.15/5.41 ( ? [Z4: num] :
% 5.15/5.41 ! [X3: num] :
% 5.15/5.41 ( ( ord_less_num @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: num] :
% 5.15/5.41 ! [X3: num] :
% 5.15/5.41 ( ( ord_less_num @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(2)
% 5.15/5.41 thf(fact_3327_minf_I2_J,axiom,
% 5.15/5.41 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.15/5.41 ( ? [Z4: nat] :
% 5.15/5.41 ! [X3: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: nat] :
% 5.15/5.41 ! [X3: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(2)
% 5.15/5.41 thf(fact_3328_minf_I2_J,axiom,
% 5.15/5.41 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.15/5.41 ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ X3 @ Z4 )
% 5.15/5.41 => ( ( Q @ X3 )
% 5.15/5.41 = ( Q6 @ X3 ) ) )
% 5.15/5.41 => ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.41 => ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P6 @ X5 )
% 5.15/5.41 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(2)
% 5.15/5.41 thf(fact_3329_minf_I3_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(3)
% 5.15/5.41 thf(fact_3330_minf_I3_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(3)
% 5.15/5.41 thf(fact_3331_minf_I3_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(3)
% 5.15/5.41 thf(fact_3332_minf_I3_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(3)
% 5.15/5.41 thf(fact_3333_minf_I3_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(3)
% 5.15/5.41 thf(fact_3334_minf_I4_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(4)
% 5.15/5.41 thf(fact_3335_minf_I4_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(4)
% 5.15/5.41 thf(fact_3336_minf_I4_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(4)
% 5.15/5.41 thf(fact_3337_minf_I4_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(4)
% 5.15/5.41 thf(fact_3338_minf_I4_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.41 => ( X5 != T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(4)
% 5.15/5.41 thf(fact_3339_minf_I5_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_real @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(5)
% 5.15/5.41 thf(fact_3340_minf_I5_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_rat @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(5)
% 5.15/5.41 thf(fact_3341_minf_I5_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_num @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(5)
% 5.15/5.41 thf(fact_3342_minf_I5_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_nat @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(5)
% 5.15/5.41 thf(fact_3343_minf_I5_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_int @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(5)
% 5.15/5.41 thf(fact_3344_minf_I7_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_real @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(7)
% 5.15/5.41 thf(fact_3345_minf_I7_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(7)
% 5.15/5.41 thf(fact_3346_minf_I7_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_num @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(7)
% 5.15/5.41 thf(fact_3347_minf_I7_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(7)
% 5.15/5.41 thf(fact_3348_minf_I7_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_int @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(7)
% 5.15/5.41 thf(fact_3349_pinf_I6_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(6)
% 5.15/5.41 thf(fact_3350_pinf_I6_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(6)
% 5.15/5.41 thf(fact_3351_pinf_I6_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(6)
% 5.15/5.41 thf(fact_3352_pinf_I6_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(6)
% 5.15/5.41 thf(fact_3353_pinf_I6_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.41 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(6)
% 5.15/5.41 thf(fact_3354_pinf_I8_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(8)
% 5.15/5.41 thf(fact_3355_pinf_I8_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(8)
% 5.15/5.41 thf(fact_3356_pinf_I8_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(8)
% 5.15/5.41 thf(fact_3357_pinf_I8_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(8)
% 5.15/5.41 thf(fact_3358_pinf_I8_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.41 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % pinf(8)
% 5.15/5.41 thf(fact_3359_minf_I6_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(6)
% 5.15/5.41 thf(fact_3360_minf_I6_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(6)
% 5.15/5.41 thf(fact_3361_minf_I6_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(6)
% 5.15/5.41 thf(fact_3362_minf_I6_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(6)
% 5.15/5.41 thf(fact_3363_minf_I6_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.41 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(6)
% 5.15/5.41 thf(fact_3364_minf_I8_J,axiom,
% 5.15/5.41 ! [T: real] :
% 5.15/5.41 ? [Z2: real] :
% 5.15/5.41 ! [X5: real] :
% 5.15/5.41 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(8)
% 5.15/5.41 thf(fact_3365_minf_I8_J,axiom,
% 5.15/5.41 ! [T: rat] :
% 5.15/5.41 ? [Z2: rat] :
% 5.15/5.41 ! [X5: rat] :
% 5.15/5.41 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(8)
% 5.15/5.41 thf(fact_3366_minf_I8_J,axiom,
% 5.15/5.41 ! [T: num] :
% 5.15/5.41 ? [Z2: num] :
% 5.15/5.41 ! [X5: num] :
% 5.15/5.41 ( ( ord_less_num @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(8)
% 5.15/5.41 thf(fact_3367_minf_I8_J,axiom,
% 5.15/5.41 ! [T: nat] :
% 5.15/5.41 ? [Z2: nat] :
% 5.15/5.41 ! [X5: nat] :
% 5.15/5.41 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(8)
% 5.15/5.41 thf(fact_3368_minf_I8_J,axiom,
% 5.15/5.41 ! [T: int] :
% 5.15/5.41 ? [Z2: int] :
% 5.15/5.41 ! [X5: int] :
% 5.15/5.41 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.41 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.15/5.41
% 5.15/5.41 % minf(8)
% 5.15/5.41 thf(fact_3369_inf__period_I2_J,axiom,
% 5.15/5.41 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.15/5.41 ( ! [X3: real,K3: real] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ( ! [X3: real,K3: real] :
% 5.15/5.41 ( ( Q @ X3 )
% 5.15/5.41 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ! [X5: real,K4: real] :
% 5.15/5.41 ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.15/5.41 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % inf_period(2)
% 5.15/5.41 thf(fact_3370_inf__period_I2_J,axiom,
% 5.15/5.41 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.15/5.41 ( ! [X3: rat,K3: rat] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ( ! [X3: rat,K3: rat] :
% 5.15/5.41 ( ( Q @ X3 )
% 5.15/5.41 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ! [X5: rat,K4: rat] :
% 5.15/5.41 ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.15/5.41 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % inf_period(2)
% 5.15/5.41 thf(fact_3371_inf__period_I2_J,axiom,
% 5.15/5.41 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.15/5.41 ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( Q @ X3 )
% 5.15/5.41 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ! [X5: int,K4: int] :
% 5.15/5.41 ( ( ( P @ X5 )
% 5.15/5.41 | ( Q @ X5 ) )
% 5.15/5.41 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.15/5.41 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % inf_period(2)
% 5.15/5.41 thf(fact_3372_inf__period_I1_J,axiom,
% 5.15/5.41 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.15/5.41 ( ! [X3: real,K3: real] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ( ! [X3: real,K3: real] :
% 5.15/5.41 ( ( Q @ X3 )
% 5.15/5.41 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ! [X5: real,K4: real] :
% 5.15/5.41 ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.15/5.41 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % inf_period(1)
% 5.15/5.41 thf(fact_3373_inf__period_I1_J,axiom,
% 5.15/5.41 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.15/5.41 ( ! [X3: rat,K3: rat] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ( ! [X3: rat,K3: rat] :
% 5.15/5.41 ( ( Q @ X3 )
% 5.15/5.41 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ! [X5: rat,K4: rat] :
% 5.15/5.41 ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.15/5.41 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % inf_period(1)
% 5.15/5.41 thf(fact_3374_inf__period_I1_J,axiom,
% 5.15/5.41 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.15/5.41 ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( Q @ X3 )
% 5.15/5.41 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.15/5.41 => ! [X5: int,K4: int] :
% 5.15/5.41 ( ( ( P @ X5 )
% 5.15/5.41 & ( Q @ X5 ) )
% 5.15/5.41 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.15/5.41 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % inf_period(1)
% 5.15/5.41 thf(fact_3375_times__int__code_I1_J,axiom,
% 5.15/5.41 ! [K: int] :
% 5.15/5.41 ( ( times_times_int @ K @ zero_zero_int )
% 5.15/5.41 = zero_zero_int ) ).
% 5.15/5.41
% 5.15/5.41 % times_int_code(1)
% 5.15/5.41 thf(fact_3376_times__int__code_I2_J,axiom,
% 5.15/5.41 ! [L: int] :
% 5.15/5.41 ( ( times_times_int @ zero_zero_int @ L )
% 5.15/5.41 = zero_zero_int ) ).
% 5.15/5.41
% 5.15/5.41 % times_int_code(2)
% 5.15/5.41 thf(fact_3377_int__distrib_I2_J,axiom,
% 5.15/5.41 ! [W: int,Z1: int,Z22: int] :
% 5.15/5.41 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.15/5.41 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % int_distrib(2)
% 5.15/5.41 thf(fact_3378_int__distrib_I1_J,axiom,
% 5.15/5.41 ! [Z1: int,Z22: int,W: int] :
% 5.15/5.41 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.15/5.41 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % int_distrib(1)
% 5.15/5.41 thf(fact_3379_int__distrib_I3_J,axiom,
% 5.15/5.41 ! [Z1: int,Z22: int,W: int] :
% 5.15/5.41 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.15/5.41 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % int_distrib(3)
% 5.15/5.41 thf(fact_3380_int__distrib_I4_J,axiom,
% 5.15/5.41 ! [W: int,Z1: int,Z22: int] :
% 5.15/5.41 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.15/5.41 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % int_distrib(4)
% 5.15/5.41 thf(fact_3381_zmult__zless__mono2,axiom,
% 5.15/5.41 ! [I: int,J: int,K: int] :
% 5.15/5.41 ( ( ord_less_int @ I @ J )
% 5.15/5.41 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.41 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % zmult_zless_mono2
% 5.15/5.41 thf(fact_3382_pos__zmult__eq__1__iff,axiom,
% 5.15/5.41 ! [M: int,N2: int] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ M )
% 5.15/5.41 => ( ( ( times_times_int @ M @ N2 )
% 5.15/5.41 = one_one_int )
% 5.15/5.41 = ( ( M = one_one_int )
% 5.15/5.41 & ( N2 = one_one_int ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % pos_zmult_eq_1_iff
% 5.15/5.41 thf(fact_3383_minusinfinity,axiom,
% 5.15/5.41 ! [D: int,P1: int > $o,P: int > $o] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ D )
% 5.15/5.41 => ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( P1 @ X3 )
% 5.15/5.41 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.15/5.41 => ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ X3 @ Z4 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P1 @ X3 ) ) )
% 5.15/5.41 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.15/5.41 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % minusinfinity
% 5.15/5.41 thf(fact_3384_plusinfinity,axiom,
% 5.15/5.41 ! [D: int,P6: int > $o,P: int > $o] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ D )
% 5.15/5.41 => ( ! [X3: int,K3: int] :
% 5.15/5.41 ( ( P6 @ X3 )
% 5.15/5.41 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.15/5.41 => ( ? [Z4: int] :
% 5.15/5.41 ! [X3: int] :
% 5.15/5.41 ( ( ord_less_int @ Z4 @ X3 )
% 5.15/5.41 => ( ( P @ X3 )
% 5.15/5.41 = ( P6 @ X3 ) ) )
% 5.15/5.41 => ( ? [X_12: int] : ( P6 @ X_12 )
% 5.15/5.41 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % plusinfinity
% 5.15/5.41 thf(fact_3385_incr__mult__lemma,axiom,
% 5.15/5.41 ! [D: int,P: int > $o,K: int] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ D )
% 5.15/5.41 => ( ! [X3: int] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 => ( P @ ( plus_plus_int @ X3 @ D ) ) )
% 5.15/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.41 => ! [X5: int] :
% 5.15/5.41 ( ( P @ X5 )
% 5.15/5.41 => ( P @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % incr_mult_lemma
% 5.15/5.41 thf(fact_3386_decr__mult__lemma,axiom,
% 5.15/5.41 ! [D: int,P: int > $o,K: int] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ D )
% 5.15/5.41 => ( ! [X3: int] :
% 5.15/5.41 ( ( P @ X3 )
% 5.15/5.41 => ( P @ ( minus_minus_int @ X3 @ D ) ) )
% 5.15/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.41 => ! [X5: int] :
% 5.15/5.41 ( ( P @ X5 )
% 5.15/5.41 => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % decr_mult_lemma
% 5.15/5.41 thf(fact_3387_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 5.15/5.41 ! [X: vEBT_VEBT,Y: nat] :
% 5.15/5.41 ( ( ( vEBT_T_m_a_x_t @ X )
% 5.15/5.41 = Y )
% 5.15/5.41 => ( ! [A5: $o,B6: $o] :
% 5.15/5.41 ( ( X
% 5.15/5.41 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.41 => ( Y
% 5.15/5.41 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B6 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.15/5.41 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.41 ( X
% 5.15/5.41 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.41 => ( Y != one_one_nat ) )
% 5.15/5.41 => ~ ( ? [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.41 ( X
% 5.15/5.41 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.41 => ( Y != one_one_nat ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.elims
% 5.15/5.41 thf(fact_3388_unset__bit__0,axiom,
% 5.15/5.41 ! [A: int] :
% 5.15/5.41 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.15/5.41 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % unset_bit_0
% 5.15/5.41 thf(fact_3389_unset__bit__0,axiom,
% 5.15/5.41 ! [A: nat] :
% 5.15/5.41 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.15/5.41 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % unset_bit_0
% 5.15/5.41 thf(fact_3390_unset__bit__Suc,axiom,
% 5.15/5.41 ! [N2: nat,A: code_integer] :
% 5.15/5.41 ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 5.15/5.41 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % unset_bit_Suc
% 5.15/5.41 thf(fact_3391_unset__bit__Suc,axiom,
% 5.15/5.41 ! [N2: nat,A: int] :
% 5.15/5.41 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 5.15/5.41 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % unset_bit_Suc
% 5.15/5.41 thf(fact_3392_unset__bit__Suc,axiom,
% 5.15/5.41 ! [N2: nat,A: nat] :
% 5.15/5.41 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 5.15/5.41 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % unset_bit_Suc
% 5.15/5.41 thf(fact_3393_flip__bit__Suc,axiom,
% 5.15/5.41 ! [N2: nat,A: code_integer] :
% 5.15/5.41 ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 5.15/5.41 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % flip_bit_Suc
% 5.15/5.41 thf(fact_3394_flip__bit__Suc,axiom,
% 5.15/5.41 ! [N2: nat,A: int] :
% 5.15/5.41 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 5.15/5.41 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % flip_bit_Suc
% 5.15/5.41 thf(fact_3395_flip__bit__Suc,axiom,
% 5.15/5.41 ! [N2: nat,A: nat] :
% 5.15/5.41 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 5.15/5.41 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % flip_bit_Suc
% 5.15/5.41 thf(fact_3396_Bolzano,axiom,
% 5.15/5.41 ! [A: real,B: real,P: real > real > $o] :
% 5.15/5.41 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.41 => ( ! [A5: real,B6: real,C2: real] :
% 5.15/5.41 ( ( P @ A5 @ B6 )
% 5.15/5.41 => ( ( P @ B6 @ C2 )
% 5.15/5.41 => ( ( ord_less_eq_real @ A5 @ B6 )
% 5.15/5.41 => ( ( ord_less_eq_real @ B6 @ C2 )
% 5.15/5.41 => ( P @ A5 @ C2 ) ) ) ) )
% 5.15/5.41 => ( ! [X3: real] :
% 5.15/5.41 ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.41 => ( ( ord_less_eq_real @ X3 @ B )
% 5.15/5.41 => ? [D5: real] :
% 5.15/5.41 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.15/5.41 & ! [A5: real,B6: real] :
% 5.15/5.41 ( ( ( ord_less_eq_real @ A5 @ X3 )
% 5.15/5.41 & ( ord_less_eq_real @ X3 @ B6 )
% 5.15/5.41 & ( ord_less_real @ ( minus_minus_real @ B6 @ A5 ) @ D5 ) )
% 5.15/5.41 => ( P @ A5 @ B6 ) ) ) ) )
% 5.15/5.41 => ( P @ A @ B ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % Bolzano
% 5.15/5.41 thf(fact_3397_divmod__algorithm__code_I8_J,axiom,
% 5.15/5.41 ! [M: num,N2: num] :
% 5.15/5.41 ( ( ( ord_less_num @ M @ N2 )
% 5.15/5.41 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.15/5.41 & ( ~ ( ord_less_num @ M @ N2 )
% 5.15/5.41 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(8)
% 5.15/5.41 thf(fact_3398_divmod__algorithm__code_I8_J,axiom,
% 5.15/5.41 ! [M: num,N2: num] :
% 5.15/5.41 ( ( ( ord_less_num @ M @ N2 )
% 5.15/5.41 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.15/5.41 & ( ~ ( ord_less_num @ M @ N2 )
% 5.15/5.41 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(8)
% 5.15/5.41 thf(fact_3399_divmod__algorithm__code_I8_J,axiom,
% 5.15/5.41 ! [M: num,N2: num] :
% 5.15/5.41 ( ( ( ord_less_num @ M @ N2 )
% 5.15/5.41 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.15/5.41 & ( ~ ( ord_less_num @ M @ N2 )
% 5.15/5.41 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(8)
% 5.15/5.41 thf(fact_3400_divmod__algorithm__code_I7_J,axiom,
% 5.15/5.41 ! [M: num,N2: num] :
% 5.15/5.41 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.15/5.41 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.15/5.41 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.15/5.41 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(7)
% 5.15/5.41 thf(fact_3401_divmod__algorithm__code_I7_J,axiom,
% 5.15/5.41 ! [M: num,N2: num] :
% 5.15/5.41 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.15/5.41 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.15/5.41 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.15/5.41 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(7)
% 5.15/5.41 thf(fact_3402_divmod__algorithm__code_I7_J,axiom,
% 5.15/5.41 ! [M: num,N2: num] :
% 5.15/5.41 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.15/5.41 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.15/5.41 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.15/5.41 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(7)
% 5.15/5.41 thf(fact_3403_unset__bit__nonnegative__int__iff,axiom,
% 5.15/5.41 ! [N2: nat,K: int] :
% 5.15/5.41 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) )
% 5.15/5.41 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.15/5.41
% 5.15/5.41 % unset_bit_nonnegative_int_iff
% 5.15/5.41 thf(fact_3404_flip__bit__nonnegative__int__iff,axiom,
% 5.15/5.41 ! [N2: nat,K: int] :
% 5.15/5.41 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) )
% 5.15/5.41 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.15/5.41
% 5.15/5.41 % flip_bit_nonnegative_int_iff
% 5.15/5.41 thf(fact_3405_unset__bit__negative__int__iff,axiom,
% 5.15/5.41 ! [N2: nat,K: int] :
% 5.15/5.41 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 5.15/5.41 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.15/5.41
% 5.15/5.41 % unset_bit_negative_int_iff
% 5.15/5.41 thf(fact_3406_flip__bit__negative__int__iff,axiom,
% 5.15/5.41 ! [N2: nat,K: int] :
% 5.15/5.41 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 5.15/5.41 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.15/5.41
% 5.15/5.41 % flip_bit_negative_int_iff
% 5.15/5.41 thf(fact_3407_divmod__algorithm__code_I2_J,axiom,
% 5.15/5.41 ! [M: num] :
% 5.15/5.41 ( ( unique5052692396658037445od_int @ M @ one )
% 5.15/5.41 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(2)
% 5.15/5.41 thf(fact_3408_divmod__algorithm__code_I2_J,axiom,
% 5.15/5.41 ! [M: num] :
% 5.15/5.41 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.15/5.41 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(2)
% 5.15/5.41 thf(fact_3409_divmod__algorithm__code_I2_J,axiom,
% 5.15/5.41 ! [M: num] :
% 5.15/5.41 ( ( unique3479559517661332726nteger @ M @ one )
% 5.15/5.41 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(2)
% 5.15/5.41 thf(fact_3410_divmod__algorithm__code_I3_J,axiom,
% 5.15/5.41 ! [N2: num] :
% 5.15/5.41 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 5.15/5.41 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(3)
% 5.15/5.41 thf(fact_3411_divmod__algorithm__code_I3_J,axiom,
% 5.15/5.41 ! [N2: num] :
% 5.15/5.41 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 5.15/5.41 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(3)
% 5.15/5.41 thf(fact_3412_divmod__algorithm__code_I3_J,axiom,
% 5.15/5.41 ! [N2: num] :
% 5.15/5.41 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 5.15/5.41 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(3)
% 5.15/5.41 thf(fact_3413_divmod__algorithm__code_I4_J,axiom,
% 5.15/5.41 ! [N2: num] :
% 5.15/5.41 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(4)
% 5.15/5.41 thf(fact_3414_divmod__algorithm__code_I4_J,axiom,
% 5.15/5.41 ! [N2: num] :
% 5.15/5.41 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(4)
% 5.15/5.41 thf(fact_3415_divmod__algorithm__code_I4_J,axiom,
% 5.15/5.41 ! [N2: num] :
% 5.15/5.41 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 5.15/5.41 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_algorithm_code(4)
% 5.15/5.41 thf(fact_3416_unset__bit__less__eq,axiom,
% 5.15/5.41 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ K ) ).
% 5.15/5.41
% 5.15/5.41 % unset_bit_less_eq
% 5.15/5.41 thf(fact_3417_divmod__int__def,axiom,
% 5.15/5.41 ( unique5052692396658037445od_int
% 5.15/5.41 = ( ^ [M5: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_int_def
% 5.15/5.41 thf(fact_3418_divmod__def,axiom,
% 5.15/5.41 ( unique5052692396658037445od_int
% 5.15/5.41 = ( ^ [M5: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_def
% 5.15/5.41 thf(fact_3419_divmod__def,axiom,
% 5.15/5.41 ( unique5055182867167087721od_nat
% 5.15/5.41 = ( ^ [M5: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_def
% 5.15/5.41 thf(fact_3420_divmod__def,axiom,
% 5.15/5.41 ( unique3479559517661332726nteger
% 5.15/5.41 = ( ^ [M5: num,N3: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N3 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N3 ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_def
% 5.15/5.41 thf(fact_3421_divmod_H__nat__def,axiom,
% 5.15/5.41 ( unique5055182867167087721od_nat
% 5.15/5.41 = ( ^ [M5: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod'_nat_def
% 5.15/5.41 thf(fact_3422_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 5.15/5.41 ! [A: $o,B: $o] :
% 5.15/5.41 ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.41 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(1)
% 5.15/5.41 thf(fact_3423_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 5.15/5.41 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.15/5.41 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.15/5.41 = one_one_nat ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(2)
% 5.15/5.41 thf(fact_3424_maxt__bound,axiom,
% 5.15/5.41 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % maxt_bound
% 5.15/5.41 thf(fact_3425_divmod__divmod__step,axiom,
% 5.15/5.41 ( unique5055182867167087721od_nat
% 5.15/5.41 = ( ^ [M5: num,N3: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M5 @ N3 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M5 ) ) @ ( unique5026877609467782581ep_nat @ N3 @ ( unique5055182867167087721od_nat @ M5 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_divmod_step
% 5.15/5.41 thf(fact_3426_divmod__divmod__step,axiom,
% 5.15/5.41 ( unique5052692396658037445od_int
% 5.15/5.41 = ( ^ [M5: num,N3: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M5 @ N3 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M5 ) ) @ ( unique5024387138958732305ep_int @ N3 @ ( unique5052692396658037445od_int @ M5 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_divmod_step
% 5.15/5.41 thf(fact_3427_divmod__divmod__step,axiom,
% 5.15/5.41 ( unique3479559517661332726nteger
% 5.15/5.41 = ( ^ [M5: num,N3: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M5 @ N3 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M5 ) ) @ ( unique4921790084139445826nteger @ N3 @ ( unique3479559517661332726nteger @ M5 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % divmod_divmod_step
% 5.15/5.41 thf(fact_3428_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 5.15/5.41 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.15/5.41 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.15/5.41 = one_one_nat ) ).
% 5.15/5.41
% 5.15/5.41 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(3)
% 5.15/5.41 thf(fact_3429_mult__le__cancel__iff2,axiom,
% 5.15/5.41 ! [Z: real,X: real,Y: real] :
% 5.15/5.41 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.15/5.41 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 5.15/5.41 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % mult_le_cancel_iff2
% 5.15/5.41 thf(fact_3430_mult__le__cancel__iff2,axiom,
% 5.15/5.41 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.41 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.15/5.41 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 5.15/5.41 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % mult_le_cancel_iff2
% 5.15/5.41 thf(fact_3431_mult__le__cancel__iff2,axiom,
% 5.15/5.41 ! [Z: int,X: int,Y: int] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.15/5.41 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 5.15/5.41 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % mult_le_cancel_iff2
% 5.15/5.41 thf(fact_3432_mult__le__cancel__iff1,axiom,
% 5.15/5.41 ! [Z: real,X: real,Y: real] :
% 5.15/5.41 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.15/5.41 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.15/5.41 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % mult_le_cancel_iff1
% 5.15/5.41 thf(fact_3433_mult__le__cancel__iff1,axiom,
% 5.15/5.41 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.41 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.15/5.41 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.15/5.41 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % mult_le_cancel_iff1
% 5.15/5.41 thf(fact_3434_mult__le__cancel__iff1,axiom,
% 5.15/5.41 ! [Z: int,X: int,Y: int] :
% 5.15/5.41 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.15/5.41 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.15/5.41 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % mult_le_cancel_iff1
% 5.15/5.41 thf(fact_3435_divides__aux__eq,axiom,
% 5.15/5.41 ! [Q3: nat,R2: nat] :
% 5.15/5.41 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.15/5.41 = ( R2 = zero_zero_nat ) ) ).
% 5.15/5.41
% 5.15/5.41 % divides_aux_eq
% 5.15/5.41 thf(fact_3436_divides__aux__eq,axiom,
% 5.15/5.41 ! [Q3: int,R2: int] :
% 5.15/5.41 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.41 = ( R2 = zero_zero_int ) ) ).
% 5.15/5.41
% 5.15/5.41 % divides_aux_eq
% 5.15/5.41 thf(fact_3437_neg__eucl__rel__int__mult__2,axiom,
% 5.15/5.41 ! [B: int,A: int,Q3: int,R2: int] :
% 5.15/5.41 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.15/5.41 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.41 => ( 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 @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % neg_eucl_rel_int_mult_2
% 5.15/5.41 thf(fact_3438_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_num,Ys: list_num] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3439_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_nat,Ys: list_num] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( product_Pair_nat_num @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3440_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_nat,Ys: list_nat] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr7617993195940197384at_nat @ ( product_nat_nat @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( product_Pair_nat_nat @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3441_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3442_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_nat,Ys: list_o] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( product_Pair_nat_o @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3443_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_Code_integer,Ys: list_o] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3444_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_nat,Ys: list_int] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr3440142176431000676at_int @ ( product_nat_int @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( product_Pair_nat_int @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3445_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3446_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3447_product__nth,axiom,
% 5.15/5.41 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.15/5.41 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.15/5.41 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N2 )
% 5.15/5.41 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % product_nth
% 5.15/5.41 thf(fact_3448_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_real,X: real > complex,Y: real > complex] :
% 5.15/5.41 ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_complex ) ) ) )
% 5.15/5.41 => ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_complex ) ) ) )
% 5.15/5.41 => ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_complex @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_complex ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3449_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 5.15/5.41 ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_complex ) ) ) )
% 5.15/5.41 => ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_complex ) ) ) )
% 5.15/5.41 => ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_complex @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_complex ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3450_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 5.15/5.41 ( ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_complex ) ) ) )
% 5.15/5.41 => ( ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_complex ) ) ) )
% 5.15/5.41 => ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_complex @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_complex ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3451_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 5.15/5.41 ( ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_complex ) ) ) )
% 5.15/5.41 => ( ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_complex ) ) ) )
% 5.15/5.41 => ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_complex @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_complex ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3452_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_real,X: real > real,Y: real > real] :
% 5.15/5.41 ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_real ) ) ) )
% 5.15/5.41 => ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_real ) ) ) )
% 5.15/5.41 => ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_real ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3453_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 5.15/5.41 ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_real ) ) ) )
% 5.15/5.41 => ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_real ) ) ) )
% 5.15/5.41 => ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_real ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3454_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_complex,X: complex > real,Y: complex > real] :
% 5.15/5.41 ( ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_real ) ) ) )
% 5.15/5.41 => ( ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_real ) ) ) )
% 5.15/5.41 => ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_real ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3455_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_int,X: int > real,Y: int > real] :
% 5.15/5.41 ( ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_real ) ) ) )
% 5.15/5.41 => ( ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_real ) ) ) )
% 5.15/5.41 => ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_real ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3456_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_real,X: real > rat,Y: real > rat] :
% 5.15/5.41 ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_rat ) ) ) )
% 5.15/5.41 => ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_rat ) ) ) )
% 5.15/5.41 => ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_rat ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3457_prod_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 5.15/5.41 ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != one_one_rat ) ) ) )
% 5.15/5.41 => ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != one_one_rat ) ) ) )
% 5.15/5.41 => ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != one_one_rat ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % prod.finite_Collect_op
% 5.15/5.41 thf(fact_3458_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_real,X: real > complex,Y: real > complex] :
% 5.15/5.41 ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_complex ) ) ) )
% 5.15/5.41 => ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_complex ) ) ) )
% 5.15/5.41 => ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_complex ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3459_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 5.15/5.41 ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_complex ) ) ) )
% 5.15/5.41 => ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_complex ) ) ) )
% 5.15/5.41 => ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_complex ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3460_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 5.15/5.41 ( ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_complex ) ) ) )
% 5.15/5.41 => ( ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_complex ) ) ) )
% 5.15/5.41 => ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_complex ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3461_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 5.15/5.41 ( ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_complex ) ) ) )
% 5.15/5.41 => ( ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_complex ) ) ) )
% 5.15/5.41 => ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_complex @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_complex ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3462_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_real,X: real > real,Y: real > real] :
% 5.15/5.41 ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_real ) ) ) )
% 5.15/5.41 => ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_real ) ) ) )
% 5.15/5.41 => ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3463_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 5.15/5.41 ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_real ) ) ) )
% 5.15/5.41 => ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_real ) ) ) )
% 5.15/5.41 => ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3464_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_complex,X: complex > real,Y: complex > real] :
% 5.15/5.41 ( ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_real ) ) ) )
% 5.15/5.41 => ( ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_real ) ) ) )
% 5.15/5.41 => ( finite3207457112153483333omplex
% 5.15/5.41 @ ( collect_complex
% 5.15/5.41 @ ^ [I3: complex] :
% 5.15/5.41 ( ( member_complex @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3465_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_int,X: int > real,Y: int > real] :
% 5.15/5.41 ( ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_real ) ) ) )
% 5.15/5.41 => ( ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_real ) ) ) )
% 5.15/5.41 => ( finite_finite_int
% 5.15/5.41 @ ( collect_int
% 5.15/5.41 @ ^ [I3: int] :
% 5.15/5.41 ( ( member_int @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3466_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_real,X: real > rat,Y: real > rat] :
% 5.15/5.41 ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_rat ) ) ) )
% 5.15/5.41 => ( ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_rat ) ) ) )
% 5.15/5.41 => ( finite_finite_real
% 5.15/5.41 @ ( collect_real
% 5.15/5.41 @ ^ [I3: real] :
% 5.15/5.41 ( ( member_real @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3467_sum_Ofinite__Collect__op,axiom,
% 5.15/5.41 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 5.15/5.41 ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( X @ I3 )
% 5.15/5.41 != zero_zero_rat ) ) ) )
% 5.15/5.41 => ( ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( Y @ I3 )
% 5.15/5.41 != zero_zero_rat ) ) ) )
% 5.15/5.41 => ( finite_finite_nat
% 5.15/5.41 @ ( collect_nat
% 5.15/5.41 @ ^ [I3: nat] :
% 5.15/5.41 ( ( member_nat @ I3 @ I5 )
% 5.15/5.41 & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 5.15/5.41 != zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % sum.finite_Collect_op
% 5.15/5.41 thf(fact_3468_dbl__inc__simps_I3_J,axiom,
% 5.15/5.41 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.15/5.41 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(3)
% 5.15/5.41 thf(fact_3469_dbl__inc__simps_I3_J,axiom,
% 5.15/5.41 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.15/5.41 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(3)
% 5.15/5.41 thf(fact_3470_dbl__inc__simps_I3_J,axiom,
% 5.15/5.41 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.15/5.41 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(3)
% 5.15/5.41 thf(fact_3471_dbl__inc__simps_I3_J,axiom,
% 5.15/5.41 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.15/5.41 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(3)
% 5.15/5.41 thf(fact_3472_dbl__inc__simps_I2_J,axiom,
% 5.15/5.41 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.15/5.41 = one_one_complex ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(2)
% 5.15/5.41 thf(fact_3473_dbl__inc__simps_I2_J,axiom,
% 5.15/5.41 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.15/5.41 = one_one_real ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(2)
% 5.15/5.41 thf(fact_3474_dbl__inc__simps_I2_J,axiom,
% 5.15/5.41 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.15/5.41 = one_one_rat ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(2)
% 5.15/5.41 thf(fact_3475_dbl__inc__simps_I2_J,axiom,
% 5.15/5.41 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.15/5.41 = one_one_int ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(2)
% 5.15/5.41 thf(fact_3476_dbl__inc__simps_I5_J,axiom,
% 5.15/5.41 ! [K: num] :
% 5.15/5.41 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.15/5.41 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(5)
% 5.15/5.41 thf(fact_3477_dbl__inc__simps_I5_J,axiom,
% 5.15/5.41 ! [K: num] :
% 5.15/5.41 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.15/5.41 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(5)
% 5.15/5.41 thf(fact_3478_dbl__inc__simps_I5_J,axiom,
% 5.15/5.41 ! [K: num] :
% 5.15/5.41 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.15/5.41 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(5)
% 5.15/5.41 thf(fact_3479_dbl__inc__simps_I5_J,axiom,
% 5.15/5.41 ! [K: num] :
% 5.15/5.41 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.15/5.41 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % dbl_inc_simps(5)
% 5.15/5.41 thf(fact_3480_length__product,axiom,
% 5.15/5.41 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.15/5.41 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.15/5.41 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % length_product
% 5.15/5.41 thf(fact_3481_length__product,axiom,
% 5.15/5.41 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.15/5.41 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.15/5.41 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % length_product
% 5.15/5.41 thf(fact_3482_length__product,axiom,
% 5.15/5.41 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.15/5.41 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 5.15/5.41 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % length_product
% 5.15/5.41 thf(fact_3483_length__product,axiom,
% 5.15/5.41 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.15/5.41 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.15/5.41 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % length_product
% 5.15/5.41 thf(fact_3484_length__product,axiom,
% 5.15/5.41 ! [Xs2: list_o,Ys: list_o] :
% 5.15/5.41 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.15/5.41 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.15/5.41
% 5.15/5.41 % length_product
% 5.15/5.42 thf(fact_3485_length__product,axiom,
% 5.15/5.42 ! [Xs2: list_o,Ys: list_int] :
% 5.15/5.42 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 5.15/5.42 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % length_product
% 5.15/5.42 thf(fact_3486_length__product,axiom,
% 5.15/5.42 ! [Xs2: list_int,Ys: list_VEBT_VEBT] :
% 5.15/5.42 ( ( size_s6639371672096860321T_VEBT @ ( produc662631939642741121T_VEBT @ Xs2 @ Ys ) )
% 5.15/5.42 = ( times_times_nat @ ( size_size_list_int @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % length_product
% 5.15/5.42 thf(fact_3487_length__product,axiom,
% 5.15/5.42 ! [Xs2: list_int,Ys: list_o] :
% 5.15/5.42 ( ( size_s4246224855604898693_int_o @ ( product_int_o @ Xs2 @ Ys ) )
% 5.15/5.42 = ( times_times_nat @ ( size_size_list_int @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % length_product
% 5.15/5.42 thf(fact_3488_length__product,axiom,
% 5.15/5.42 ! [Xs2: list_int,Ys: list_int] :
% 5.15/5.42 ( ( size_s5157815400016825771nt_int @ ( product_int_int @ Xs2 @ Ys ) )
% 5.15/5.42 = ( times_times_nat @ ( size_size_list_int @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % length_product
% 5.15/5.42 thf(fact_3489_unique__quotient,axiom,
% 5.15/5.42 ! [A: int,B: int,Q3: int,R2: int,Q5: int,R4: int] :
% 5.15/5.42 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.42 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.15/5.42 => ( Q3 = Q5 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unique_quotient
% 5.15/5.42 thf(fact_3490_unique__remainder,axiom,
% 5.15/5.42 ! [A: int,B: int,Q3: int,R2: int,Q5: int,R4: int] :
% 5.15/5.42 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.42 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.15/5.42 => ( R2 = R4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unique_remainder
% 5.15/5.42 thf(fact_3491_eucl__rel__int__by0,axiom,
% 5.15/5.42 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.15/5.42
% 5.15/5.42 % eucl_rel_int_by0
% 5.15/5.42 thf(fact_3492_div__int__unique,axiom,
% 5.15/5.42 ! [K: int,L: int,Q3: int,R2: int] :
% 5.15/5.42 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.42 => ( ( divide_divide_int @ K @ L )
% 5.15/5.42 = Q3 ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_int_unique
% 5.15/5.42 thf(fact_3493_mod__int__unique,axiom,
% 5.15/5.42 ! [K: int,L: int,Q3: int,R2: int] :
% 5.15/5.42 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.42 => ( ( modulo_modulo_int @ K @ L )
% 5.15/5.42 = R2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % mod_int_unique
% 5.15/5.42 thf(fact_3494_eucl__rel__int__dividesI,axiom,
% 5.15/5.42 ! [L: int,K: int,Q3: int] :
% 5.15/5.42 ( ( L != zero_zero_int )
% 5.15/5.42 => ( ( K
% 5.15/5.42 = ( times_times_int @ Q3 @ L ) )
% 5.15/5.42 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % eucl_rel_int_dividesI
% 5.15/5.42 thf(fact_3495_eucl__rel__int,axiom,
% 5.15/5.42 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % eucl_rel_int
% 5.15/5.42 thf(fact_3496_dbl__inc__def,axiom,
% 5.15/5.42 ( neg_nu8295874005876285629c_real
% 5.15/5.42 = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_inc_def
% 5.15/5.42 thf(fact_3497_dbl__inc__def,axiom,
% 5.15/5.42 ( neg_nu5219082963157363817nc_rat
% 5.15/5.42 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_inc_def
% 5.15/5.42 thf(fact_3498_dbl__inc__def,axiom,
% 5.15/5.42 ( neg_nu5851722552734809277nc_int
% 5.15/5.42 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_inc_def
% 5.15/5.42 thf(fact_3499_dbl__inc__def,axiom,
% 5.15/5.42 ( neg_nu8557863876264182079omplex
% 5.15/5.42 = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_inc_def
% 5.15/5.42 thf(fact_3500_eucl__rel__int__iff,axiom,
% 5.15/5.42 ! [K: int,L: int,Q3: int,R2: int] :
% 5.15/5.42 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.42 = ( ( K
% 5.15/5.42 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 5.15/5.42 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.15/5.42 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.15/5.42 & ( ord_less_int @ R2 @ L ) ) )
% 5.15/5.42 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.15/5.42 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.15/5.42 => ( ( ord_less_int @ L @ R2 )
% 5.15/5.42 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.15/5.42 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.15/5.42 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % eucl_rel_int_iff
% 5.15/5.42 thf(fact_3501_mult__less__iff1,axiom,
% 5.15/5.42 ! [Z: real,X: real,Y: real] :
% 5.15/5.42 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.15/5.42 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.15/5.42 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % mult_less_iff1
% 5.15/5.42 thf(fact_3502_mult__less__iff1,axiom,
% 5.15/5.42 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.42 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.15/5.42 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.15/5.42 = ( ord_less_rat @ X @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % mult_less_iff1
% 5.15/5.42 thf(fact_3503_mult__less__iff1,axiom,
% 5.15/5.42 ! [Z: int,X: int,Y: int] :
% 5.15/5.42 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.15/5.42 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.15/5.42 = ( ord_less_int @ X @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % mult_less_iff1
% 5.15/5.42 thf(fact_3504_pos__eucl__rel__int__mult__2,axiom,
% 5.15/5.42 ! [B: int,A: int,Q3: int,R2: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.42 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.42 => ( 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 @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % pos_eucl_rel_int_mult_2
% 5.15/5.42 thf(fact_3505_prod_Oinject,axiom,
% 5.15/5.42 ! [X1: code_integer,X22: $o,Y1: code_integer,Y22: $o] :
% 5.15/5.42 ( ( ( produc6677183202524767010eger_o @ X1 @ X22 )
% 5.15/5.42 = ( produc6677183202524767010eger_o @ Y1 @ Y22 ) )
% 5.15/5.42 = ( ( X1 = Y1 )
% 5.15/5.42 & ( X22 = Y22 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod.inject
% 5.15/5.42 thf(fact_3506_prod_Oinject,axiom,
% 5.15/5.42 ! [X1: num,X22: num,Y1: num,Y22: num] :
% 5.15/5.42 ( ( ( product_Pair_num_num @ X1 @ X22 )
% 5.15/5.42 = ( product_Pair_num_num @ Y1 @ Y22 ) )
% 5.15/5.42 = ( ( X1 = Y1 )
% 5.15/5.42 & ( X22 = Y22 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod.inject
% 5.15/5.42 thf(fact_3507_prod_Oinject,axiom,
% 5.15/5.42 ! [X1: nat,X22: num,Y1: nat,Y22: num] :
% 5.15/5.42 ( ( ( product_Pair_nat_num @ X1 @ X22 )
% 5.15/5.42 = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 5.15/5.42 = ( ( X1 = Y1 )
% 5.15/5.42 & ( X22 = Y22 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod.inject
% 5.15/5.42 thf(fact_3508_prod_Oinject,axiom,
% 5.15/5.42 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 5.15/5.42 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 5.15/5.42 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 5.15/5.42 = ( ( X1 = Y1 )
% 5.15/5.42 & ( X22 = Y22 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod.inject
% 5.15/5.42 thf(fact_3509_prod_Oinject,axiom,
% 5.15/5.42 ! [X1: int,X22: int,Y1: int,Y22: int] :
% 5.15/5.42 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 5.15/5.42 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 5.15/5.42 = ( ( X1 = Y1 )
% 5.15/5.42 & ( X22 = Y22 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod.inject
% 5.15/5.42 thf(fact_3510_old_Oprod_Oinject,axiom,
% 5.15/5.42 ! [A: code_integer,B: $o,A4: code_integer,B4: $o] :
% 5.15/5.42 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.15/5.42 = ( produc6677183202524767010eger_o @ A4 @ B4 ) )
% 5.15/5.42 = ( ( A = A4 )
% 5.15/5.42 & ( B = B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.inject
% 5.15/5.42 thf(fact_3511_old_Oprod_Oinject,axiom,
% 5.15/5.42 ! [A: num,B: num,A4: num,B4: num] :
% 5.15/5.42 ( ( ( product_Pair_num_num @ A @ B )
% 5.15/5.42 = ( product_Pair_num_num @ A4 @ B4 ) )
% 5.15/5.42 = ( ( A = A4 )
% 5.15/5.42 & ( B = B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.inject
% 5.15/5.42 thf(fact_3512_old_Oprod_Oinject,axiom,
% 5.15/5.42 ! [A: nat,B: num,A4: nat,B4: num] :
% 5.15/5.42 ( ( ( product_Pair_nat_num @ A @ B )
% 5.15/5.42 = ( product_Pair_nat_num @ A4 @ B4 ) )
% 5.15/5.42 = ( ( A = A4 )
% 5.15/5.42 & ( B = B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.inject
% 5.15/5.42 thf(fact_3513_old_Oprod_Oinject,axiom,
% 5.15/5.42 ! [A: nat,B: nat,A4: nat,B4: nat] :
% 5.15/5.42 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.15/5.42 = ( product_Pair_nat_nat @ A4 @ B4 ) )
% 5.15/5.42 = ( ( A = A4 )
% 5.15/5.42 & ( B = B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.inject
% 5.15/5.42 thf(fact_3514_old_Oprod_Oinject,axiom,
% 5.15/5.42 ! [A: int,B: int,A4: int,B4: int] :
% 5.15/5.42 ( ( ( product_Pair_int_int @ A @ B )
% 5.15/5.42 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.15/5.42 = ( ( A = A4 )
% 5.15/5.42 & ( B = B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.inject
% 5.15/5.42 thf(fact_3515_old_Oprod_Oexhaust,axiom,
% 5.15/5.42 ! [Y: produc6271795597528267376eger_o] :
% 5.15/5.42 ~ ! [A5: code_integer,B6: $o] :
% 5.15/5.42 ( Y
% 5.15/5.42 != ( produc6677183202524767010eger_o @ A5 @ B6 ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.exhaust
% 5.15/5.42 thf(fact_3516_old_Oprod_Oexhaust,axiom,
% 5.15/5.42 ! [Y: product_prod_num_num] :
% 5.15/5.42 ~ ! [A5: num,B6: num] :
% 5.15/5.42 ( Y
% 5.15/5.42 != ( product_Pair_num_num @ A5 @ B6 ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.exhaust
% 5.15/5.42 thf(fact_3517_old_Oprod_Oexhaust,axiom,
% 5.15/5.42 ! [Y: product_prod_nat_num] :
% 5.15/5.42 ~ ! [A5: nat,B6: num] :
% 5.15/5.42 ( Y
% 5.15/5.42 != ( product_Pair_nat_num @ A5 @ B6 ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.exhaust
% 5.15/5.42 thf(fact_3518_old_Oprod_Oexhaust,axiom,
% 5.15/5.42 ! [Y: product_prod_nat_nat] :
% 5.15/5.42 ~ ! [A5: nat,B6: nat] :
% 5.15/5.42 ( Y
% 5.15/5.42 != ( product_Pair_nat_nat @ A5 @ B6 ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.exhaust
% 5.15/5.42 thf(fact_3519_old_Oprod_Oexhaust,axiom,
% 5.15/5.42 ! [Y: product_prod_int_int] :
% 5.15/5.42 ~ ! [A5: int,B6: int] :
% 5.15/5.42 ( Y
% 5.15/5.42 != ( product_Pair_int_int @ A5 @ B6 ) ) ).
% 5.15/5.42
% 5.15/5.42 % old.prod.exhaust
% 5.15/5.42 thf(fact_3520_surj__pair,axiom,
% 5.15/5.42 ! [P2: produc6271795597528267376eger_o] :
% 5.15/5.42 ? [X3: code_integer,Y3: $o] :
% 5.15/5.42 ( P2
% 5.15/5.42 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) ) ).
% 5.15/5.42
% 5.15/5.42 % surj_pair
% 5.15/5.42 thf(fact_3521_surj__pair,axiom,
% 5.15/5.42 ! [P2: product_prod_num_num] :
% 5.15/5.42 ? [X3: num,Y3: num] :
% 5.15/5.42 ( P2
% 5.15/5.42 = ( product_Pair_num_num @ X3 @ Y3 ) ) ).
% 5.15/5.42
% 5.15/5.42 % surj_pair
% 5.15/5.42 thf(fact_3522_surj__pair,axiom,
% 5.15/5.42 ! [P2: product_prod_nat_num] :
% 5.15/5.42 ? [X3: nat,Y3: num] :
% 5.15/5.42 ( P2
% 5.15/5.42 = ( product_Pair_nat_num @ X3 @ Y3 ) ) ).
% 5.15/5.42
% 5.15/5.42 % surj_pair
% 5.15/5.42 thf(fact_3523_surj__pair,axiom,
% 5.15/5.42 ! [P2: product_prod_nat_nat] :
% 5.15/5.42 ? [X3: nat,Y3: nat] :
% 5.15/5.42 ( P2
% 5.15/5.42 = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 5.15/5.42
% 5.15/5.42 % surj_pair
% 5.15/5.42 thf(fact_3524_surj__pair,axiom,
% 5.15/5.42 ! [P2: product_prod_int_int] :
% 5.15/5.42 ? [X3: int,Y3: int] :
% 5.15/5.42 ( P2
% 5.15/5.42 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 5.15/5.42
% 5.15/5.42 % surj_pair
% 5.15/5.42 thf(fact_3525_prod__cases,axiom,
% 5.15/5.42 ! [P: produc6271795597528267376eger_o > $o,P2: produc6271795597528267376eger_o] :
% 5.15/5.42 ( ! [A5: code_integer,B6: $o] : ( P @ ( produc6677183202524767010eger_o @ A5 @ B6 ) )
% 5.15/5.42 => ( P @ P2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod_cases
% 5.15/5.42 thf(fact_3526_prod__cases,axiom,
% 5.15/5.42 ! [P: product_prod_num_num > $o,P2: product_prod_num_num] :
% 5.15/5.42 ( ! [A5: num,B6: num] : ( P @ ( product_Pair_num_num @ A5 @ B6 ) )
% 5.15/5.42 => ( P @ P2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod_cases
% 5.15/5.42 thf(fact_3527_prod__cases,axiom,
% 5.15/5.42 ! [P: product_prod_nat_num > $o,P2: product_prod_nat_num] :
% 5.15/5.42 ( ! [A5: nat,B6: num] : ( P @ ( product_Pair_nat_num @ A5 @ B6 ) )
% 5.15/5.42 => ( P @ P2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod_cases
% 5.15/5.42 thf(fact_3528_prod__cases,axiom,
% 5.15/5.42 ! [P: product_prod_nat_nat > $o,P2: product_prod_nat_nat] :
% 5.15/5.42 ( ! [A5: nat,B6: nat] : ( P @ ( product_Pair_nat_nat @ A5 @ B6 ) )
% 5.15/5.42 => ( P @ P2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod_cases
% 5.15/5.42 thf(fact_3529_prod__cases,axiom,
% 5.15/5.42 ! [P: product_prod_int_int > $o,P2: product_prod_int_int] :
% 5.15/5.42 ( ! [A5: int,B6: int] : ( P @ ( product_Pair_int_int @ A5 @ B6 ) )
% 5.15/5.42 => ( P @ P2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod_cases
% 5.15/5.42 thf(fact_3530_Pair__inject,axiom,
% 5.15/5.42 ! [A: code_integer,B: $o,A4: code_integer,B4: $o] :
% 5.15/5.42 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.15/5.42 = ( produc6677183202524767010eger_o @ A4 @ B4 ) )
% 5.15/5.42 => ~ ( ( A = A4 )
% 5.15/5.42 => ( B = ~ B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % Pair_inject
% 5.15/5.42 thf(fact_3531_Pair__inject,axiom,
% 5.15/5.42 ! [A: num,B: num,A4: num,B4: num] :
% 5.15/5.42 ( ( ( product_Pair_num_num @ A @ B )
% 5.15/5.42 = ( product_Pair_num_num @ A4 @ B4 ) )
% 5.15/5.42 => ~ ( ( A = A4 )
% 5.15/5.42 => ( B != B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % Pair_inject
% 5.15/5.42 thf(fact_3532_Pair__inject,axiom,
% 5.15/5.42 ! [A: nat,B: num,A4: nat,B4: num] :
% 5.15/5.42 ( ( ( product_Pair_nat_num @ A @ B )
% 5.15/5.42 = ( product_Pair_nat_num @ A4 @ B4 ) )
% 5.15/5.42 => ~ ( ( A = A4 )
% 5.15/5.42 => ( B != B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % Pair_inject
% 5.15/5.42 thf(fact_3533_Pair__inject,axiom,
% 5.15/5.42 ! [A: nat,B: nat,A4: nat,B4: nat] :
% 5.15/5.42 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.15/5.42 = ( product_Pair_nat_nat @ A4 @ B4 ) )
% 5.15/5.42 => ~ ( ( A = A4 )
% 5.15/5.42 => ( B != B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % Pair_inject
% 5.15/5.42 thf(fact_3534_Pair__inject,axiom,
% 5.15/5.42 ! [A: int,B: int,A4: int,B4: int] :
% 5.15/5.42 ( ( ( product_Pair_int_int @ A @ B )
% 5.15/5.42 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.15/5.42 => ~ ( ( A = A4 )
% 5.15/5.42 => ( B != B4 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % Pair_inject
% 5.15/5.42 thf(fact_3535_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 5.15/5.42 ! [A: $o,B: $o] :
% 5.15/5.42 ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 5.15/5.42 = zero_zero_nat ) ).
% 5.15/5.42
% 5.15/5.42 % VEBT_internal.height.simps(1)
% 5.15/5.42 thf(fact_3536_divmod__BitM__2__eq,axiom,
% 5.15/5.42 ! [M: num] :
% 5.15/5.42 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.15/5.42 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.15/5.42
% 5.15/5.42 % divmod_BitM_2_eq
% 5.15/5.42 thf(fact_3537_insert__simp__excp,axiom,
% 5.15/5.42 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.15/5.42 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.42 => ( ( ord_less_nat @ X @ Mi )
% 5.15/5.42 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.42 => ( ( X != Ma )
% 5.15/5.42 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % insert_simp_excp
% 5.15/5.42 thf(fact_3538_insert__simp__norm,axiom,
% 5.15/5.42 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.15/5.42 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.42 => ( ( ord_less_nat @ Mi @ X )
% 5.15/5.42 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.15/5.42 => ( ( X != Ma )
% 5.15/5.42 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.15/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % insert_simp_norm
% 5.15/5.42 thf(fact_3539_gcd__nat__induct,axiom,
% 5.15/5.42 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.15/5.42 ( ! [M3: nat] : ( P @ M3 @ zero_zero_nat )
% 5.15/5.42 => ( ! [M3: nat,N: nat] :
% 5.15/5.42 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.15/5.42 => ( ( P @ N @ ( modulo_modulo_nat @ M3 @ N ) )
% 5.15/5.42 => ( P @ M3 @ N ) ) )
% 5.15/5.42 => ( P @ M @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % gcd_nat_induct
% 5.15/5.42 thf(fact_3540_concat__bit__Suc,axiom,
% 5.15/5.42 ! [N2: nat,K: int,L: int] :
% 5.15/5.42 ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L )
% 5.15/5.42 = ( 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 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % concat_bit_Suc
% 5.15/5.42 thf(fact_3541_dbl__simps_I3_J,axiom,
% 5.15/5.42 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.15/5.42 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(3)
% 5.15/5.42 thf(fact_3542_dbl__simps_I3_J,axiom,
% 5.15/5.42 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.15/5.42 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(3)
% 5.15/5.42 thf(fact_3543_dbl__simps_I3_J,axiom,
% 5.15/5.42 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.15/5.42 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(3)
% 5.15/5.42 thf(fact_3544_dbl__simps_I3_J,axiom,
% 5.15/5.42 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.15/5.42 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(3)
% 5.15/5.42 thf(fact_3545_list__update__overwrite,axiom,
% 5.15/5.42 ! [Xs2: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.15/5.42 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ I @ Y )
% 5.15/5.42 = ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ Y ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_overwrite
% 5.15/5.42 thf(fact_3546_length__list__update,axiom,
% 5.15/5.42 ! [Xs2: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 5.15/5.42 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) )
% 5.15/5.42 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % length_list_update
% 5.15/5.42 thf(fact_3547_length__list__update,axiom,
% 5.15/5.42 ! [Xs2: list_o,I: nat,X: $o] :
% 5.15/5.42 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I @ X ) )
% 5.15/5.42 = ( size_size_list_o @ Xs2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % length_list_update
% 5.15/5.42 thf(fact_3548_length__list__update,axiom,
% 5.15/5.42 ! [Xs2: list_int,I: nat,X: int] :
% 5.15/5.42 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I @ X ) )
% 5.15/5.42 = ( size_size_list_int @ Xs2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % length_list_update
% 5.15/5.42 thf(fact_3549_max__Suc__Suc,axiom,
% 5.15/5.42 ! [M: nat,N2: nat] :
% 5.15/5.42 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.15/5.42 = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_Suc_Suc
% 5.15/5.42 thf(fact_3550_max__0R,axiom,
% 5.15/5.42 ! [N2: nat] :
% 5.15/5.42 ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 5.15/5.42 = N2 ) ).
% 5.15/5.42
% 5.15/5.42 % max_0R
% 5.15/5.42 thf(fact_3551_max__0L,axiom,
% 5.15/5.42 ! [N2: nat] :
% 5.15/5.42 ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 = N2 ) ).
% 5.15/5.42
% 5.15/5.42 % max_0L
% 5.15/5.42 thf(fact_3552_max__nat_Oright__neutral,axiom,
% 5.15/5.42 ! [A: nat] :
% 5.15/5.42 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.15/5.42 = A ) ).
% 5.15/5.42
% 5.15/5.42 % max_nat.right_neutral
% 5.15/5.42 thf(fact_3553_max__nat_Oneutr__eq__iff,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( zero_zero_nat
% 5.15/5.42 = ( ord_max_nat @ A @ B ) )
% 5.15/5.42 = ( ( A = zero_zero_nat )
% 5.15/5.42 & ( B = zero_zero_nat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_nat.neutr_eq_iff
% 5.15/5.42 thf(fact_3554_max__nat_Oleft__neutral,axiom,
% 5.15/5.42 ! [A: nat] :
% 5.15/5.42 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.15/5.42 = A ) ).
% 5.15/5.42
% 5.15/5.42 % max_nat.left_neutral
% 5.15/5.42 thf(fact_3555_max__nat_Oeq__neutr__iff,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( ( ord_max_nat @ A @ B )
% 5.15/5.42 = zero_zero_nat )
% 5.15/5.42 = ( ( A = zero_zero_nat )
% 5.15/5.42 & ( B = zero_zero_nat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_nat.eq_neutr_iff
% 5.15/5.42 thf(fact_3556_nth__list__update__neq,axiom,
% 5.15/5.42 ! [I: nat,J: nat,Xs2: list_int,X: int] :
% 5.15/5.42 ( ( I != J )
% 5.15/5.42 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = ( nth_int @ Xs2 @ J ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update_neq
% 5.15/5.42 thf(fact_3557_nth__list__update__neq,axiom,
% 5.15/5.42 ! [I: nat,J: nat,Xs2: list_nat,X: nat] :
% 5.15/5.42 ( ( I != J )
% 5.15/5.42 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update_neq
% 5.15/5.42 thf(fact_3558_nth__list__update__neq,axiom,
% 5.15/5.42 ! [I: nat,J: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.15/5.42 ( ( I != J )
% 5.15/5.42 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update_neq
% 5.15/5.42 thf(fact_3559_list__update__id,axiom,
% 5.15/5.42 ! [Xs2: list_int,I: nat] :
% 5.15/5.42 ( ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ I ) )
% 5.15/5.42 = Xs2 ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_id
% 5.15/5.42 thf(fact_3560_list__update__id,axiom,
% 5.15/5.42 ! [Xs2: list_nat,I: nat] :
% 5.15/5.42 ( ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ I ) )
% 5.15/5.42 = Xs2 ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_id
% 5.15/5.42 thf(fact_3561_list__update__id,axiom,
% 5.15/5.42 ! [Xs2: list_VEBT_VEBT,I: nat] :
% 5.15/5.42 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 5.15/5.42 = Xs2 ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_id
% 5.15/5.42 thf(fact_3562_concat__bit__0,axiom,
% 5.15/5.42 ! [K: int,L: int] :
% 5.15/5.42 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 5.15/5.42 = L ) ).
% 5.15/5.42
% 5.15/5.42 % concat_bit_0
% 5.15/5.42 thf(fact_3563_dbl__simps_I2_J,axiom,
% 5.15/5.42 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.15/5.42 = zero_zero_complex ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(2)
% 5.15/5.42 thf(fact_3564_dbl__simps_I2_J,axiom,
% 5.15/5.42 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.15/5.42 = zero_zero_real ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(2)
% 5.15/5.42 thf(fact_3565_dbl__simps_I2_J,axiom,
% 5.15/5.42 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.15/5.42 = zero_zero_rat ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(2)
% 5.15/5.42 thf(fact_3566_dbl__simps_I2_J,axiom,
% 5.15/5.42 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.15/5.42 = zero_zero_int ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(2)
% 5.15/5.42 thf(fact_3567_max__number__of_I1_J,axiom,
% 5.15/5.42 ! [U: num,V: num] :
% 5.15/5.42 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.15/5.42 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.15/5.42 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.15/5.42 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.15/5.42 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.15/5.42 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_number_of(1)
% 5.15/5.42 thf(fact_3568_max__number__of_I1_J,axiom,
% 5.15/5.42 ! [U: num,V: num] :
% 5.15/5.42 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.42 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.42 = ( numeral_numeral_real @ V ) ) )
% 5.15/5.42 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.42 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.42 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_number_of(1)
% 5.15/5.42 thf(fact_3569_max__number__of_I1_J,axiom,
% 5.15/5.42 ! [U: num,V: num] :
% 5.15/5.42 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.42 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.42 = ( numeral_numeral_rat @ V ) ) )
% 5.15/5.42 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.42 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.42 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_number_of(1)
% 5.15/5.42 thf(fact_3570_max__number__of_I1_J,axiom,
% 5.15/5.42 ! [U: num,V: num] :
% 5.15/5.42 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.15/5.42 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.15/5.42 = ( numeral_numeral_nat @ V ) ) )
% 5.15/5.42 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.15/5.42 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.15/5.42 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_number_of(1)
% 5.15/5.42 thf(fact_3571_max__number__of_I1_J,axiom,
% 5.15/5.42 ! [U: num,V: num] :
% 5.15/5.42 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.42 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.42 = ( numeral_numeral_int @ V ) ) )
% 5.15/5.42 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.42 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.42 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_number_of(1)
% 5.15/5.42 thf(fact_3572_max__0__1_I4_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 5.15/5.42 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(4)
% 5.15/5.42 thf(fact_3573_max__0__1_I4_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 5.15/5.42 = ( numeral_numeral_real @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(4)
% 5.15/5.42 thf(fact_3574_max__0__1_I4_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 5.15/5.42 = ( numeral_numeral_rat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(4)
% 5.15/5.42 thf(fact_3575_max__0__1_I4_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 5.15/5.42 = ( numeral_numeral_nat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(4)
% 5.15/5.42 thf(fact_3576_max__0__1_I4_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 5.15/5.42 = ( numeral_numeral_int @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(4)
% 5.15/5.42 thf(fact_3577_max__0__1_I3_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.15/5.42 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(3)
% 5.15/5.42 thf(fact_3578_max__0__1_I3_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 5.15/5.42 = ( numeral_numeral_real @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(3)
% 5.15/5.42 thf(fact_3579_max__0__1_I3_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 5.15/5.42 = ( numeral_numeral_rat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(3)
% 5.15/5.42 thf(fact_3580_max__0__1_I3_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 5.15/5.42 = ( numeral_numeral_nat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(3)
% 5.15/5.42 thf(fact_3581_max__0__1_I3_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 5.15/5.42 = ( numeral_numeral_int @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(3)
% 5.15/5.42 thf(fact_3582_max__0__1_I2_J,axiom,
% 5.15/5.42 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.15/5.42 = one_one_real ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(2)
% 5.15/5.42 thf(fact_3583_max__0__1_I2_J,axiom,
% 5.15/5.42 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.15/5.42 = one_one_rat ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(2)
% 5.15/5.42 thf(fact_3584_max__0__1_I2_J,axiom,
% 5.15/5.42 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.15/5.42 = one_one_nat ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(2)
% 5.15/5.42 thf(fact_3585_max__0__1_I2_J,axiom,
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.15/5.42 = one_on7984719198319812577d_enat ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(2)
% 5.15/5.42 thf(fact_3586_max__0__1_I2_J,axiom,
% 5.15/5.42 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.15/5.42 = one_one_int ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(2)
% 5.15/5.42 thf(fact_3587_max__0__1_I1_J,axiom,
% 5.15/5.42 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.15/5.42 = one_one_real ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(1)
% 5.15/5.42 thf(fact_3588_max__0__1_I1_J,axiom,
% 5.15/5.42 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.15/5.42 = one_one_rat ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(1)
% 5.15/5.42 thf(fact_3589_max__0__1_I1_J,axiom,
% 5.15/5.42 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.15/5.42 = one_one_nat ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(1)
% 5.15/5.42 thf(fact_3590_max__0__1_I1_J,axiom,
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.15/5.42 = one_on7984719198319812577d_enat ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(1)
% 5.15/5.42 thf(fact_3591_max__0__1_I1_J,axiom,
% 5.15/5.42 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.15/5.42 = one_one_int ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(1)
% 5.15/5.42 thf(fact_3592_max__0__1_I5_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.15/5.42 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(5)
% 5.15/5.42 thf(fact_3593_max__0__1_I5_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.15/5.42 = ( numeral_numeral_real @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(5)
% 5.15/5.42 thf(fact_3594_max__0__1_I5_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.15/5.42 = ( numeral_numeral_rat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(5)
% 5.15/5.42 thf(fact_3595_max__0__1_I5_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.15/5.42 = ( numeral_numeral_nat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(5)
% 5.15/5.42 thf(fact_3596_max__0__1_I5_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.15/5.42 = ( numeral_numeral_int @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(5)
% 5.15/5.42 thf(fact_3597_max__0__1_I6_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 5.15/5.42 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(6)
% 5.15/5.42 thf(fact_3598_max__0__1_I6_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 5.15/5.42 = ( numeral_numeral_real @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(6)
% 5.15/5.42 thf(fact_3599_max__0__1_I6_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 5.15/5.42 = ( numeral_numeral_rat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(6)
% 5.15/5.42 thf(fact_3600_max__0__1_I6_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 5.15/5.42 = ( numeral_numeral_nat @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(6)
% 5.15/5.42 thf(fact_3601_max__0__1_I6_J,axiom,
% 5.15/5.42 ! [X: num] :
% 5.15/5.42 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 5.15/5.42 = ( numeral_numeral_int @ X ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_0_1(6)
% 5.15/5.42 thf(fact_3602_list__update__beyond,axiom,
% 5.15/5.42 ! [Xs2: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 5.15/5.42 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I )
% 5.15/5.42 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X )
% 5.15/5.42 = Xs2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_beyond
% 5.15/5.42 thf(fact_3603_list__update__beyond,axiom,
% 5.15/5.42 ! [Xs2: list_o,I: nat,X: $o] :
% 5.15/5.42 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I )
% 5.15/5.42 => ( ( list_update_o @ Xs2 @ I @ X )
% 5.15/5.42 = Xs2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_beyond
% 5.15/5.42 thf(fact_3604_list__update__beyond,axiom,
% 5.15/5.42 ! [Xs2: list_int,I: nat,X: int] :
% 5.15/5.42 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I )
% 5.15/5.42 => ( ( list_update_int @ Xs2 @ I @ X )
% 5.15/5.42 = Xs2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_beyond
% 5.15/5.42 thf(fact_3605_concat__bit__nonnegative__iff,axiom,
% 5.15/5.42 ! [N2: nat,K: int,L: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K @ L ) )
% 5.15/5.42 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.15/5.42
% 5.15/5.42 % concat_bit_nonnegative_iff
% 5.15/5.42 thf(fact_3606_concat__bit__negative__iff,axiom,
% 5.15/5.42 ! [N2: nat,K: int,L: int] :
% 5.15/5.42 ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K @ L ) @ zero_zero_int )
% 5.15/5.42 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.15/5.42
% 5.15/5.42 % concat_bit_negative_iff
% 5.15/5.42 thf(fact_3607_dbl__simps_I5_J,axiom,
% 5.15/5.42 ! [K: num] :
% 5.15/5.42 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.15/5.42 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(5)
% 5.15/5.42 thf(fact_3608_dbl__simps_I5_J,axiom,
% 5.15/5.42 ! [K: num] :
% 5.15/5.42 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.15/5.42 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(5)
% 5.15/5.42 thf(fact_3609_dbl__simps_I5_J,axiom,
% 5.15/5.42 ! [K: num] :
% 5.15/5.42 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.15/5.42 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(5)
% 5.15/5.42 thf(fact_3610_dbl__simps_I5_J,axiom,
% 5.15/5.42 ! [K: num] :
% 5.15/5.42 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.15/5.42 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_simps(5)
% 5.15/5.42 thf(fact_3611_nth__list__update__eq,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_nat,X: nat] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.42 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X ) @ I )
% 5.15/5.42 = X ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update_eq
% 5.15/5.42 thf(fact_3612_nth__list__update__eq,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.42 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ I )
% 5.15/5.42 = X ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update_eq
% 5.15/5.42 thf(fact_3613_nth__list__update__eq,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_o,X: $o] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.42 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X ) @ I )
% 5.15/5.42 = X ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update_eq
% 5.15/5.42 thf(fact_3614_nth__list__update__eq,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_int,X: int] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.42 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X ) @ I )
% 5.15/5.42 = X ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update_eq
% 5.15/5.42 thf(fact_3615_set__swap,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_nat,J: nat] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.42 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.42 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I ) ) )
% 5.15/5.42 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_swap
% 5.15/5.42 thf(fact_3616_set__swap,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.42 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.42 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) )
% 5.15/5.42 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_swap
% 5.15/5.42 thf(fact_3617_set__swap,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_o,J: nat] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.42 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.42 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I ) ) )
% 5.15/5.42 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_swap
% 5.15/5.42 thf(fact_3618_set__swap,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_int,J: nat] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.42 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.42 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I ) ) )
% 5.15/5.42 = ( set_int2 @ Xs2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_swap
% 5.15/5.42 thf(fact_3619_list__update__swap,axiom,
% 5.15/5.42 ! [I: nat,I6: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT,X7: vEBT_VEBT] :
% 5.15/5.42 ( ( I != I6 )
% 5.15/5.42 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ I6 @ X7 )
% 5.15/5.42 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I6 @ X7 ) @ I @ X ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_swap
% 5.15/5.42 thf(fact_3620_max__add__distrib__right,axiom,
% 5.15/5.42 ! [X: real,Y: real,Z: real] :
% 5.15/5.42 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 5.15/5.42 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_add_distrib_right
% 5.15/5.42 thf(fact_3621_max__add__distrib__right,axiom,
% 5.15/5.42 ! [X: rat,Y: rat,Z: rat] :
% 5.15/5.42 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 5.15/5.42 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_add_distrib_right
% 5.15/5.42 thf(fact_3622_max__add__distrib__right,axiom,
% 5.15/5.42 ! [X: nat,Y: nat,Z: nat] :
% 5.15/5.42 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 5.15/5.42 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_add_distrib_right
% 5.15/5.42 thf(fact_3623_max__add__distrib__right,axiom,
% 5.15/5.42 ! [X: int,Y: int,Z: int] :
% 5.15/5.42 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 5.15/5.42 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_add_distrib_right
% 5.15/5.42 thf(fact_3624_max__add__distrib__left,axiom,
% 5.15/5.42 ! [X: real,Y: real,Z: real] :
% 5.15/5.42 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.15/5.42 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_add_distrib_left
% 5.15/5.42 thf(fact_3625_max__add__distrib__left,axiom,
% 5.15/5.42 ! [X: rat,Y: rat,Z: rat] :
% 5.15/5.42 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.15/5.42 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_add_distrib_left
% 5.15/5.42 thf(fact_3626_max__add__distrib__left,axiom,
% 5.15/5.42 ! [X: nat,Y: nat,Z: nat] :
% 5.15/5.42 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 5.15/5.42 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_add_distrib_left
% 5.15/5.42 thf(fact_3627_max__add__distrib__left,axiom,
% 5.15/5.42 ! [X: int,Y: int,Z: int] :
% 5.15/5.42 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.15/5.42 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_add_distrib_left
% 5.15/5.42 thf(fact_3628_max__diff__distrib__left,axiom,
% 5.15/5.42 ! [X: real,Y: real,Z: real] :
% 5.15/5.42 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.15/5.42 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_diff_distrib_left
% 5.15/5.42 thf(fact_3629_max__diff__distrib__left,axiom,
% 5.15/5.42 ! [X: rat,Y: rat,Z: rat] :
% 5.15/5.42 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.15/5.42 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_diff_distrib_left
% 5.15/5.42 thf(fact_3630_max__diff__distrib__left,axiom,
% 5.15/5.42 ! [X: int,Y: int,Z: int] :
% 5.15/5.42 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.15/5.42 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_diff_distrib_left
% 5.15/5.42 thf(fact_3631_nat__add__max__right,axiom,
% 5.15/5.42 ! [M: nat,N2: nat,Q3: nat] :
% 5.15/5.42 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q3 ) )
% 5.15/5.42 = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nat_add_max_right
% 5.15/5.42 thf(fact_3632_nat__add__max__left,axiom,
% 5.15/5.42 ! [M: nat,N2: nat,Q3: nat] :
% 5.15/5.42 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q3 )
% 5.15/5.42 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N2 @ Q3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nat_add_max_left
% 5.15/5.42 thf(fact_3633_nat__mult__max__right,axiom,
% 5.15/5.42 ! [M: nat,N2: nat,Q3: nat] :
% 5.15/5.42 ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q3 ) )
% 5.15/5.42 = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nat_mult_max_right
% 5.15/5.42 thf(fact_3634_nat__mult__max__left,axiom,
% 5.15/5.42 ! [M: nat,N2: nat,Q3: nat] :
% 5.15/5.42 ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q3 )
% 5.15/5.42 = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nat_mult_max_left
% 5.15/5.42 thf(fact_3635_semiring__norm_I26_J,axiom,
% 5.15/5.42 ( ( bitM @ one )
% 5.15/5.42 = one ) ).
% 5.15/5.42
% 5.15/5.42 % semiring_norm(26)
% 5.15/5.42 thf(fact_3636_max__def__raw,axiom,
% 5.15/5.42 ( ord_ma741700101516333627d_enat
% 5.15/5.42 = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_def_raw
% 5.15/5.42 thf(fact_3637_max__def__raw,axiom,
% 5.15/5.42 ( ord_max_set_nat
% 5.15/5.42 = ( ^ [A3: set_nat,B2: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_def_raw
% 5.15/5.42 thf(fact_3638_max__def__raw,axiom,
% 5.15/5.42 ( ord_max_rat
% 5.15/5.42 = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_def_raw
% 5.15/5.42 thf(fact_3639_max__def__raw,axiom,
% 5.15/5.42 ( ord_max_num
% 5.15/5.42 = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_def_raw
% 5.15/5.42 thf(fact_3640_max__def__raw,axiom,
% 5.15/5.42 ( ord_max_nat
% 5.15/5.42 = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_def_raw
% 5.15/5.42 thf(fact_3641_max__def__raw,axiom,
% 5.15/5.42 ( ord_max_int
% 5.15/5.42 = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_def_raw
% 5.15/5.42 thf(fact_3642_concat__bit__assoc,axiom,
% 5.15/5.42 ! [N2: nat,K: int,M: nat,L: int,R2: int] :
% 5.15/5.42 ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L @ R2 ) )
% 5.15/5.42 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L ) @ R2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % concat_bit_assoc
% 5.15/5.42 thf(fact_3643_nat__minus__add__max,axiom,
% 5.15/5.42 ! [N2: nat,M: nat] :
% 5.15/5.42 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 5.15/5.42 = ( ord_max_nat @ N2 @ M ) ) ).
% 5.15/5.42
% 5.15/5.42 % nat_minus_add_max
% 5.15/5.42 thf(fact_3644_set__update__subsetI,axiom,
% 5.15/5.42 ! [Xs2: list_complex,A2: set_complex,X: complex,I: nat] :
% 5.15/5.42 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 5.15/5.42 => ( ( member_complex @ X @ A2 )
% 5.15/5.42 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_subsetI
% 5.15/5.42 thf(fact_3645_set__update__subsetI,axiom,
% 5.15/5.42 ! [Xs2: list_real,A2: set_real,X: real,I: nat] :
% 5.15/5.42 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 5.15/5.42 => ( ( member_real @ X @ A2 )
% 5.15/5.42 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_subsetI
% 5.15/5.42 thf(fact_3646_set__update__subsetI,axiom,
% 5.15/5.42 ! [Xs2: list_set_nat,A2: set_set_nat,X: set_nat,I: nat] :
% 5.15/5.42 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ A2 )
% 5.15/5.42 => ( ( member_set_nat @ X @ A2 )
% 5.15/5.42 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_subsetI
% 5.15/5.42 thf(fact_3647_set__update__subsetI,axiom,
% 5.15/5.42 ! [Xs2: list_int,A2: set_int,X: int,I: nat] :
% 5.15/5.42 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 5.15/5.42 => ( ( member_int @ X @ A2 )
% 5.15/5.42 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_subsetI
% 5.15/5.42 thf(fact_3648_set__update__subsetI,axiom,
% 5.15/5.42 ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 5.15/5.42 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 5.15/5.42 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.42 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_subsetI
% 5.15/5.42 thf(fact_3649_set__update__subsetI,axiom,
% 5.15/5.42 ! [Xs2: list_nat,A2: set_nat,X: nat,I: nat] :
% 5.15/5.42 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 5.15/5.42 => ( ( member_nat @ X @ A2 )
% 5.15/5.42 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_subsetI
% 5.15/5.42 thf(fact_3650_dbl__def,axiom,
% 5.15/5.42 ( neg_numeral_dbl_real
% 5.15/5.42 = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_def
% 5.15/5.42 thf(fact_3651_dbl__def,axiom,
% 5.15/5.42 ( neg_numeral_dbl_rat
% 5.15/5.42 = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_def
% 5.15/5.42 thf(fact_3652_dbl__def,axiom,
% 5.15/5.42 ( neg_numeral_dbl_int
% 5.15/5.42 = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_def
% 5.15/5.42 thf(fact_3653_dbl__def,axiom,
% 5.15/5.42 ( neg_nu7009210354673126013omplex
% 5.15/5.42 = ( ^ [X2: complex] : ( plus_plus_complex @ X2 @ X2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dbl_def
% 5.15/5.42 thf(fact_3654_semiring__norm_I27_J,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( bitM @ ( bit0 @ N2 ) )
% 5.15/5.42 = ( bit1 @ ( bitM @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % semiring_norm(27)
% 5.15/5.42 thf(fact_3655_semiring__norm_I28_J,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( bitM @ ( bit1 @ N2 ) )
% 5.15/5.42 = ( bit1 @ ( bit0 @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % semiring_norm(28)
% 5.15/5.42 thf(fact_3656_set__update__memI,axiom,
% 5.15/5.42 ! [N2: nat,Xs2: list_complex,X: complex] :
% 5.15/5.42 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.15/5.42 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_memI
% 5.15/5.42 thf(fact_3657_set__update__memI,axiom,
% 5.15/5.42 ! [N2: nat,Xs2: list_real,X: real] :
% 5.15/5.42 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.15/5.42 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_memI
% 5.15/5.42 thf(fact_3658_set__update__memI,axiom,
% 5.15/5.42 ! [N2: nat,Xs2: list_set_nat,X: set_nat] :
% 5.15/5.42 ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.15/5.42 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_memI
% 5.15/5.42 thf(fact_3659_set__update__memI,axiom,
% 5.15/5.42 ! [N2: nat,Xs2: list_nat,X: nat] :
% 5.15/5.42 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.42 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_memI
% 5.15/5.42 thf(fact_3660_set__update__memI,axiom,
% 5.15/5.42 ! [N2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.15/5.42 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.42 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_memI
% 5.15/5.42 thf(fact_3661_set__update__memI,axiom,
% 5.15/5.42 ! [N2: nat,Xs2: list_o,X: $o] :
% 5.15/5.42 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.42 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_memI
% 5.15/5.42 thf(fact_3662_set__update__memI,axiom,
% 5.15/5.42 ! [N2: nat,Xs2: list_int,X: int] :
% 5.15/5.42 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.42 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_update_memI
% 5.15/5.42 thf(fact_3663_list__update__same__conv,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_nat,X: nat] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.42 => ( ( ( list_update_nat @ Xs2 @ I @ X )
% 5.15/5.42 = Xs2 )
% 5.15/5.42 = ( ( nth_nat @ Xs2 @ I )
% 5.15/5.42 = X ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_same_conv
% 5.15/5.42 thf(fact_3664_list__update__same__conv,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.42 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X )
% 5.15/5.42 = Xs2 )
% 5.15/5.42 = ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 5.15/5.42 = X ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_same_conv
% 5.15/5.42 thf(fact_3665_list__update__same__conv,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_o,X: $o] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.42 => ( ( ( list_update_o @ Xs2 @ I @ X )
% 5.15/5.42 = Xs2 )
% 5.15/5.42 = ( ( nth_o @ Xs2 @ I )
% 5.15/5.42 = X ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_same_conv
% 5.15/5.42 thf(fact_3666_list__update__same__conv,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_int,X: int] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.42 => ( ( ( list_update_int @ Xs2 @ I @ X )
% 5.15/5.42 = Xs2 )
% 5.15/5.42 = ( ( nth_int @ Xs2 @ I )
% 5.15/5.42 = X ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_update_same_conv
% 5.15/5.42 thf(fact_3667_nth__list__update,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_nat,J: nat,X: nat] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.15/5.42 => ( ( ( I = J )
% 5.15/5.42 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = X ) )
% 5.15/5.42 & ( ( I != J )
% 5.15/5.42 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update
% 5.15/5.42 thf(fact_3668_nth__list__update,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.15/5.42 => ( ( ( I = J )
% 5.15/5.42 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = X ) )
% 5.15/5.42 & ( ( I != J )
% 5.15/5.42 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update
% 5.15/5.42 thf(fact_3669_nth__list__update,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_o,X: $o,J: nat] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.15/5.42 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = ( ( ( I = J )
% 5.15/5.42 => X )
% 5.15/5.42 & ( ( I != J )
% 5.15/5.42 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update
% 5.15/5.42 thf(fact_3670_nth__list__update,axiom,
% 5.15/5.42 ! [I: nat,Xs2: list_int,J: nat,X: int] :
% 5.15/5.42 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.15/5.42 => ( ( ( I = J )
% 5.15/5.42 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = X ) )
% 5.15/5.42 & ( ( I != J )
% 5.15/5.42 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X ) @ J )
% 5.15/5.42 = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nth_list_update
% 5.15/5.42 thf(fact_3671_eval__nat__numeral_I2_J,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.15/5.42 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % eval_nat_numeral(2)
% 5.15/5.42 thf(fact_3672_one__plus__BitM,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 5.15/5.42 = ( bit0 @ N2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % one_plus_BitM
% 5.15/5.42 thf(fact_3673_BitM__plus__one,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 5.15/5.42 = ( bit0 @ N2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % BitM_plus_one
% 5.15/5.42 thf(fact_3674_numeral__BitM,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( numera6690914467698888265omplex @ ( bitM @ N2 ) )
% 5.15/5.42 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N2 ) ) @ one_one_complex ) ) ).
% 5.15/5.42
% 5.15/5.42 % numeral_BitM
% 5.15/5.42 thf(fact_3675_numeral__BitM,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( numeral_numeral_real @ ( bitM @ N2 ) )
% 5.15/5.42 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N2 ) ) @ one_one_real ) ) ).
% 5.15/5.42
% 5.15/5.42 % numeral_BitM
% 5.15/5.42 thf(fact_3676_numeral__BitM,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( numeral_numeral_rat @ ( bitM @ N2 ) )
% 5.15/5.42 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N2 ) ) @ one_one_rat ) ) ).
% 5.15/5.42
% 5.15/5.42 % numeral_BitM
% 5.15/5.42 thf(fact_3677_numeral__BitM,axiom,
% 5.15/5.42 ! [N2: num] :
% 5.15/5.42 ( ( numeral_numeral_int @ ( bitM @ N2 ) )
% 5.15/5.42 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ one_one_int ) ) ).
% 5.15/5.42
% 5.15/5.42 % numeral_BitM
% 5.15/5.42 thf(fact_3678_Euclid__induct,axiom,
% 5.15/5.42 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.15/5.42 ( ! [A5: nat,B6: nat] :
% 5.15/5.42 ( ( P @ A5 @ B6 )
% 5.15/5.42 = ( P @ B6 @ A5 ) )
% 5.15/5.42 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 5.15/5.42 => ( ! [A5: nat,B6: nat] :
% 5.15/5.42 ( ( P @ A5 @ B6 )
% 5.15/5.42 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B6 ) ) )
% 5.15/5.42 => ( P @ A @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % Euclid_induct
% 5.15/5.42 thf(fact_3679_VEBT__internal_Oheight_Ocases,axiom,
% 5.15/5.42 ! [X: vEBT_VEBT] :
% 5.15/5.42 ( ! [A5: $o,B6: $o] :
% 5.15/5.42 ( X
% 5.15/5.42 != ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.42 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.42 ( X
% 5.15/5.42 != ( vEBT_Node @ Uu2 @ Deg2 @ TreeList3 @ Summary2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % VEBT_internal.height.cases
% 5.15/5.42 thf(fact_3680_vebt__insert_Osimps_I5_J,axiom,
% 5.15/5.42 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.15/5.42 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.15/5.42 = ( if_VEBT_VEBT
% 5.15/5.42 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.15/5.42 & ~ ( ( X = Mi )
% 5.15/5.42 | ( X = Ma ) ) )
% 5.15/5.42 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.15/5.42 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % vebt_insert.simps(5)
% 5.15/5.42 thf(fact_3681_vebt__insert_Oelims,axiom,
% 5.15/5.42 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.15/5.42 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.15/5.42 = Y )
% 5.15/5.42 => ( ! [A5: $o,B6: $o] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.42 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.42 => ( Y
% 5.15/5.42 = ( vEBT_Leaf @ $true @ B6 ) ) )
% 5.15/5.42 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.42 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.42 => ( Y
% 5.15/5.42 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.15/5.42 & ( ( Xa2 != one_one_nat )
% 5.15/5.42 => ( Y
% 5.15/5.42 = ( vEBT_Leaf @ A5 @ B6 ) ) ) ) ) ) )
% 5.15/5.42 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.15/5.42 => ( Y
% 5.15/5.42 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) )
% 5.15/5.42 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.15/5.42 => ( Y
% 5.15/5.42 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) )
% 5.15/5.42 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.42 => ( Y
% 5.15/5.42 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.15/5.42 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.42 => ( Y
% 5.15/5.42 != ( if_VEBT_VEBT
% 5.15/5.42 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.42 & ~ ( ( Xa2 = Mi2 )
% 5.15/5.42 | ( Xa2 = Ma2 ) ) )
% 5.15/5.42 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.15/5.42 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % vebt_insert.elims
% 5.15/5.42 thf(fact_3682_vebt__insert_Opelims,axiom,
% 5.15/5.42 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.15/5.42 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.15/5.42 = Y )
% 5.15/5.42 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.42 => ( ! [A5: $o,B6: $o] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.42 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.42 => ( Y
% 5.15/5.42 = ( vEBT_Leaf @ $true @ B6 ) ) )
% 5.15/5.42 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.42 => ( ( ( Xa2 = one_one_nat )
% 5.15/5.42 => ( Y
% 5.15/5.42 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.15/5.42 & ( ( Xa2 != one_one_nat )
% 5.15/5.42 => ( Y
% 5.15/5.42 = ( vEBT_Leaf @ A5 @ B6 ) ) ) ) ) )
% 5.15/5.42 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B6 ) @ Xa2 ) ) ) )
% 5.15/5.42 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.15/5.42 => ( ( Y
% 5.15/5.42 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 5.15/5.42 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.15/5.42 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.15/5.42 => ( ( Y
% 5.15/5.42 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 5.15/5.42 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 5.15/5.42 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.42 => ( ( Y
% 5.15/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.42 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.15/5.42 => ~ ! [Mi2: nat,Ma2: nat,Va3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.42 ( ( X
% 5.15/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) )
% 5.15/5.42 => ( ( Y
% 5.15/5.42 = ( if_VEBT_VEBT
% 5.15/5.42 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.15/5.42 & ~ ( ( Xa2 = Mi2 )
% 5.15/5.42 | ( Xa2 = Ma2 ) ) )
% 5.15/5.42 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.15/5.42 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.15/5.42 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % vebt_insert.pelims
% 5.15/5.42 thf(fact_3683_max_Oabsorb3,axiom,
% 5.15/5.42 ! [B: extended_enat,A: extended_enat] :
% 5.15/5.42 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.15/5.42 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb3
% 5.15/5.42 thf(fact_3684_max_Oabsorb3,axiom,
% 5.15/5.42 ! [B: real,A: real] :
% 5.15/5.42 ( ( ord_less_real @ B @ A )
% 5.15/5.42 => ( ( ord_max_real @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb3
% 5.15/5.42 thf(fact_3685_max_Oabsorb3,axiom,
% 5.15/5.42 ! [B: rat,A: rat] :
% 5.15/5.42 ( ( ord_less_rat @ B @ A )
% 5.15/5.42 => ( ( ord_max_rat @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb3
% 5.15/5.42 thf(fact_3686_max_Oabsorb3,axiom,
% 5.15/5.42 ! [B: num,A: num] :
% 5.15/5.42 ( ( ord_less_num @ B @ A )
% 5.15/5.42 => ( ( ord_max_num @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb3
% 5.15/5.42 thf(fact_3687_max_Oabsorb3,axiom,
% 5.15/5.42 ! [B: nat,A: nat] :
% 5.15/5.42 ( ( ord_less_nat @ B @ A )
% 5.15/5.42 => ( ( ord_max_nat @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb3
% 5.15/5.42 thf(fact_3688_max_Oabsorb3,axiom,
% 5.15/5.42 ! [B: int,A: int] :
% 5.15/5.42 ( ( ord_less_int @ B @ A )
% 5.15/5.42 => ( ( ord_max_int @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb3
% 5.15/5.42 thf(fact_3689_max_Oabsorb4,axiom,
% 5.15/5.42 ! [A: extended_enat,B: extended_enat] :
% 5.15/5.42 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.15/5.42 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb4
% 5.15/5.42 thf(fact_3690_max_Oabsorb4,axiom,
% 5.15/5.42 ! [A: real,B: real] :
% 5.15/5.42 ( ( ord_less_real @ A @ B )
% 5.15/5.42 => ( ( ord_max_real @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb4
% 5.15/5.42 thf(fact_3691_max_Oabsorb4,axiom,
% 5.15/5.42 ! [A: rat,B: rat] :
% 5.15/5.42 ( ( ord_less_rat @ A @ B )
% 5.15/5.42 => ( ( ord_max_rat @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb4
% 5.15/5.42 thf(fact_3692_max_Oabsorb4,axiom,
% 5.15/5.42 ! [A: num,B: num] :
% 5.15/5.42 ( ( ord_less_num @ A @ B )
% 5.15/5.42 => ( ( ord_max_num @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb4
% 5.15/5.42 thf(fact_3693_max_Oabsorb4,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( ord_less_nat @ A @ B )
% 5.15/5.42 => ( ( ord_max_nat @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb4
% 5.15/5.42 thf(fact_3694_max_Oabsorb4,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( ord_less_int @ A @ B )
% 5.15/5.42 => ( ( ord_max_int @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb4
% 5.15/5.42 thf(fact_3695_max__less__iff__conj,axiom,
% 5.15/5.42 ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 5.15/5.42 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y ) @ Z )
% 5.15/5.42 = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 5.15/5.42 & ( ord_le72135733267957522d_enat @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_less_iff_conj
% 5.15/5.42 thf(fact_3696_max__less__iff__conj,axiom,
% 5.15/5.42 ! [X: real,Y: real,Z: real] :
% 5.15/5.42 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.15/5.42 = ( ( ord_less_real @ X @ Z )
% 5.15/5.42 & ( ord_less_real @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_less_iff_conj
% 5.15/5.42 thf(fact_3697_max__less__iff__conj,axiom,
% 5.15/5.42 ! [X: rat,Y: rat,Z: rat] :
% 5.15/5.42 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.15/5.42 = ( ( ord_less_rat @ X @ Z )
% 5.15/5.42 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_less_iff_conj
% 5.15/5.42 thf(fact_3698_max__less__iff__conj,axiom,
% 5.15/5.42 ! [X: num,Y: num,Z: num] :
% 5.15/5.42 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 5.15/5.42 = ( ( ord_less_num @ X @ Z )
% 5.15/5.42 & ( ord_less_num @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_less_iff_conj
% 5.15/5.42 thf(fact_3699_max__less__iff__conj,axiom,
% 5.15/5.42 ! [X: nat,Y: nat,Z: nat] :
% 5.15/5.42 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 5.15/5.42 = ( ( ord_less_nat @ X @ Z )
% 5.15/5.42 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_less_iff_conj
% 5.15/5.42 thf(fact_3700_max__less__iff__conj,axiom,
% 5.15/5.42 ! [X: int,Y: int,Z: int] :
% 5.15/5.42 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.15/5.42 = ( ( ord_less_int @ X @ Z )
% 5.15/5.42 & ( ord_less_int @ Y @ Z ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max_less_iff_conj
% 5.15/5.42 thf(fact_3701_max_Obounded__iff,axiom,
% 5.15/5.42 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.15/5.42 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.15/5.42 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.bounded_iff
% 5.15/5.42 thf(fact_3702_max_Obounded__iff,axiom,
% 5.15/5.42 ! [B: rat,C: rat,A: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.15/5.42 = ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.42 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.bounded_iff
% 5.15/5.42 thf(fact_3703_max_Obounded__iff,axiom,
% 5.15/5.42 ! [B: num,C: num,A: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.15/5.42 = ( ( ord_less_eq_num @ B @ A )
% 5.15/5.42 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.bounded_iff
% 5.15/5.42 thf(fact_3704_max_Obounded__iff,axiom,
% 5.15/5.42 ! [B: nat,C: nat,A: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.15/5.42 = ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.42 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.bounded_iff
% 5.15/5.42 thf(fact_3705_max_Obounded__iff,axiom,
% 5.15/5.42 ! [B: int,C: int,A: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.15/5.42 = ( ( ord_less_eq_int @ B @ A )
% 5.15/5.42 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.bounded_iff
% 5.15/5.42 thf(fact_3706_max_Oabsorb2,axiom,
% 5.15/5.42 ! [A: extended_enat,B: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.15/5.42 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb2
% 5.15/5.42 thf(fact_3707_max_Oabsorb2,axiom,
% 5.15/5.42 ! [A: rat,B: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.42 => ( ( ord_max_rat @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb2
% 5.15/5.42 thf(fact_3708_max_Oabsorb2,axiom,
% 5.15/5.42 ! [A: num,B: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ A @ B )
% 5.15/5.42 => ( ( ord_max_num @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb2
% 5.15/5.42 thf(fact_3709_max_Oabsorb2,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.42 => ( ( ord_max_nat @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb2
% 5.15/5.42 thf(fact_3710_max_Oabsorb2,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.42 => ( ( ord_max_int @ A @ B )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb2
% 5.15/5.42 thf(fact_3711_max_Oabsorb1,axiom,
% 5.15/5.42 ! [B: extended_enat,A: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.15/5.42 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb1
% 5.15/5.42 thf(fact_3712_max_Oabsorb1,axiom,
% 5.15/5.42 ! [B: rat,A: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.42 => ( ( ord_max_rat @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb1
% 5.15/5.42 thf(fact_3713_max_Oabsorb1,axiom,
% 5.15/5.42 ! [B: num,A: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ B @ A )
% 5.15/5.42 => ( ( ord_max_num @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb1
% 5.15/5.42 thf(fact_3714_max_Oabsorb1,axiom,
% 5.15/5.42 ! [B: nat,A: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.42 => ( ( ord_max_nat @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb1
% 5.15/5.42 thf(fact_3715_max_Oabsorb1,axiom,
% 5.15/5.42 ! [B: int,A: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ B @ A )
% 5.15/5.42 => ( ( ord_max_int @ A @ B )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb1
% 5.15/5.42 thf(fact_3716_max__enat__simps_I3_J,axiom,
% 5.15/5.42 ! [Q3: extended_enat] :
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 5.15/5.42 = Q3 ) ).
% 5.15/5.42
% 5.15/5.42 % max_enat_simps(3)
% 5.15/5.42 thf(fact_3717_max__enat__simps_I2_J,axiom,
% 5.15/5.42 ! [Q3: extended_enat] :
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 5.15/5.42 = Q3 ) ).
% 5.15/5.42
% 5.15/5.42 % max_enat_simps(2)
% 5.15/5.42 thf(fact_3718_prod__decode__aux_Ocases,axiom,
% 5.15/5.42 ! [X: product_prod_nat_nat] :
% 5.15/5.42 ~ ! [K3: nat,M3: nat] :
% 5.15/5.42 ( X
% 5.15/5.42 != ( product_Pair_nat_nat @ K3 @ M3 ) ) ).
% 5.15/5.42
% 5.15/5.42 % prod_decode_aux.cases
% 5.15/5.42 thf(fact_3719_list__decode_Ocases,axiom,
% 5.15/5.42 ! [X: nat] :
% 5.15/5.42 ( ( X != zero_zero_nat )
% 5.15/5.42 => ~ ! [N: nat] :
% 5.15/5.42 ( X
% 5.15/5.42 != ( suc @ N ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % list_decode.cases
% 5.15/5.42 thf(fact_3720_max_Omono,axiom,
% 5.15/5.42 ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.15/5.42 => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 5.15/5.42 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.mono
% 5.15/5.42 thf(fact_3721_max_Omono,axiom,
% 5.15/5.42 ! [C: rat,A: rat,D: rat,B: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ C @ A )
% 5.15/5.42 => ( ( ord_less_eq_rat @ D @ B )
% 5.15/5.42 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.mono
% 5.15/5.42 thf(fact_3722_max_Omono,axiom,
% 5.15/5.42 ! [C: num,A: num,D: num,B: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ C @ A )
% 5.15/5.42 => ( ( ord_less_eq_num @ D @ B )
% 5.15/5.42 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.mono
% 5.15/5.42 thf(fact_3723_max_Omono,axiom,
% 5.15/5.42 ! [C: nat,A: nat,D: nat,B: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ C @ A )
% 5.15/5.42 => ( ( ord_less_eq_nat @ D @ B )
% 5.15/5.42 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.mono
% 5.15/5.42 thf(fact_3724_max_Omono,axiom,
% 5.15/5.42 ! [C: int,A: int,D: int,B: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ C @ A )
% 5.15/5.42 => ( ( ord_less_eq_int @ D @ B )
% 5.15/5.42 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.mono
% 5.15/5.42 thf(fact_3725_max_OorderE,axiom,
% 5.15/5.42 ! [B: extended_enat,A: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.15/5.42 => ( A
% 5.15/5.42 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderE
% 5.15/5.42 thf(fact_3726_max_OorderE,axiom,
% 5.15/5.42 ! [B: rat,A: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.42 => ( A
% 5.15/5.42 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderE
% 5.15/5.42 thf(fact_3727_max_OorderE,axiom,
% 5.15/5.42 ! [B: num,A: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ B @ A )
% 5.15/5.42 => ( A
% 5.15/5.42 = ( ord_max_num @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderE
% 5.15/5.42 thf(fact_3728_max_OorderE,axiom,
% 5.15/5.42 ! [B: nat,A: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.42 => ( A
% 5.15/5.42 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderE
% 5.15/5.42 thf(fact_3729_max_OorderE,axiom,
% 5.15/5.42 ! [B: int,A: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ B @ A )
% 5.15/5.42 => ( A
% 5.15/5.42 = ( ord_max_int @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderE
% 5.15/5.42 thf(fact_3730_max_OorderI,axiom,
% 5.15/5.42 ! [A: extended_enat,B: extended_enat] :
% 5.15/5.42 ( ( A
% 5.15/5.42 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.15/5.42 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderI
% 5.15/5.42 thf(fact_3731_max_OorderI,axiom,
% 5.15/5.42 ! [A: rat,B: rat] :
% 5.15/5.42 ( ( A
% 5.15/5.42 = ( ord_max_rat @ A @ B ) )
% 5.15/5.42 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderI
% 5.15/5.42 thf(fact_3732_max_OorderI,axiom,
% 5.15/5.42 ! [A: num,B: num] :
% 5.15/5.42 ( ( A
% 5.15/5.42 = ( ord_max_num @ A @ B ) )
% 5.15/5.42 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderI
% 5.15/5.42 thf(fact_3733_max_OorderI,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( A
% 5.15/5.42 = ( ord_max_nat @ A @ B ) )
% 5.15/5.42 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderI
% 5.15/5.42 thf(fact_3734_max_OorderI,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( A
% 5.15/5.42 = ( ord_max_int @ A @ B ) )
% 5.15/5.42 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.orderI
% 5.15/5.42 thf(fact_3735_max_OboundedE,axiom,
% 5.15/5.42 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.15/5.42 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedE
% 5.15/5.42 thf(fact_3736_max_OboundedE,axiom,
% 5.15/5.42 ! [B: rat,C: rat,A: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.42 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedE
% 5.15/5.42 thf(fact_3737_max_OboundedE,axiom,
% 5.15/5.42 ! [B: num,C: num,A: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.15/5.42 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedE
% 5.15/5.42 thf(fact_3738_max_OboundedE,axiom,
% 5.15/5.42 ! [B: nat,C: nat,A: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.42 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedE
% 5.15/5.42 thf(fact_3739_max_OboundedE,axiom,
% 5.15/5.42 ! [B: int,C: int,A: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.15/5.42 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedE
% 5.15/5.42 thf(fact_3740_max_OboundedI,axiom,
% 5.15/5.42 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.15/5.42 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.15/5.42 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedI
% 5.15/5.42 thf(fact_3741_max_OboundedI,axiom,
% 5.15/5.42 ! [B: rat,A: rat,C: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ B @ A )
% 5.15/5.42 => ( ( ord_less_eq_rat @ C @ A )
% 5.15/5.42 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedI
% 5.15/5.42 thf(fact_3742_max_OboundedI,axiom,
% 5.15/5.42 ! [B: num,A: num,C: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ B @ A )
% 5.15/5.42 => ( ( ord_less_eq_num @ C @ A )
% 5.15/5.42 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedI
% 5.15/5.42 thf(fact_3743_max_OboundedI,axiom,
% 5.15/5.42 ! [B: nat,A: nat,C: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ B @ A )
% 5.15/5.42 => ( ( ord_less_eq_nat @ C @ A )
% 5.15/5.42 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedI
% 5.15/5.42 thf(fact_3744_max_OboundedI,axiom,
% 5.15/5.42 ! [B: int,A: int,C: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ B @ A )
% 5.15/5.42 => ( ( ord_less_eq_int @ C @ A )
% 5.15/5.42 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.boundedI
% 5.15/5.42 thf(fact_3745_max_Oorder__iff,axiom,
% 5.15/5.42 ( ord_le2932123472753598470d_enat
% 5.15/5.42 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.15/5.42 ( A3
% 5.15/5.42 = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.order_iff
% 5.15/5.42 thf(fact_3746_max_Oorder__iff,axiom,
% 5.15/5.42 ( ord_less_eq_rat
% 5.15/5.42 = ( ^ [B2: rat,A3: rat] :
% 5.15/5.42 ( A3
% 5.15/5.42 = ( ord_max_rat @ A3 @ B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.order_iff
% 5.15/5.42 thf(fact_3747_max_Oorder__iff,axiom,
% 5.15/5.42 ( ord_less_eq_num
% 5.15/5.42 = ( ^ [B2: num,A3: num] :
% 5.15/5.42 ( A3
% 5.15/5.42 = ( ord_max_num @ A3 @ B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.order_iff
% 5.15/5.42 thf(fact_3748_max_Oorder__iff,axiom,
% 5.15/5.42 ( ord_less_eq_nat
% 5.15/5.42 = ( ^ [B2: nat,A3: nat] :
% 5.15/5.42 ( A3
% 5.15/5.42 = ( ord_max_nat @ A3 @ B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.order_iff
% 5.15/5.42 thf(fact_3749_max_Oorder__iff,axiom,
% 5.15/5.42 ( ord_less_eq_int
% 5.15/5.42 = ( ^ [B2: int,A3: int] :
% 5.15/5.42 ( A3
% 5.15/5.42 = ( ord_max_int @ A3 @ B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.order_iff
% 5.15/5.42 thf(fact_3750_max_Ocobounded1,axiom,
% 5.15/5.42 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded1
% 5.15/5.42 thf(fact_3751_max_Ocobounded1,axiom,
% 5.15/5.42 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded1
% 5.15/5.42 thf(fact_3752_max_Ocobounded1,axiom,
% 5.15/5.42 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded1
% 5.15/5.42 thf(fact_3753_max_Ocobounded1,axiom,
% 5.15/5.42 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded1
% 5.15/5.42 thf(fact_3754_max_Ocobounded1,axiom,
% 5.15/5.42 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded1
% 5.15/5.42 thf(fact_3755_max_Ocobounded2,axiom,
% 5.15/5.42 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded2
% 5.15/5.42 thf(fact_3756_max_Ocobounded2,axiom,
% 5.15/5.42 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded2
% 5.15/5.42 thf(fact_3757_max_Ocobounded2,axiom,
% 5.15/5.42 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded2
% 5.15/5.42 thf(fact_3758_max_Ocobounded2,axiom,
% 5.15/5.42 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded2
% 5.15/5.42 thf(fact_3759_max_Ocobounded2,axiom,
% 5.15/5.42 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.cobounded2
% 5.15/5.42 thf(fact_3760_le__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 5.15/5.42 = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 5.15/5.42 | ( ord_le2932123472753598470d_enat @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % le_max_iff_disj
% 5.15/5.42 thf(fact_3761_le__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_eq_rat @ Z @ X )
% 5.15/5.42 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % le_max_iff_disj
% 5.15/5.42 thf(fact_3762_le__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: num,X: num,Y: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_eq_num @ Z @ X )
% 5.15/5.42 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % le_max_iff_disj
% 5.15/5.42 thf(fact_3763_le__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: nat,X: nat,Y: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_eq_nat @ Z @ X )
% 5.15/5.42 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % le_max_iff_disj
% 5.15/5.42 thf(fact_3764_le__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: int,X: int,Y: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_eq_int @ Z @ X )
% 5.15/5.42 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % le_max_iff_disj
% 5.15/5.42 thf(fact_3765_max_Oabsorb__iff1,axiom,
% 5.15/5.42 ( ord_le2932123472753598470d_enat
% 5.15/5.42 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 5.15/5.42 = A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff1
% 5.15/5.42 thf(fact_3766_max_Oabsorb__iff1,axiom,
% 5.15/5.42 ( ord_less_eq_rat
% 5.15/5.42 = ( ^ [B2: rat,A3: rat] :
% 5.15/5.42 ( ( ord_max_rat @ A3 @ B2 )
% 5.15/5.42 = A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff1
% 5.15/5.42 thf(fact_3767_max_Oabsorb__iff1,axiom,
% 5.15/5.42 ( ord_less_eq_num
% 5.15/5.42 = ( ^ [B2: num,A3: num] :
% 5.15/5.42 ( ( ord_max_num @ A3 @ B2 )
% 5.15/5.42 = A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff1
% 5.15/5.42 thf(fact_3768_max_Oabsorb__iff1,axiom,
% 5.15/5.42 ( ord_less_eq_nat
% 5.15/5.42 = ( ^ [B2: nat,A3: nat] :
% 5.15/5.42 ( ( ord_max_nat @ A3 @ B2 )
% 5.15/5.42 = A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff1
% 5.15/5.42 thf(fact_3769_max_Oabsorb__iff1,axiom,
% 5.15/5.42 ( ord_less_eq_int
% 5.15/5.42 = ( ^ [B2: int,A3: int] :
% 5.15/5.42 ( ( ord_max_int @ A3 @ B2 )
% 5.15/5.42 = A3 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff1
% 5.15/5.42 thf(fact_3770_max_Oabsorb__iff2,axiom,
% 5.15/5.42 ( ord_le2932123472753598470d_enat
% 5.15/5.42 = ( ^ [A3: extended_enat,B2: extended_enat] :
% 5.15/5.42 ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 5.15/5.42 = B2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff2
% 5.15/5.42 thf(fact_3771_max_Oabsorb__iff2,axiom,
% 5.15/5.42 ( ord_less_eq_rat
% 5.15/5.42 = ( ^ [A3: rat,B2: rat] :
% 5.15/5.42 ( ( ord_max_rat @ A3 @ B2 )
% 5.15/5.42 = B2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff2
% 5.15/5.42 thf(fact_3772_max_Oabsorb__iff2,axiom,
% 5.15/5.42 ( ord_less_eq_num
% 5.15/5.42 = ( ^ [A3: num,B2: num] :
% 5.15/5.42 ( ( ord_max_num @ A3 @ B2 )
% 5.15/5.42 = B2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff2
% 5.15/5.42 thf(fact_3773_max_Oabsorb__iff2,axiom,
% 5.15/5.42 ( ord_less_eq_nat
% 5.15/5.42 = ( ^ [A3: nat,B2: nat] :
% 5.15/5.42 ( ( ord_max_nat @ A3 @ B2 )
% 5.15/5.42 = B2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff2
% 5.15/5.42 thf(fact_3774_max_Oabsorb__iff2,axiom,
% 5.15/5.42 ( ord_less_eq_int
% 5.15/5.42 = ( ^ [A3: int,B2: int] :
% 5.15/5.42 ( ( ord_max_int @ A3 @ B2 )
% 5.15/5.42 = B2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.absorb_iff2
% 5.15/5.42 thf(fact_3775_max_OcoboundedI1,axiom,
% 5.15/5.42 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.15/5.42 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI1
% 5.15/5.42 thf(fact_3776_max_OcoboundedI1,axiom,
% 5.15/5.42 ! [C: rat,A: rat,B: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ C @ A )
% 5.15/5.42 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI1
% 5.15/5.42 thf(fact_3777_max_OcoboundedI1,axiom,
% 5.15/5.42 ! [C: num,A: num,B: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ C @ A )
% 5.15/5.42 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI1
% 5.15/5.42 thf(fact_3778_max_OcoboundedI1,axiom,
% 5.15/5.42 ! [C: nat,A: nat,B: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ C @ A )
% 5.15/5.42 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI1
% 5.15/5.42 thf(fact_3779_max_OcoboundedI1,axiom,
% 5.15/5.42 ! [C: int,A: int,B: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ C @ A )
% 5.15/5.42 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI1
% 5.15/5.42 thf(fact_3780_max_OcoboundedI2,axiom,
% 5.15/5.42 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.15/5.42 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.15/5.42 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI2
% 5.15/5.42 thf(fact_3781_max_OcoboundedI2,axiom,
% 5.15/5.42 ! [C: rat,B: rat,A: rat] :
% 5.15/5.42 ( ( ord_less_eq_rat @ C @ B )
% 5.15/5.42 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI2
% 5.15/5.42 thf(fact_3782_max_OcoboundedI2,axiom,
% 5.15/5.42 ! [C: num,B: num,A: num] :
% 5.15/5.42 ( ( ord_less_eq_num @ C @ B )
% 5.15/5.42 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI2
% 5.15/5.42 thf(fact_3783_max_OcoboundedI2,axiom,
% 5.15/5.42 ! [C: nat,B: nat,A: nat] :
% 5.15/5.42 ( ( ord_less_eq_nat @ C @ B )
% 5.15/5.42 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI2
% 5.15/5.42 thf(fact_3784_max_OcoboundedI2,axiom,
% 5.15/5.42 ! [C: int,B: int,A: int] :
% 5.15/5.42 ( ( ord_less_eq_int @ C @ B )
% 5.15/5.42 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.coboundedI2
% 5.15/5.42 thf(fact_3785_max_Ostrict__coboundedI2,axiom,
% 5.15/5.42 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.15/5.42 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.15/5.42 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI2
% 5.15/5.42 thf(fact_3786_max_Ostrict__coboundedI2,axiom,
% 5.15/5.42 ! [C: real,B: real,A: real] :
% 5.15/5.42 ( ( ord_less_real @ C @ B )
% 5.15/5.42 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI2
% 5.15/5.42 thf(fact_3787_max_Ostrict__coboundedI2,axiom,
% 5.15/5.42 ! [C: rat,B: rat,A: rat] :
% 5.15/5.42 ( ( ord_less_rat @ C @ B )
% 5.15/5.42 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI2
% 5.15/5.42 thf(fact_3788_max_Ostrict__coboundedI2,axiom,
% 5.15/5.42 ! [C: num,B: num,A: num] :
% 5.15/5.42 ( ( ord_less_num @ C @ B )
% 5.15/5.42 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI2
% 5.15/5.42 thf(fact_3789_max_Ostrict__coboundedI2,axiom,
% 5.15/5.42 ! [C: nat,B: nat,A: nat] :
% 5.15/5.42 ( ( ord_less_nat @ C @ B )
% 5.15/5.42 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI2
% 5.15/5.42 thf(fact_3790_max_Ostrict__coboundedI2,axiom,
% 5.15/5.42 ! [C: int,B: int,A: int] :
% 5.15/5.42 ( ( ord_less_int @ C @ B )
% 5.15/5.42 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI2
% 5.15/5.42 thf(fact_3791_max_Ostrict__coboundedI1,axiom,
% 5.15/5.42 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.15/5.42 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.15/5.42 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI1
% 5.15/5.42 thf(fact_3792_max_Ostrict__coboundedI1,axiom,
% 5.15/5.42 ! [C: real,A: real,B: real] :
% 5.15/5.42 ( ( ord_less_real @ C @ A )
% 5.15/5.42 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI1
% 5.15/5.42 thf(fact_3793_max_Ostrict__coboundedI1,axiom,
% 5.15/5.42 ! [C: rat,A: rat,B: rat] :
% 5.15/5.42 ( ( ord_less_rat @ C @ A )
% 5.15/5.42 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI1
% 5.15/5.42 thf(fact_3794_max_Ostrict__coboundedI1,axiom,
% 5.15/5.42 ! [C: num,A: num,B: num] :
% 5.15/5.42 ( ( ord_less_num @ C @ A )
% 5.15/5.42 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI1
% 5.15/5.42 thf(fact_3795_max_Ostrict__coboundedI1,axiom,
% 5.15/5.42 ! [C: nat,A: nat,B: nat] :
% 5.15/5.42 ( ( ord_less_nat @ C @ A )
% 5.15/5.42 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI1
% 5.15/5.42 thf(fact_3796_max_Ostrict__coboundedI1,axiom,
% 5.15/5.42 ! [C: int,A: int,B: int] :
% 5.15/5.42 ( ( ord_less_int @ C @ A )
% 5.15/5.42 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_coboundedI1
% 5.15/5.42 thf(fact_3797_max_Ostrict__order__iff,axiom,
% 5.15/5.42 ( ord_le72135733267957522d_enat
% 5.15/5.42 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.15/5.42 ( ( A3
% 5.15/5.42 = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) )
% 5.15/5.42 & ( A3 != B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_order_iff
% 5.15/5.42 thf(fact_3798_max_Ostrict__order__iff,axiom,
% 5.15/5.42 ( ord_less_real
% 5.15/5.42 = ( ^ [B2: real,A3: real] :
% 5.15/5.42 ( ( A3
% 5.15/5.42 = ( ord_max_real @ A3 @ B2 ) )
% 5.15/5.42 & ( A3 != B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_order_iff
% 5.15/5.42 thf(fact_3799_max_Ostrict__order__iff,axiom,
% 5.15/5.42 ( ord_less_rat
% 5.15/5.42 = ( ^ [B2: rat,A3: rat] :
% 5.15/5.42 ( ( A3
% 5.15/5.42 = ( ord_max_rat @ A3 @ B2 ) )
% 5.15/5.42 & ( A3 != B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_order_iff
% 5.15/5.42 thf(fact_3800_max_Ostrict__order__iff,axiom,
% 5.15/5.42 ( ord_less_num
% 5.15/5.42 = ( ^ [B2: num,A3: num] :
% 5.15/5.42 ( ( A3
% 5.15/5.42 = ( ord_max_num @ A3 @ B2 ) )
% 5.15/5.42 & ( A3 != B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_order_iff
% 5.15/5.42 thf(fact_3801_max_Ostrict__order__iff,axiom,
% 5.15/5.42 ( ord_less_nat
% 5.15/5.42 = ( ^ [B2: nat,A3: nat] :
% 5.15/5.42 ( ( A3
% 5.15/5.42 = ( ord_max_nat @ A3 @ B2 ) )
% 5.15/5.42 & ( A3 != B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_order_iff
% 5.15/5.42 thf(fact_3802_max_Ostrict__order__iff,axiom,
% 5.15/5.42 ( ord_less_int
% 5.15/5.42 = ( ^ [B2: int,A3: int] :
% 5.15/5.42 ( ( A3
% 5.15/5.42 = ( ord_max_int @ A3 @ B2 ) )
% 5.15/5.42 & ( A3 != B2 ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_order_iff
% 5.15/5.42 thf(fact_3803_max_Ostrict__boundedE,axiom,
% 5.15/5.42 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.15/5.42 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.15/5.42 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_boundedE
% 5.15/5.42 thf(fact_3804_max_Ostrict__boundedE,axiom,
% 5.15/5.42 ! [B: real,C: real,A: real] :
% 5.15/5.42 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_real @ B @ A )
% 5.15/5.42 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_boundedE
% 5.15/5.42 thf(fact_3805_max_Ostrict__boundedE,axiom,
% 5.15/5.42 ! [B: rat,C: rat,A: rat] :
% 5.15/5.42 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_rat @ B @ A )
% 5.15/5.42 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_boundedE
% 5.15/5.42 thf(fact_3806_max_Ostrict__boundedE,axiom,
% 5.15/5.42 ! [B: num,C: num,A: num] :
% 5.15/5.42 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_num @ B @ A )
% 5.15/5.42 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_boundedE
% 5.15/5.42 thf(fact_3807_max_Ostrict__boundedE,axiom,
% 5.15/5.42 ! [B: nat,C: nat,A: nat] :
% 5.15/5.42 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_nat @ B @ A )
% 5.15/5.42 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_boundedE
% 5.15/5.42 thf(fact_3808_max_Ostrict__boundedE,axiom,
% 5.15/5.42 ! [B: int,C: int,A: int] :
% 5.15/5.42 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.15/5.42 => ~ ( ( ord_less_int @ B @ A )
% 5.15/5.42 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % max.strict_boundedE
% 5.15/5.42 thf(fact_3809_less__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 5.15/5.42 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 5.15/5.42 = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 5.15/5.42 | ( ord_le72135733267957522d_enat @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % less_max_iff_disj
% 5.15/5.42 thf(fact_3810_less__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: real,X: real,Y: real] :
% 5.15/5.42 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_real @ Z @ X )
% 5.15/5.42 | ( ord_less_real @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % less_max_iff_disj
% 5.15/5.42 thf(fact_3811_less__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.42 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_rat @ Z @ X )
% 5.15/5.42 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % less_max_iff_disj
% 5.15/5.42 thf(fact_3812_less__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: num,X: num,Y: num] :
% 5.15/5.42 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_num @ Z @ X )
% 5.15/5.42 | ( ord_less_num @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % less_max_iff_disj
% 5.15/5.42 thf(fact_3813_less__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: nat,X: nat,Y: nat] :
% 5.15/5.42 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_nat @ Z @ X )
% 5.15/5.42 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % less_max_iff_disj
% 5.15/5.42 thf(fact_3814_less__max__iff__disj,axiom,
% 5.15/5.42 ! [Z: int,X: int,Y: int] :
% 5.15/5.42 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 5.15/5.42 = ( ( ord_less_int @ Z @ X )
% 5.15/5.42 | ( ord_less_int @ Z @ Y ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % less_max_iff_disj
% 5.15/5.42 thf(fact_3815_triangle__def,axiom,
% 5.15/5.42 ( nat_triangle
% 5.15/5.42 = ( ^ [N3: nat] : ( divide_divide_nat @ ( times_times_nat @ N3 @ ( suc @ N3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % triangle_def
% 5.15/5.42 thf(fact_3816_even__succ__mod__exp,axiom,
% 5.15/5.42 ! [A: nat,N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.42 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_succ_mod_exp
% 5.15/5.42 thf(fact_3817_even__succ__mod__exp,axiom,
% 5.15/5.42 ! [A: int,N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.42 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_succ_mod_exp
% 5.15/5.42 thf(fact_3818_even__succ__mod__exp,axiom,
% 5.15/5.42 ! [A: code_integer,N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.42 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_succ_mod_exp
% 5.15/5.42 thf(fact_3819_divmod__algorithm__code_I6_J,axiom,
% 5.15/5.42 ! [M: num,N2: num] :
% 5.15/5.42 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.42 = ( produc4245557441103728435nt_int
% 5.15/5.42 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.15/5.42 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % divmod_algorithm_code(6)
% 5.15/5.42 thf(fact_3820_divmod__algorithm__code_I6_J,axiom,
% 5.15/5.42 ! [M: num,N2: num] :
% 5.15/5.42 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.42 = ( produc2626176000494625587at_nat
% 5.15/5.42 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.15/5.42 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % divmod_algorithm_code(6)
% 5.15/5.42 thf(fact_3821_divmod__algorithm__code_I6_J,axiom,
% 5.15/5.42 ! [M: num,N2: num] :
% 5.15/5.42 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.42 = ( produc6916734918728496179nteger
% 5.15/5.42 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.15/5.42 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % divmod_algorithm_code(6)
% 5.15/5.42 thf(fact_3822_even__succ__div__exp,axiom,
% 5.15/5.42 ! [A: code_integer,N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.42 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_succ_div_exp
% 5.15/5.42 thf(fact_3823_even__succ__div__exp,axiom,
% 5.15/5.42 ! [A: nat,N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.42 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_succ_div_exp
% 5.15/5.42 thf(fact_3824_even__succ__div__exp,axiom,
% 5.15/5.42 ! [A: int,N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.42 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_succ_div_exp
% 5.15/5.42 thf(fact_3825_option_Osize__gen_I2_J,axiom,
% 5.15/5.42 ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.15/5.42 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.15/5.42 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % option.size_gen(2)
% 5.15/5.42 thf(fact_3826_option_Osize__gen_I2_J,axiom,
% 5.15/5.42 ! [X: nat > nat,X22: nat] :
% 5.15/5.42 ( ( size_option_nat @ X @ ( some_nat @ X22 ) )
% 5.15/5.42 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % option.size_gen(2)
% 5.15/5.42 thf(fact_3827_option_Osize__gen_I2_J,axiom,
% 5.15/5.42 ! [X: num > nat,X22: num] :
% 5.15/5.42 ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 5.15/5.42 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % option.size_gen(2)
% 5.15/5.42 thf(fact_3828_signed__take__bit__Suc,axiom,
% 5.15/5.42 ! [N2: nat,A: code_integer] :
% 5.15/5.42 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 5.15/5.42 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % signed_take_bit_Suc
% 5.15/5.42 thf(fact_3829_signed__take__bit__Suc,axiom,
% 5.15/5.42 ! [N2: nat,A: int] :
% 5.15/5.42 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 5.15/5.42 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % signed_take_bit_Suc
% 5.15/5.42 thf(fact_3830_set__decode__Suc,axiom,
% 5.15/5.42 ! [N2: nat,X: nat] :
% 5.15/5.42 ( ( member_nat @ ( suc @ N2 ) @ ( nat_set_decode @ X ) )
% 5.15/5.42 = ( member_nat @ N2 @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % set_decode_Suc
% 5.15/5.42 thf(fact_3831_nat__dvd__1__iff__1,axiom,
% 5.15/5.42 ! [M: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.15/5.42 = ( M = one_one_nat ) ) ).
% 5.15/5.42
% 5.15/5.42 % nat_dvd_1_iff_1
% 5.15/5.42 thf(fact_3832_dvd__0__left__iff,axiom,
% 5.15/5.42 ! [A: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.15/5.42 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_left_iff
% 5.15/5.42 thf(fact_3833_dvd__0__left__iff,axiom,
% 5.15/5.42 ! [A: complex] :
% 5.15/5.42 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.15/5.42 = ( A = zero_zero_complex ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_left_iff
% 5.15/5.42 thf(fact_3834_dvd__0__left__iff,axiom,
% 5.15/5.42 ! [A: real] :
% 5.15/5.42 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.15/5.42 = ( A = zero_zero_real ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_left_iff
% 5.15/5.42 thf(fact_3835_dvd__0__left__iff,axiom,
% 5.15/5.42 ! [A: rat] :
% 5.15/5.42 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.15/5.42 = ( A = zero_zero_rat ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_left_iff
% 5.15/5.42 thf(fact_3836_dvd__0__left__iff,axiom,
% 5.15/5.42 ! [A: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.15/5.42 = ( A = zero_zero_nat ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_left_iff
% 5.15/5.42 thf(fact_3837_dvd__0__left__iff,axiom,
% 5.15/5.42 ! [A: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.15/5.42 = ( A = zero_zero_int ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_left_iff
% 5.15/5.42 thf(fact_3838_dvd__0__right,axiom,
% 5.15/5.42 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_right
% 5.15/5.42 thf(fact_3839_dvd__0__right,axiom,
% 5.15/5.42 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_right
% 5.15/5.42 thf(fact_3840_dvd__0__right,axiom,
% 5.15/5.42 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_right
% 5.15/5.42 thf(fact_3841_dvd__0__right,axiom,
% 5.15/5.42 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_right
% 5.15/5.42 thf(fact_3842_dvd__0__right,axiom,
% 5.15/5.42 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_right
% 5.15/5.42 thf(fact_3843_dvd__0__right,axiom,
% 5.15/5.42 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_0_right
% 5.15/5.42 thf(fact_3844_dvd__1__left,axiom,
% 5.15/5.42 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_1_left
% 5.15/5.42 thf(fact_3845_dvd__1__iff__1,axiom,
% 5.15/5.42 ! [M: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.15/5.42 = ( M
% 5.15/5.42 = ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_1_iff_1
% 5.15/5.42 thf(fact_3846_dvd__add__triv__right__iff,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.15/5.42 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_right_iff
% 5.15/5.42 thf(fact_3847_dvd__add__triv__right__iff,axiom,
% 5.15/5.42 ! [A: real,B: real] :
% 5.15/5.42 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.15/5.42 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_right_iff
% 5.15/5.42 thf(fact_3848_dvd__add__triv__right__iff,axiom,
% 5.15/5.42 ! [A: rat,B: rat] :
% 5.15/5.42 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.15/5.42 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_right_iff
% 5.15/5.42 thf(fact_3849_dvd__add__triv__right__iff,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.15/5.42 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_right_iff
% 5.15/5.42 thf(fact_3850_dvd__add__triv__right__iff,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.15/5.42 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_right_iff
% 5.15/5.42 thf(fact_3851_dvd__add__triv__right__iff,axiom,
% 5.15/5.42 ! [A: complex,B: complex] :
% 5.15/5.42 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ A ) )
% 5.15/5.42 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_right_iff
% 5.15/5.42 thf(fact_3852_dvd__add__triv__left__iff,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.15/5.42 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_left_iff
% 5.15/5.42 thf(fact_3853_dvd__add__triv__left__iff,axiom,
% 5.15/5.42 ! [A: real,B: real] :
% 5.15/5.42 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.15/5.42 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_left_iff
% 5.15/5.42 thf(fact_3854_dvd__add__triv__left__iff,axiom,
% 5.15/5.42 ! [A: rat,B: rat] :
% 5.15/5.42 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.15/5.42 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_left_iff
% 5.15/5.42 thf(fact_3855_dvd__add__triv__left__iff,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.15/5.42 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_left_iff
% 5.15/5.42 thf(fact_3856_dvd__add__triv__left__iff,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.15/5.42 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_left_iff
% 5.15/5.42 thf(fact_3857_dvd__add__triv__left__iff,axiom,
% 5.15/5.42 ! [A: complex,B: complex] :
% 5.15/5.42 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.15/5.42 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_triv_left_iff
% 5.15/5.42 thf(fact_3858_div__dvd__div,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.42 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.15/5.42 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.15/5.42 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_dvd_div
% 5.15/5.42 thf(fact_3859_div__dvd__div,axiom,
% 5.15/5.42 ! [A: nat,B: nat,C: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.42 => ( ( dvd_dvd_nat @ A @ C )
% 5.15/5.42 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.15/5.42 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_dvd_div
% 5.15/5.42 thf(fact_3860_div__dvd__div,axiom,
% 5.15/5.42 ! [A: int,B: int,C: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.42 => ( ( dvd_dvd_int @ A @ C )
% 5.15/5.42 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.15/5.42 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_dvd_div
% 5.15/5.42 thf(fact_3861_nat__mult__dvd__cancel__disj,axiom,
% 5.15/5.42 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.42 = ( ( K = zero_zero_nat )
% 5.15/5.42 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % nat_mult_dvd_cancel_disj
% 5.15/5.42 thf(fact_3862_signed__take__bit__of__0,axiom,
% 5.15/5.42 ! [N2: nat] :
% 5.15/5.42 ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 5.15/5.42 = zero_zero_int ) ).
% 5.15/5.42
% 5.15/5.42 % signed_take_bit_of_0
% 5.15/5.42 thf(fact_3863_case__prod__conv,axiom,
% 5.15/5.42 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.15/5.42 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.15/5.42 = ( F @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % case_prod_conv
% 5.15/5.42 thf(fact_3864_case__prod__conv,axiom,
% 5.15/5.42 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.15/5.42 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.15/5.42 = ( F @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % case_prod_conv
% 5.15/5.42 thf(fact_3865_case__prod__conv,axiom,
% 5.15/5.42 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.15/5.42 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.15/5.42 = ( F @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % case_prod_conv
% 5.15/5.42 thf(fact_3866_case__prod__conv,axiom,
% 5.15/5.42 ! [F: int > int > $o,A: int,B: int] :
% 5.15/5.42 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.15/5.42 = ( F @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % case_prod_conv
% 5.15/5.42 thf(fact_3867_case__prod__conv,axiom,
% 5.15/5.42 ! [F: int > int > int,A: int,B: int] :
% 5.15/5.42 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.15/5.42 = ( F @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % case_prod_conv
% 5.15/5.42 thf(fact_3868_dvd__times__right__cancel__iff,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.42 ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.42 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.15/5.42 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_times_right_cancel_iff
% 5.15/5.42 thf(fact_3869_dvd__times__right__cancel__iff,axiom,
% 5.15/5.42 ! [A: nat,B: nat,C: nat] :
% 5.15/5.42 ( ( A != zero_zero_nat )
% 5.15/5.42 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.15/5.42 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_times_right_cancel_iff
% 5.15/5.42 thf(fact_3870_dvd__times__right__cancel__iff,axiom,
% 5.15/5.42 ! [A: int,B: int,C: int] :
% 5.15/5.42 ( ( A != zero_zero_int )
% 5.15/5.42 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.15/5.42 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_times_right_cancel_iff
% 5.15/5.42 thf(fact_3871_dvd__times__left__cancel__iff,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.42 ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.42 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.15/5.42 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_times_left_cancel_iff
% 5.15/5.42 thf(fact_3872_dvd__times__left__cancel__iff,axiom,
% 5.15/5.42 ! [A: nat,B: nat,C: nat] :
% 5.15/5.42 ( ( A != zero_zero_nat )
% 5.15/5.42 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.15/5.42 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_times_left_cancel_iff
% 5.15/5.42 thf(fact_3873_dvd__times__left__cancel__iff,axiom,
% 5.15/5.42 ! [A: int,B: int,C: int] :
% 5.15/5.42 ( ( A != zero_zero_int )
% 5.15/5.42 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.15/5.42 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_times_left_cancel_iff
% 5.15/5.42 thf(fact_3874_dvd__mult__cancel__right,axiom,
% 5.15/5.42 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.15/5.42 = ( ( C = zero_z3403309356797280102nteger )
% 5.15/5.42 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_right
% 5.15/5.42 thf(fact_3875_dvd__mult__cancel__right,axiom,
% 5.15/5.42 ! [A: complex,C: complex,B: complex] :
% 5.15/5.42 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.15/5.42 = ( ( C = zero_zero_complex )
% 5.15/5.42 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_right
% 5.15/5.42 thf(fact_3876_dvd__mult__cancel__right,axiom,
% 5.15/5.42 ! [A: real,C: real,B: real] :
% 5.15/5.42 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.15/5.42 = ( ( C = zero_zero_real )
% 5.15/5.42 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_right
% 5.15/5.42 thf(fact_3877_dvd__mult__cancel__right,axiom,
% 5.15/5.42 ! [A: rat,C: rat,B: rat] :
% 5.15/5.42 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.15/5.42 = ( ( C = zero_zero_rat )
% 5.15/5.42 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_right
% 5.15/5.42 thf(fact_3878_dvd__mult__cancel__right,axiom,
% 5.15/5.42 ! [A: int,C: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.15/5.42 = ( ( C = zero_zero_int )
% 5.15/5.42 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_right
% 5.15/5.42 thf(fact_3879_dvd__mult__cancel__left,axiom,
% 5.15/5.42 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.15/5.42 = ( ( C = zero_z3403309356797280102nteger )
% 5.15/5.42 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_left
% 5.15/5.42 thf(fact_3880_dvd__mult__cancel__left,axiom,
% 5.15/5.42 ! [C: complex,A: complex,B: complex] :
% 5.15/5.42 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.15/5.42 = ( ( C = zero_zero_complex )
% 5.15/5.42 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_left
% 5.15/5.42 thf(fact_3881_dvd__mult__cancel__left,axiom,
% 5.15/5.42 ! [C: real,A: real,B: real] :
% 5.15/5.42 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.15/5.42 = ( ( C = zero_zero_real )
% 5.15/5.42 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_left
% 5.15/5.42 thf(fact_3882_dvd__mult__cancel__left,axiom,
% 5.15/5.42 ! [C: rat,A: rat,B: rat] :
% 5.15/5.42 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.15/5.42 = ( ( C = zero_zero_rat )
% 5.15/5.42 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_left
% 5.15/5.42 thf(fact_3883_dvd__mult__cancel__left,axiom,
% 5.15/5.42 ! [C: int,A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.42 = ( ( C = zero_zero_int )
% 5.15/5.42 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_cancel_left
% 5.15/5.42 thf(fact_3884_unit__prod,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.42 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.42 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_prod
% 5.15/5.42 thf(fact_3885_unit__prod,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.42 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.42 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_prod
% 5.15/5.42 thf(fact_3886_unit__prod,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.42 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.42 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_prod
% 5.15/5.42 thf(fact_3887_dvd__add__times__triv__right__iff,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.15/5.42 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_right_iff
% 5.15/5.42 thf(fact_3888_dvd__add__times__triv__right__iff,axiom,
% 5.15/5.42 ! [A: complex,B: complex,C: complex] :
% 5.15/5.42 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 5.15/5.42 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_right_iff
% 5.15/5.42 thf(fact_3889_dvd__add__times__triv__right__iff,axiom,
% 5.15/5.42 ! [A: real,B: real,C: real] :
% 5.15/5.42 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.15/5.42 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_right_iff
% 5.15/5.42 thf(fact_3890_dvd__add__times__triv__right__iff,axiom,
% 5.15/5.42 ! [A: rat,B: rat,C: rat] :
% 5.15/5.42 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.15/5.42 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_right_iff
% 5.15/5.42 thf(fact_3891_dvd__add__times__triv__right__iff,axiom,
% 5.15/5.42 ! [A: nat,B: nat,C: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.15/5.42 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_right_iff
% 5.15/5.42 thf(fact_3892_dvd__add__times__triv__right__iff,axiom,
% 5.15/5.42 ! [A: int,B: int,C: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.15/5.42 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_right_iff
% 5.15/5.42 thf(fact_3893_dvd__add__times__triv__left__iff,axiom,
% 5.15/5.42 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.15/5.42 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_left_iff
% 5.15/5.42 thf(fact_3894_dvd__add__times__triv__left__iff,axiom,
% 5.15/5.42 ! [A: complex,C: complex,B: complex] :
% 5.15/5.42 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 5.15/5.42 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_left_iff
% 5.15/5.42 thf(fact_3895_dvd__add__times__triv__left__iff,axiom,
% 5.15/5.42 ! [A: real,C: real,B: real] :
% 5.15/5.42 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.15/5.42 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_left_iff
% 5.15/5.42 thf(fact_3896_dvd__add__times__triv__left__iff,axiom,
% 5.15/5.42 ! [A: rat,C: rat,B: rat] :
% 5.15/5.42 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.15/5.42 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_left_iff
% 5.15/5.42 thf(fact_3897_dvd__add__times__triv__left__iff,axiom,
% 5.15/5.42 ! [A: nat,C: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.15/5.42 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_left_iff
% 5.15/5.42 thf(fact_3898_dvd__add__times__triv__left__iff,axiom,
% 5.15/5.42 ! [A: int,C: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.15/5.42 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_add_times_triv_left_iff
% 5.15/5.42 thf(fact_3899_dvd__mult__div__cancel,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.42 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_div_cancel
% 5.15/5.42 thf(fact_3900_dvd__mult__div__cancel,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.42 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_div_cancel
% 5.15/5.42 thf(fact_3901_dvd__mult__div__cancel,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.42 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_mult_div_cancel
% 5.15/5.42 thf(fact_3902_dvd__div__mult__self,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.42 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_div_mult_self
% 5.15/5.42 thf(fact_3903_dvd__div__mult__self,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.42 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_div_mult_self
% 5.15/5.42 thf(fact_3904_dvd__div__mult__self,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.42 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_div_mult_self
% 5.15/5.42 thf(fact_3905_unit__div__1__div__1,axiom,
% 5.15/5.42 ! [A: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.42 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_1_div_1
% 5.15/5.42 thf(fact_3906_unit__div__1__div__1,axiom,
% 5.15/5.42 ! [A: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.42 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_1_div_1
% 5.15/5.42 thf(fact_3907_unit__div__1__div__1,axiom,
% 5.15/5.42 ! [A: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.42 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.15/5.42 = A ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_1_div_1
% 5.15/5.42 thf(fact_3908_unit__div__1__unit,axiom,
% 5.15/5.42 ! [A: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.42 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_1_unit
% 5.15/5.42 thf(fact_3909_unit__div__1__unit,axiom,
% 5.15/5.42 ! [A: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.42 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_1_unit
% 5.15/5.42 thf(fact_3910_unit__div__1__unit,axiom,
% 5.15/5.42 ! [A: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.42 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_1_unit
% 5.15/5.42 thf(fact_3911_unit__div,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.42 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.42 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div
% 5.15/5.42 thf(fact_3912_unit__div,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.42 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.42 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div
% 5.15/5.42 thf(fact_3913_unit__div,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.42 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.42 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div
% 5.15/5.42 thf(fact_3914_div__add,axiom,
% 5.15/5.42 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.15/5.42 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.42 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.15/5.42 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_add
% 5.15/5.42 thf(fact_3915_div__add,axiom,
% 5.15/5.42 ! [C: nat,A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ C @ A )
% 5.15/5.42 => ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.42 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.42 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_add
% 5.15/5.42 thf(fact_3916_div__add,axiom,
% 5.15/5.42 ! [C: int,A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ C @ A )
% 5.15/5.42 => ( ( dvd_dvd_int @ C @ B )
% 5.15/5.42 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.42 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_add
% 5.15/5.42 thf(fact_3917_div__diff,axiom,
% 5.15/5.42 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.15/5.42 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.42 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.15/5.42 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_diff
% 5.15/5.42 thf(fact_3918_div__diff,axiom,
% 5.15/5.42 ! [C: int,A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ C @ A )
% 5.15/5.42 => ( ( dvd_dvd_int @ C @ B )
% 5.15/5.42 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.15/5.42 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % div_diff
% 5.15/5.42 thf(fact_3919_dvd__imp__mod__0,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.42 => ( ( modulo_modulo_nat @ B @ A )
% 5.15/5.42 = zero_zero_nat ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_imp_mod_0
% 5.15/5.42 thf(fact_3920_dvd__imp__mod__0,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.42 => ( ( modulo_modulo_int @ B @ A )
% 5.15/5.42 = zero_zero_int ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_imp_mod_0
% 5.15/5.42 thf(fact_3921_dvd__imp__mod__0,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.42 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.15/5.42 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.42
% 5.15/5.42 % dvd_imp_mod_0
% 5.15/5.42 thf(fact_3922_signed__take__bit__Suc__1,axiom,
% 5.15/5.42 ! [N2: nat] :
% 5.15/5.42 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 5.15/5.42 = one_one_int ) ).
% 5.15/5.42
% 5.15/5.42 % signed_take_bit_Suc_1
% 5.15/5.42 thf(fact_3923_signed__take__bit__numeral__of__1,axiom,
% 5.15/5.42 ! [K: num] :
% 5.15/5.42 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.15/5.42 = one_one_int ) ).
% 5.15/5.42
% 5.15/5.42 % signed_take_bit_numeral_of_1
% 5.15/5.42 thf(fact_3924_triangle__Suc,axiom,
% 5.15/5.42 ! [N2: nat] :
% 5.15/5.42 ( ( nat_triangle @ ( suc @ N2 ) )
% 5.15/5.42 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % triangle_Suc
% 5.15/5.42 thf(fact_3925_even__Suc__Suc__iff,axiom,
% 5.15/5.42 ! [N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N2 ) ) )
% 5.15/5.42 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_Suc_Suc_iff
% 5.15/5.42 thf(fact_3926_even__Suc,axiom,
% 5.15/5.42 ! [N2: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) )
% 5.15/5.42 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_Suc
% 5.15/5.42 thf(fact_3927_unit__div__mult__self,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.42 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_mult_self
% 5.15/5.42 thf(fact_3928_unit__div__mult__self,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.42 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_mult_self
% 5.15/5.42 thf(fact_3929_unit__div__mult__self,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.42 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.15/5.42 = B ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_div_mult_self
% 5.15/5.42 thf(fact_3930_unit__mult__div__div,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.42 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.15/5.42 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_mult_div_div
% 5.15/5.42 thf(fact_3931_unit__mult__div__div,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.42 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.15/5.42 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_mult_div_div
% 5.15/5.42 thf(fact_3932_unit__mult__div__div,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.42 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.15/5.42 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % unit_mult_div_div
% 5.15/5.42 thf(fact_3933_pow__divides__pow__iff,axiom,
% 5.15/5.42 ! [N2: nat,A: nat,B: nat] :
% 5.15/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.15/5.42 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % pow_divides_pow_iff
% 5.15/5.42 thf(fact_3934_pow__divides__pow__iff,axiom,
% 5.15/5.42 ! [N2: nat,A: int,B: int] :
% 5.15/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.42 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.15/5.42 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % pow_divides_pow_iff
% 5.15/5.42 thf(fact_3935_even__mult__iff,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.15/5.42 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_mult_iff
% 5.15/5.42 thf(fact_3936_even__mult__iff,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.15/5.42 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_mult_iff
% 5.15/5.42 thf(fact_3937_even__mult__iff,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.15/5.42 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_mult_iff
% 5.15/5.42 thf(fact_3938_even__add,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.15/5.42 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_add
% 5.15/5.42 thf(fact_3939_even__add,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.15/5.42 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_add
% 5.15/5.42 thf(fact_3940_even__add,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.15/5.42 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.42 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % even_add
% 5.15/5.42 thf(fact_3941_odd__add,axiom,
% 5.15/5.42 ! [A: code_integer,B: code_integer] :
% 5.15/5.42 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.15/5.42 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.42 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % odd_add
% 5.15/5.42 thf(fact_3942_odd__add,axiom,
% 5.15/5.42 ! [A: nat,B: nat] :
% 5.15/5.42 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.15/5.42 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.42 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % odd_add
% 5.15/5.42 thf(fact_3943_odd__add,axiom,
% 5.15/5.42 ! [A: int,B: int] :
% 5.15/5.42 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.15/5.42 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.42 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.15/5.42
% 5.15/5.42 % odd_add
% 5.15/5.42 thf(fact_3944_even__mod__2__iff,axiom,
% 5.15/5.42 ! [A: nat] :
% 5.15/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.43 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_mod_2_iff
% 5.15/5.43 thf(fact_3945_even__mod__2__iff,axiom,
% 5.15/5.43 ! [A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.15/5.43 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_mod_2_iff
% 5.15/5.43 thf(fact_3946_even__mod__2__iff,axiom,
% 5.15/5.43 ! [A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_mod_2_iff
% 5.15/5.43 thf(fact_3947_even__Suc__div__two,axiom,
% 5.15/5.43 ! [N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.43 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_Suc_div_two
% 5.15/5.43 thf(fact_3948_odd__Suc__div__two,axiom,
% 5.15/5.43 ! [N2: nat] :
% 5.15/5.43 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.43 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_Suc_div_two
% 5.15/5.43 thf(fact_3949_signed__take__bit__Suc__bit0,axiom,
% 5.15/5.43 ! [N2: nat,K: num] :
% 5.15/5.43 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.15/5.43 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % signed_take_bit_Suc_bit0
% 5.15/5.43 thf(fact_3950_dvd__numeral__simp,axiom,
% 5.15/5.43 ! [M: num,N2: num] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.43 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N2 @ M ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_numeral_simp
% 5.15/5.43 thf(fact_3951_dvd__numeral__simp,axiom,
% 5.15/5.43 ! [M: num,N2: num] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.43 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N2 @ M ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_numeral_simp
% 5.15/5.43 thf(fact_3952_dvd__numeral__simp,axiom,
% 5.15/5.43 ! [M: num,N2: num] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.15/5.43 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N2 @ M ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_numeral_simp
% 5.15/5.43 thf(fact_3953_set__decode__0,axiom,
% 5.15/5.43 ! [X: nat] :
% 5.15/5.43 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % set_decode_0
% 5.15/5.43 thf(fact_3954_zero__le__power__eq__numeral,axiom,
% 5.15/5.43 ! [A: real,W: num] :
% 5.15/5.43 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.15/5.43 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zero_le_power_eq_numeral
% 5.15/5.43 thf(fact_3955_zero__le__power__eq__numeral,axiom,
% 5.15/5.43 ! [A: rat,W: num] :
% 5.15/5.43 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.15/5.43 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zero_le_power_eq_numeral
% 5.15/5.43 thf(fact_3956_zero__le__power__eq__numeral,axiom,
% 5.15/5.43 ! [A: int,W: num] :
% 5.15/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.15/5.43 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zero_le_power_eq_numeral
% 5.15/5.43 thf(fact_3957_power__less__zero__eq__numeral,axiom,
% 5.15/5.43 ! [A: real,W: num] :
% 5.15/5.43 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_less_zero_eq_numeral
% 5.15/5.43 thf(fact_3958_power__less__zero__eq__numeral,axiom,
% 5.15/5.43 ! [A: rat,W: num] :
% 5.15/5.43 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_less_zero_eq_numeral
% 5.15/5.43 thf(fact_3959_power__less__zero__eq__numeral,axiom,
% 5.15/5.43 ! [A: int,W: num] :
% 5.15/5.43 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_less_zero_eq_numeral
% 5.15/5.43 thf(fact_3960_power__less__zero__eq,axiom,
% 5.15/5.43 ! [A: real,N2: nat] :
% 5.15/5.43 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.43 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_less_zero_eq
% 5.15/5.43 thf(fact_3961_power__less__zero__eq,axiom,
% 5.15/5.43 ! [A: rat,N2: nat] :
% 5.15/5.43 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.43 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_less_zero_eq
% 5.15/5.43 thf(fact_3962_power__less__zero__eq,axiom,
% 5.15/5.43 ! [A: int,N2: nat] :
% 5.15/5.43 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.43 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_less_zero_eq
% 5.15/5.43 thf(fact_3963_even__plus__one__iff,axiom,
% 5.15/5.43 ! [A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_plus_one_iff
% 5.15/5.43 thf(fact_3964_even__plus__one__iff,axiom,
% 5.15/5.43 ! [A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_plus_one_iff
% 5.15/5.43 thf(fact_3965_even__plus__one__iff,axiom,
% 5.15/5.43 ! [A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_plus_one_iff
% 5.15/5.43 thf(fact_3966_even__diff,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_diff
% 5.15/5.43 thf(fact_3967_even__diff,axiom,
% 5.15/5.43 ! [A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.15/5.43 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_diff
% 5.15/5.43 thf(fact_3968_odd__Suc__minus__one,axiom,
% 5.15/5.43 ! [N2: nat] :
% 5.15/5.43 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.43 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.15/5.43 = N2 ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_Suc_minus_one
% 5.15/5.43 thf(fact_3969_even__diff__nat,axiom,
% 5.15/5.43 ! [M: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.43 = ( ( ord_less_nat @ M @ N2 )
% 5.15/5.43 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_diff_nat
% 5.15/5.43 thf(fact_3970_zero__less__power__eq__numeral,axiom,
% 5.15/5.43 ! [A: real,W: num] :
% 5.15/5.43 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.15/5.43 = ( ( ( numeral_numeral_nat @ W )
% 5.15/5.43 = zero_zero_nat )
% 5.15/5.43 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( A != zero_zero_real ) )
% 5.15/5.43 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zero_less_power_eq_numeral
% 5.15/5.43 thf(fact_3971_zero__less__power__eq__numeral,axiom,
% 5.15/5.43 ! [A: rat,W: num] :
% 5.15/5.43 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.15/5.43 = ( ( ( numeral_numeral_nat @ W )
% 5.15/5.43 = zero_zero_nat )
% 5.15/5.43 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( A != zero_zero_rat ) )
% 5.15/5.43 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zero_less_power_eq_numeral
% 5.15/5.43 thf(fact_3972_zero__less__power__eq__numeral,axiom,
% 5.15/5.43 ! [A: int,W: num] :
% 5.15/5.43 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.15/5.43 = ( ( ( numeral_numeral_nat @ W )
% 5.15/5.43 = zero_zero_nat )
% 5.15/5.43 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( A != zero_zero_int ) )
% 5.15/5.43 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zero_less_power_eq_numeral
% 5.15/5.43 thf(fact_3973_even__succ__div__2,axiom,
% 5.15/5.43 ! [A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_succ_div_2
% 5.15/5.43 thf(fact_3974_even__succ__div__2,axiom,
% 5.15/5.43 ! [A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_succ_div_2
% 5.15/5.43 thf(fact_3975_even__succ__div__2,axiom,
% 5.15/5.43 ! [A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_succ_div_2
% 5.15/5.43 thf(fact_3976_even__succ__div__two,axiom,
% 5.15/5.43 ! [A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_succ_div_two
% 5.15/5.43 thf(fact_3977_even__succ__div__two,axiom,
% 5.15/5.43 ! [A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_succ_div_two
% 5.15/5.43 thf(fact_3978_even__succ__div__two,axiom,
% 5.15/5.43 ! [A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_succ_div_two
% 5.15/5.43 thf(fact_3979_odd__succ__div__two,axiom,
% 5.15/5.43 ! [A: code_integer] :
% 5.15/5.43 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_succ_div_two
% 5.15/5.43 thf(fact_3980_odd__succ__div__two,axiom,
% 5.15/5.43 ! [A: nat] :
% 5.15/5.43 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_succ_div_two
% 5.15/5.43 thf(fact_3981_odd__succ__div__two,axiom,
% 5.15/5.43 ! [A: int] :
% 5.15/5.43 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.43 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_succ_div_two
% 5.15/5.43 thf(fact_3982_even__power,axiom,
% 5.15/5.43 ! [A: code_integer,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.15/5.43 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_power
% 5.15/5.43 thf(fact_3983_even__power,axiom,
% 5.15/5.43 ! [A: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 5.15/5.43 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_power
% 5.15/5.43 thf(fact_3984_even__power,axiom,
% 5.15/5.43 ! [A: int,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 5.15/5.43 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_power
% 5.15/5.43 thf(fact_3985_odd__two__times__div__two__nat,axiom,
% 5.15/5.43 ! [N2: nat] :
% 5.15/5.43 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.43 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.43 = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_two_times_div_two_nat
% 5.15/5.43 thf(fact_3986_divmod__algorithm__code_I5_J,axiom,
% 5.15/5.43 ! [M: num,N2: num] :
% 5.15/5.43 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.43 = ( produc4245557441103728435nt_int
% 5.15/5.43 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.15/5.43 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % divmod_algorithm_code(5)
% 5.15/5.43 thf(fact_3987_divmod__algorithm__code_I5_J,axiom,
% 5.15/5.43 ! [M: num,N2: num] :
% 5.15/5.43 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.43 = ( produc2626176000494625587at_nat
% 5.15/5.43 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.15/5.43 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % divmod_algorithm_code(5)
% 5.15/5.43 thf(fact_3988_divmod__algorithm__code_I5_J,axiom,
% 5.15/5.43 ! [M: num,N2: num] :
% 5.15/5.43 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.43 = ( produc6916734918728496179nteger
% 5.15/5.43 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.15/5.43 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % divmod_algorithm_code(5)
% 5.15/5.43 thf(fact_3989_odd__two__times__div__two__succ,axiom,
% 5.15/5.43 ! [A: code_integer] :
% 5.15/5.43 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.15/5.43 = A ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_two_times_div_two_succ
% 5.15/5.43 thf(fact_3990_odd__two__times__div__two__succ,axiom,
% 5.15/5.43 ! [A: nat] :
% 5.15/5.43 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.15/5.43 = A ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_two_times_div_two_succ
% 5.15/5.43 thf(fact_3991_odd__two__times__div__two__succ,axiom,
% 5.15/5.43 ! [A: int] :
% 5.15/5.43 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.43 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.15/5.43 = A ) ) ).
% 5.15/5.43
% 5.15/5.43 % odd_two_times_div_two_succ
% 5.15/5.43 thf(fact_3992_power__le__zero__eq__numeral,axiom,
% 5.15/5.43 ! [A: real,W: num] :
% 5.15/5.43 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.15/5.43 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.15/5.43 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_le_zero_eq_numeral
% 5.15/5.43 thf(fact_3993_power__le__zero__eq__numeral,axiom,
% 5.15/5.43 ! [A: rat,W: num] :
% 5.15/5.43 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.15/5.43 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.15/5.43 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_le_zero_eq_numeral
% 5.15/5.43 thf(fact_3994_power__le__zero__eq__numeral,axiom,
% 5.15/5.43 ! [A: int,W: num] :
% 5.15/5.43 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.15/5.43 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.15/5.43 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.43 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_le_zero_eq_numeral
% 5.15/5.43 thf(fact_3995_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.15/5.43 ! [N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 5.15/5.43 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.43
% 5.15/5.43 % semiring_parity_class.even_mask_iff
% 5.15/5.43 thf(fact_3996_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.15/5.43 ! [N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 5.15/5.43 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.43
% 5.15/5.43 % semiring_parity_class.even_mask_iff
% 5.15/5.43 thf(fact_3997_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.15/5.43 ! [N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.15/5.43 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.43
% 5.15/5.43 % semiring_parity_class.even_mask_iff
% 5.15/5.43 thf(fact_3998_signed__take__bit__Suc__bit1,axiom,
% 5.15/5.43 ! [N2: nat,K: num] :
% 5.15/5.43 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.15/5.43 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.15/5.43
% 5.15/5.43 % signed_take_bit_Suc_bit1
% 5.15/5.43 thf(fact_3999_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.15/5.43 = ( produc4947309494688390418_int_o
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4000_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: $o > int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.15/5.43 = ( produc8211389475949308722nt_int
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4001_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.15/5.43 = ( produc4947309494688390418_int_o
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4002_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.15/5.43 = ( produc8211389475949308722nt_int
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4003_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.15/5.43 = ( produc4947309494688390418_int_o
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4004_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.15/5.43 = ( produc8211389475949308722nt_int
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4005_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: $o > product_prod_int_int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.15/5.43 = ( produc4245557441103728435nt_int
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4006_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.15/5.43 = ( produc4245557441103728435nt_int
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4007_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.15/5.43 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.15/5.43 = ( produc4245557441103728435nt_int
% 5.15/5.43 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4008_prod_Ocase__distrib,axiom,
% 5.15/5.43 ! [H2: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 5.15/5.43 ( ( H2 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 5.15/5.43 = ( produc8739625826339149834_nat_o
% 5.15/5.43 @ ^ [X15: nat,X24: nat] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.15/5.43 @ Prod ) ) ).
% 5.15/5.43
% 5.15/5.43 % prod.case_distrib
% 5.15/5.43 thf(fact_4009_dvd__trans,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ B @ C )
% 5.15/5.43 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_trans
% 5.15/5.43 thf(fact_4010_dvd__trans,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ B @ C )
% 5.15/5.43 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_trans
% 5.15/5.43 thf(fact_4011_dvd__trans,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_trans
% 5.15/5.43 thf(fact_4012_dvd__refl,axiom,
% 5.15/5.43 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_refl
% 5.15/5.43 thf(fact_4013_dvd__refl,axiom,
% 5.15/5.43 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_refl
% 5.15/5.43 thf(fact_4014_dvd__refl,axiom,
% 5.15/5.43 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_refl
% 5.15/5.43 thf(fact_4015_dvd__0__left,axiom,
% 5.15/5.43 ! [A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.15/5.43 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_0_left
% 5.15/5.43 thf(fact_4016_dvd__0__left,axiom,
% 5.15/5.43 ! [A: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.15/5.43 => ( A = zero_zero_complex ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_0_left
% 5.15/5.43 thf(fact_4017_dvd__0__left,axiom,
% 5.15/5.43 ! [A: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.15/5.43 => ( A = zero_zero_real ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_0_left
% 5.15/5.43 thf(fact_4018_dvd__0__left,axiom,
% 5.15/5.43 ! [A: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.15/5.43 => ( A = zero_zero_rat ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_0_left
% 5.15/5.43 thf(fact_4019_dvd__0__left,axiom,
% 5.15/5.43 ! [A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.15/5.43 => ( A = zero_zero_nat ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_0_left
% 5.15/5.43 thf(fact_4020_dvd__0__left,axiom,
% 5.15/5.43 ! [A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.15/5.43 => ( A = zero_zero_int ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_0_left
% 5.15/5.43 thf(fact_4021_dvd__field__iff,axiom,
% 5.15/5.43 ( dvd_dvd_complex
% 5.15/5.43 = ( ^ [A3: complex,B2: complex] :
% 5.15/5.43 ( ( A3 = zero_zero_complex )
% 5.15/5.43 => ( B2 = zero_zero_complex ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_field_iff
% 5.15/5.43 thf(fact_4022_dvd__field__iff,axiom,
% 5.15/5.43 ( dvd_dvd_real
% 5.15/5.43 = ( ^ [A3: real,B2: real] :
% 5.15/5.43 ( ( A3 = zero_zero_real )
% 5.15/5.43 => ( B2 = zero_zero_real ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_field_iff
% 5.15/5.43 thf(fact_4023_dvd__field__iff,axiom,
% 5.15/5.43 ( dvd_dvd_rat
% 5.15/5.43 = ( ^ [A3: rat,B2: rat] :
% 5.15/5.43 ( ( A3 = zero_zero_rat )
% 5.15/5.43 => ( B2 = zero_zero_rat ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_field_iff
% 5.15/5.43 thf(fact_4024_dvd__productE,axiom,
% 5.15/5.43 ! [P2: nat,A: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ P2 @ ( times_times_nat @ A @ B ) )
% 5.15/5.43 => ~ ! [X3: nat,Y3: nat] :
% 5.15/5.43 ( ( P2
% 5.15/5.43 = ( times_times_nat @ X3 @ Y3 ) )
% 5.15/5.43 => ( ( dvd_dvd_nat @ X3 @ A )
% 5.15/5.43 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_productE
% 5.15/5.43 thf(fact_4025_dvd__productE,axiom,
% 5.15/5.43 ! [P2: int,A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ P2 @ ( times_times_int @ A @ B ) )
% 5.15/5.43 => ~ ! [X3: int,Y3: int] :
% 5.15/5.43 ( ( P2
% 5.15/5.43 = ( times_times_int @ X3 @ Y3 ) )
% 5.15/5.43 => ( ( dvd_dvd_int @ X3 @ A )
% 5.15/5.43 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_productE
% 5.15/5.43 thf(fact_4026_division__decomp,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.15/5.43 => ? [B7: nat,C4: nat] :
% 5.15/5.43 ( ( A
% 5.15/5.43 = ( times_times_nat @ B7 @ C4 ) )
% 5.15/5.43 & ( dvd_dvd_nat @ B7 @ B )
% 5.15/5.43 & ( dvd_dvd_nat @ C4 @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % division_decomp
% 5.15/5.43 thf(fact_4027_division__decomp,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.43 => ? [B7: int,C4: int] :
% 5.15/5.43 ( ( A
% 5.15/5.43 = ( times_times_int @ B7 @ C4 ) )
% 5.15/5.43 & ( dvd_dvd_int @ B7 @ B )
% 5.15/5.43 & ( dvd_dvd_int @ C4 @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % division_decomp
% 5.15/5.43 thf(fact_4028_dvd__triv__right,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_right
% 5.15/5.43 thf(fact_4029_dvd__triv__right,axiom,
% 5.15/5.43 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_right
% 5.15/5.43 thf(fact_4030_dvd__triv__right,axiom,
% 5.15/5.43 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_right
% 5.15/5.43 thf(fact_4031_dvd__triv__right,axiom,
% 5.15/5.43 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_right
% 5.15/5.43 thf(fact_4032_dvd__triv__right,axiom,
% 5.15/5.43 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_right
% 5.15/5.43 thf(fact_4033_dvd__mult__right,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_right
% 5.15/5.43 thf(fact_4034_dvd__mult__right,axiom,
% 5.15/5.43 ! [A: real,B: real,C: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_right
% 5.15/5.43 thf(fact_4035_dvd__mult__right,axiom,
% 5.15/5.43 ! [A: rat,B: rat,C: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_right
% 5.15/5.43 thf(fact_4036_dvd__mult__right,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_right
% 5.15/5.43 thf(fact_4037_dvd__mult__right,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_right
% 5.15/5.43 thf(fact_4038_mult__dvd__mono,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_dvd_mono
% 5.15/5.43 thf(fact_4039_mult__dvd__mono,axiom,
% 5.15/5.43 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_real @ C @ D )
% 5.15/5.43 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_dvd_mono
% 5.15/5.43 thf(fact_4040_mult__dvd__mono,axiom,
% 5.15/5.43 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_rat @ C @ D )
% 5.15/5.43 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_dvd_mono
% 5.15/5.43 thf(fact_4041_mult__dvd__mono,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ D )
% 5.15/5.43 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_dvd_mono
% 5.15/5.43 thf(fact_4042_mult__dvd__mono,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ D )
% 5.15/5.43 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_dvd_mono
% 5.15/5.43 thf(fact_4043_dvd__triv__left,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_left
% 5.15/5.43 thf(fact_4044_dvd__triv__left,axiom,
% 5.15/5.43 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_left
% 5.15/5.43 thf(fact_4045_dvd__triv__left,axiom,
% 5.15/5.43 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_left
% 5.15/5.43 thf(fact_4046_dvd__triv__left,axiom,
% 5.15/5.43 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_left
% 5.15/5.43 thf(fact_4047_dvd__triv__left,axiom,
% 5.15/5.43 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_triv_left
% 5.15/5.43 thf(fact_4048_dvd__mult__left,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_left
% 5.15/5.43 thf(fact_4049_dvd__mult__left,axiom,
% 5.15/5.43 ! [A: real,B: real,C: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_left
% 5.15/5.43 thf(fact_4050_dvd__mult__left,axiom,
% 5.15/5.43 ! [A: rat,B: rat,C: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_left
% 5.15/5.43 thf(fact_4051_dvd__mult__left,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_left
% 5.15/5.43 thf(fact_4052_dvd__mult__left,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.15/5.43 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_left
% 5.15/5.43 thf(fact_4053_dvd__mult2,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult2
% 5.15/5.43 thf(fact_4054_dvd__mult2,axiom,
% 5.15/5.43 ! [A: real,B: real,C: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ A @ B )
% 5.15/5.43 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult2
% 5.15/5.43 thf(fact_4055_dvd__mult2,axiom,
% 5.15/5.43 ! [A: rat,B: rat,C: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ A @ B )
% 5.15/5.43 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult2
% 5.15/5.43 thf(fact_4056_dvd__mult2,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult2
% 5.15/5.43 thf(fact_4057_dvd__mult2,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult2
% 5.15/5.43 thf(fact_4058_dvd__mult,axiom,
% 5.15/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult
% 5.15/5.43 thf(fact_4059_dvd__mult,axiom,
% 5.15/5.43 ! [A: real,C: real,B: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ A @ C )
% 5.15/5.43 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult
% 5.15/5.43 thf(fact_4060_dvd__mult,axiom,
% 5.15/5.43 ! [A: rat,C: rat,B: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ A @ C )
% 5.15/5.43 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult
% 5.15/5.43 thf(fact_4061_dvd__mult,axiom,
% 5.15/5.43 ! [A: nat,C: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ C )
% 5.15/5.43 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult
% 5.15/5.43 thf(fact_4062_dvd__mult,axiom,
% 5.15/5.43 ! [A: int,C: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ C )
% 5.15/5.43 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult
% 5.15/5.43 thf(fact_4063_dvd__def,axiom,
% 5.15/5.43 ( dvd_dvd_Code_integer
% 5.15/5.43 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.15/5.43 ? [K2: code_integer] :
% 5.15/5.43 ( A3
% 5.15/5.43 = ( times_3573771949741848930nteger @ B2 @ K2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_def
% 5.15/5.43 thf(fact_4064_dvd__def,axiom,
% 5.15/5.43 ( dvd_dvd_real
% 5.15/5.43 = ( ^ [B2: real,A3: real] :
% 5.15/5.43 ? [K2: real] :
% 5.15/5.43 ( A3
% 5.15/5.43 = ( times_times_real @ B2 @ K2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_def
% 5.15/5.43 thf(fact_4065_dvd__def,axiom,
% 5.15/5.43 ( dvd_dvd_rat
% 5.15/5.43 = ( ^ [B2: rat,A3: rat] :
% 5.15/5.43 ? [K2: rat] :
% 5.15/5.43 ( A3
% 5.15/5.43 = ( times_times_rat @ B2 @ K2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_def
% 5.15/5.43 thf(fact_4066_dvd__def,axiom,
% 5.15/5.43 ( dvd_dvd_nat
% 5.15/5.43 = ( ^ [B2: nat,A3: nat] :
% 5.15/5.43 ? [K2: nat] :
% 5.15/5.43 ( A3
% 5.15/5.43 = ( times_times_nat @ B2 @ K2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_def
% 5.15/5.43 thf(fact_4067_dvd__def,axiom,
% 5.15/5.43 ( dvd_dvd_int
% 5.15/5.43 = ( ^ [B2: int,A3: int] :
% 5.15/5.43 ? [K2: int] :
% 5.15/5.43 ( A3
% 5.15/5.43 = ( times_times_int @ B2 @ K2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_def
% 5.15/5.43 thf(fact_4068_dvdI,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.15/5.43 ( ( A
% 5.15/5.43 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdI
% 5.15/5.43 thf(fact_4069_dvdI,axiom,
% 5.15/5.43 ! [A: real,B: real,K: real] :
% 5.15/5.43 ( ( A
% 5.15/5.43 = ( times_times_real @ B @ K ) )
% 5.15/5.43 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdI
% 5.15/5.43 thf(fact_4070_dvdI,axiom,
% 5.15/5.43 ! [A: rat,B: rat,K: rat] :
% 5.15/5.43 ( ( A
% 5.15/5.43 = ( times_times_rat @ B @ K ) )
% 5.15/5.43 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdI
% 5.15/5.43 thf(fact_4071_dvdI,axiom,
% 5.15/5.43 ! [A: nat,B: nat,K: nat] :
% 5.15/5.43 ( ( A
% 5.15/5.43 = ( times_times_nat @ B @ K ) )
% 5.15/5.43 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdI
% 5.15/5.43 thf(fact_4072_dvdI,axiom,
% 5.15/5.43 ! [A: int,B: int,K: int] :
% 5.15/5.43 ( ( A
% 5.15/5.43 = ( times_times_int @ B @ K ) )
% 5.15/5.43 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdI
% 5.15/5.43 thf(fact_4073_dvdE,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.43 => ~ ! [K3: code_integer] :
% 5.15/5.43 ( A
% 5.15/5.43 != ( times_3573771949741848930nteger @ B @ K3 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdE
% 5.15/5.43 thf(fact_4074_dvdE,axiom,
% 5.15/5.43 ! [B: real,A: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ B @ A )
% 5.15/5.43 => ~ ! [K3: real] :
% 5.15/5.43 ( A
% 5.15/5.43 != ( times_times_real @ B @ K3 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdE
% 5.15/5.43 thf(fact_4075_dvdE,axiom,
% 5.15/5.43 ! [B: rat,A: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ B @ A )
% 5.15/5.43 => ~ ! [K3: rat] :
% 5.15/5.43 ( A
% 5.15/5.43 != ( times_times_rat @ B @ K3 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdE
% 5.15/5.43 thf(fact_4076_dvdE,axiom,
% 5.15/5.43 ! [B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ A )
% 5.15/5.43 => ~ ! [K3: nat] :
% 5.15/5.43 ( A
% 5.15/5.43 != ( times_times_nat @ B @ K3 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdE
% 5.15/5.43 thf(fact_4077_dvdE,axiom,
% 5.15/5.43 ! [B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ A )
% 5.15/5.43 => ~ ! [K3: int] :
% 5.15/5.43 ( A
% 5.15/5.43 != ( times_times_int @ B @ K3 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvdE
% 5.15/5.43 thf(fact_4078_dvd__unit__imp__unit,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_unit_imp_unit
% 5.15/5.43 thf(fact_4079_dvd__unit__imp__unit,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_unit_imp_unit
% 5.15/5.43 thf(fact_4080_dvd__unit__imp__unit,axiom,
% 5.15/5.43 ! [A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_unit_imp_unit
% 5.15/5.43 thf(fact_4081_unit__imp__dvd,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_imp_dvd
% 5.15/5.43 thf(fact_4082_unit__imp__dvd,axiom,
% 5.15/5.43 ! [B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_imp_dvd
% 5.15/5.43 thf(fact_4083_unit__imp__dvd,axiom,
% 5.15/5.43 ! [B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_imp_dvd
% 5.15/5.43 thf(fact_4084_one__dvd,axiom,
% 5.15/5.43 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.15/5.43
% 5.15/5.43 % one_dvd
% 5.15/5.43 thf(fact_4085_one__dvd,axiom,
% 5.15/5.43 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.15/5.43
% 5.15/5.43 % one_dvd
% 5.15/5.43 thf(fact_4086_one__dvd,axiom,
% 5.15/5.43 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.15/5.43
% 5.15/5.43 % one_dvd
% 5.15/5.43 thf(fact_4087_one__dvd,axiom,
% 5.15/5.43 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.15/5.43
% 5.15/5.43 % one_dvd
% 5.15/5.43 thf(fact_4088_one__dvd,axiom,
% 5.15/5.43 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.15/5.43
% 5.15/5.43 % one_dvd
% 5.15/5.43 thf(fact_4089_one__dvd,axiom,
% 5.15/5.43 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.15/5.43
% 5.15/5.43 % one_dvd
% 5.15/5.43 thf(fact_4090_dvd__add__right__iff,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_right_iff
% 5.15/5.43 thf(fact_4091_dvd__add__right__iff,axiom,
% 5.15/5.43 ! [A: real,B: real,C: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_right_iff
% 5.15/5.43 thf(fact_4092_dvd__add__right__iff,axiom,
% 5.15/5.43 ! [A: rat,B: rat,C: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_right_iff
% 5.15/5.43 thf(fact_4093_dvd__add__right__iff,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_right_iff
% 5.15/5.43 thf(fact_4094_dvd__add__right__iff,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_right_iff
% 5.15/5.43 thf(fact_4095_dvd__add__right__iff,axiom,
% 5.15/5.43 ! [A: complex,B: complex,C: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_complex @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_right_iff
% 5.15/5.43 thf(fact_4096_dvd__add__left__iff,axiom,
% 5.15/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_left_iff
% 5.15/5.43 thf(fact_4097_dvd__add__left__iff,axiom,
% 5.15/5.43 ! [A: real,C: real,B: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ A @ C )
% 5.15/5.43 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_left_iff
% 5.15/5.43 thf(fact_4098_dvd__add__left__iff,axiom,
% 5.15/5.43 ! [A: rat,C: rat,B: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ A @ C )
% 5.15/5.43 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_left_iff
% 5.15/5.43 thf(fact_4099_dvd__add__left__iff,axiom,
% 5.15/5.43 ! [A: nat,C: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ C )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_left_iff
% 5.15/5.43 thf(fact_4100_dvd__add__left__iff,axiom,
% 5.15/5.43 ! [A: int,C: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ C )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_left_iff
% 5.15/5.43 thf(fact_4101_dvd__add__left__iff,axiom,
% 5.15/5.43 ! [A: complex,C: complex,B: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ A @ C )
% 5.15/5.43 => ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add_left_iff
% 5.15/5.43 thf(fact_4102_dvd__add,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add
% 5.15/5.43 thf(fact_4103_dvd__add,axiom,
% 5.15/5.43 ! [A: real,B: real,C: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_real @ A @ C )
% 5.15/5.43 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add
% 5.15/5.43 thf(fact_4104_dvd__add,axiom,
% 5.15/5.43 ! [A: rat,B: rat,C: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_rat @ A @ C )
% 5.15/5.43 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add
% 5.15/5.43 thf(fact_4105_dvd__add,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ C )
% 5.15/5.43 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add
% 5.15/5.43 thf(fact_4106_dvd__add,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ C )
% 5.15/5.43 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add
% 5.15/5.43 thf(fact_4107_dvd__add,axiom,
% 5.15/5.43 ! [A: complex,B: complex,C: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_complex @ A @ C )
% 5.15/5.43 => ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_add
% 5.15/5.43 thf(fact_4108_dvd__diff__commute,axiom,
% 5.15/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diff_commute
% 5.15/5.43 thf(fact_4109_dvd__diff__commute,axiom,
% 5.15/5.43 ! [A: int,C: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.15/5.43 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diff_commute
% 5.15/5.43 thf(fact_4110_dvd__diff,axiom,
% 5.15/5.43 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ X @ Z )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diff
% 5.15/5.43 thf(fact_4111_dvd__diff,axiom,
% 5.15/5.43 ! [X: real,Y: real,Z: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ X @ Y )
% 5.15/5.43 => ( ( dvd_dvd_real @ X @ Z )
% 5.15/5.43 => ( dvd_dvd_real @ X @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diff
% 5.15/5.43 thf(fact_4112_dvd__diff,axiom,
% 5.15/5.43 ! [X: rat,Y: rat,Z: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ X @ Y )
% 5.15/5.43 => ( ( dvd_dvd_rat @ X @ Z )
% 5.15/5.43 => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diff
% 5.15/5.43 thf(fact_4113_dvd__diff,axiom,
% 5.15/5.43 ! [X: int,Y: int,Z: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ X @ Y )
% 5.15/5.43 => ( ( dvd_dvd_int @ X @ Z )
% 5.15/5.43 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diff
% 5.15/5.43 thf(fact_4114_div__div__div__same,axiom,
% 5.15/5.43 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_div_div_same
% 5.15/5.43 thf(fact_4115_div__div__div__same,axiom,
% 5.15/5.43 ! [D: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ D @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ B @ A )
% 5.15/5.43 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.15/5.43 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_div_div_same
% 5.15/5.43 thf(fact_4116_div__div__div__same,axiom,
% 5.15/5.43 ! [D: int,B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ D @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ B @ A )
% 5.15/5.43 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.15/5.43 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_div_div_same
% 5.15/5.43 thf(fact_4117_dvd__div__eq__cancel,axiom,
% 5.15/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.43 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.15/5.43 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_cancel
% 5.15/5.43 thf(fact_4118_dvd__div__eq__cancel,axiom,
% 5.15/5.43 ! [A: complex,C: complex,B: complex] :
% 5.15/5.43 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.15/5.43 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.43 => ( ( dvd_dvd_complex @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_complex @ C @ B )
% 5.15/5.43 => ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_cancel
% 5.15/5.43 thf(fact_4119_dvd__div__eq__cancel,axiom,
% 5.15/5.43 ! [A: real,C: real,B: real] :
% 5.15/5.43 ( ( ( divide_divide_real @ A @ C )
% 5.15/5.43 = ( divide_divide_real @ B @ C ) )
% 5.15/5.43 => ( ( dvd_dvd_real @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_real @ C @ B )
% 5.15/5.43 => ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_cancel
% 5.15/5.43 thf(fact_4120_dvd__div__eq__cancel,axiom,
% 5.15/5.43 ! [A: rat,C: rat,B: rat] :
% 5.15/5.43 ( ( ( divide_divide_rat @ A @ C )
% 5.15/5.43 = ( divide_divide_rat @ B @ C ) )
% 5.15/5.43 => ( ( dvd_dvd_rat @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_rat @ C @ B )
% 5.15/5.43 => ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_cancel
% 5.15/5.43 thf(fact_4121_dvd__div__eq__cancel,axiom,
% 5.15/5.43 ! [A: nat,C: nat,B: nat] :
% 5.15/5.43 ( ( ( divide_divide_nat @ A @ C )
% 5.15/5.43 = ( divide_divide_nat @ B @ C ) )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_cancel
% 5.15/5.43 thf(fact_4122_dvd__div__eq__cancel,axiom,
% 5.15/5.43 ! [A: int,C: int,B: int] :
% 5.15/5.43 ( ( ( divide_divide_int @ A @ C )
% 5.15/5.43 = ( divide_divide_int @ B @ C ) )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_cancel
% 5.15/5.43 thf(fact_4123_dvd__div__eq__iff,axiom,
% 5.15/5.43 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.15/5.43 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.15/5.43 = ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_iff
% 5.15/5.43 thf(fact_4124_dvd__div__eq__iff,axiom,
% 5.15/5.43 ! [C: complex,A: complex,B: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_complex @ C @ B )
% 5.15/5.43 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.15/5.43 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.43 = ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_iff
% 5.15/5.43 thf(fact_4125_dvd__div__eq__iff,axiom,
% 5.15/5.43 ! [C: real,A: real,B: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_real @ C @ B )
% 5.15/5.43 => ( ( ( divide_divide_real @ A @ C )
% 5.15/5.43 = ( divide_divide_real @ B @ C ) )
% 5.15/5.43 = ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_iff
% 5.15/5.43 thf(fact_4126_dvd__div__eq__iff,axiom,
% 5.15/5.43 ! [C: rat,A: rat,B: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_rat @ C @ B )
% 5.15/5.43 => ( ( ( divide_divide_rat @ A @ C )
% 5.15/5.43 = ( divide_divide_rat @ B @ C ) )
% 5.15/5.43 = ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_iff
% 5.15/5.43 thf(fact_4127_dvd__div__eq__iff,axiom,
% 5.15/5.43 ! [C: nat,A: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( ( ( divide_divide_nat @ A @ C )
% 5.15/5.43 = ( divide_divide_nat @ B @ C ) )
% 5.15/5.43 = ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_iff
% 5.15/5.43 thf(fact_4128_dvd__div__eq__iff,axiom,
% 5.15/5.43 ! [C: int,A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ A )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( ( ( divide_divide_int @ A @ C )
% 5.15/5.43 = ( divide_divide_int @ B @ C ) )
% 5.15/5.43 = ( A = B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_iff
% 5.15/5.43 thf(fact_4129_dvd__power__same,axiom,
% 5.15/5.43 ! [X: code_integer,Y: code_integer,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_same
% 5.15/5.43 thf(fact_4130_dvd__power__same,axiom,
% 5.15/5.43 ! [X: nat,Y: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ X @ Y )
% 5.15/5.43 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_same
% 5.15/5.43 thf(fact_4131_dvd__power__same,axiom,
% 5.15/5.43 ! [X: real,Y: real,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_real @ X @ Y )
% 5.15/5.43 => ( dvd_dvd_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_same
% 5.15/5.43 thf(fact_4132_dvd__power__same,axiom,
% 5.15/5.43 ! [X: complex,Y: complex,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_complex @ X @ Y )
% 5.15/5.43 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_same
% 5.15/5.43 thf(fact_4133_dvd__power__same,axiom,
% 5.15/5.43 ! [X: int,Y: int,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_int @ X @ Y )
% 5.15/5.43 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_same
% 5.15/5.43 thf(fact_4134_old_Oprod_Ocase,axiom,
% 5.15/5.43 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 5.15/5.43 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.15/5.43 = ( F @ X1 @ X22 ) ) ).
% 5.15/5.43
% 5.15/5.43 % old.prod.case
% 5.15/5.43 thf(fact_4135_old_Oprod_Ocase,axiom,
% 5.15/5.43 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 5.15/5.43 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.15/5.43 = ( F @ X1 @ X22 ) ) ).
% 5.15/5.43
% 5.15/5.43 % old.prod.case
% 5.15/5.43 thf(fact_4136_old_Oprod_Ocase,axiom,
% 5.15/5.43 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 5.15/5.43 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.15/5.43 = ( F @ X1 @ X22 ) ) ).
% 5.15/5.43
% 5.15/5.43 % old.prod.case
% 5.15/5.43 thf(fact_4137_old_Oprod_Ocase,axiom,
% 5.15/5.43 ! [F: int > int > $o,X1: int,X22: int] :
% 5.15/5.43 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.15/5.43 = ( F @ X1 @ X22 ) ) ).
% 5.15/5.43
% 5.15/5.43 % old.prod.case
% 5.15/5.43 thf(fact_4138_old_Oprod_Ocase,axiom,
% 5.15/5.43 ! [F: int > int > int,X1: int,X22: int] :
% 5.15/5.43 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.15/5.43 = ( F @ X1 @ X22 ) ) ).
% 5.15/5.43
% 5.15/5.43 % old.prod.case
% 5.15/5.43 thf(fact_4139_dvd__mod__imp__dvd,axiom,
% 5.15/5.43 ! [C: nat,A: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod_imp_dvd
% 5.15/5.43 thf(fact_4140_dvd__mod__imp__dvd,axiom,
% 5.15/5.43 ! [C: int,A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod_imp_dvd
% 5.15/5.43 thf(fact_4141_dvd__mod__imp__dvd,axiom,
% 5.15/5.43 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod_imp_dvd
% 5.15/5.43 thf(fact_4142_dvd__mod__iff,axiom,
% 5.15/5.43 ! [C: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.15/5.43 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod_iff
% 5.15/5.43 thf(fact_4143_dvd__mod__iff,axiom,
% 5.15/5.43 ! [C: int,B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.15/5.43 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod_iff
% 5.15/5.43 thf(fact_4144_dvd__mod__iff,axiom,
% 5.15/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod_iff
% 5.15/5.43 thf(fact_4145_mod__mod__cancel,axiom,
% 5.15/5.43 ! [C: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.15/5.43 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_mod_cancel
% 5.15/5.43 thf(fact_4146_mod__mod__cancel,axiom,
% 5.15/5.43 ! [C: int,B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.15/5.43 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_mod_cancel
% 5.15/5.43 thf(fact_4147_mod__mod__cancel,axiom,
% 5.15/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.15/5.43 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_mod_cancel
% 5.15/5.43 thf(fact_4148_dvd__mod,axiom,
% 5.15/5.43 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ K @ M )
% 5.15/5.43 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.15/5.43 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod
% 5.15/5.43 thf(fact_4149_dvd__mod,axiom,
% 5.15/5.43 ! [K: int,M: int,N2: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ K @ M )
% 5.15/5.43 => ( ( dvd_dvd_int @ K @ N2 )
% 5.15/5.43 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod
% 5.15/5.43 thf(fact_4150_dvd__mod,axiom,
% 5.15/5.43 ! [K: code_integer,M: code_integer,N2: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ K @ N2 )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mod
% 5.15/5.43 thf(fact_4151_signed__take__bit__mult,axiom,
% 5.15/5.43 ! [N2: nat,K: int,L: int] :
% 5.15/5.43 ( ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 5.15/5.43 = ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % signed_take_bit_mult
% 5.15/5.43 thf(fact_4152_signed__take__bit__add,axiom,
% 5.15/5.43 ! [N2: nat,K: int,L: int] :
% 5.15/5.43 ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 5.15/5.43 = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % signed_take_bit_add
% 5.15/5.43 thf(fact_4153_dvd__diff__nat,axiom,
% 5.15/5.43 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ K @ M )
% 5.15/5.43 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.15/5.43 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diff_nat
% 5.15/5.43 thf(fact_4154_signed__take__bit__diff,axiom,
% 5.15/5.43 ! [N2: nat,K: int,L: int] :
% 5.15/5.43 ( ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 5.15/5.43 = ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % signed_take_bit_diff
% 5.15/5.43 thf(fact_4155_subset__divisors__dvd,axiom,
% 5.15/5.43 ! [A: complex,B: complex] :
% 5.15/5.43 ( ( ord_le211207098394363844omplex
% 5.15/5.43 @ ( collect_complex
% 5.15/5.43 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.15/5.43 @ ( collect_complex
% 5.15/5.43 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.15/5.43 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % subset_divisors_dvd
% 5.15/5.43 thf(fact_4156_subset__divisors__dvd,axiom,
% 5.15/5.43 ! [A: int,B: int] :
% 5.15/5.43 ( ( ord_less_eq_set_int
% 5.15/5.43 @ ( collect_int
% 5.15/5.43 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.15/5.43 @ ( collect_int
% 5.15/5.43 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.15/5.43 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % subset_divisors_dvd
% 5.15/5.43 thf(fact_4157_subset__divisors__dvd,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( ord_le7084787975880047091nteger
% 5.15/5.43 @ ( collect_Code_integer
% 5.15/5.43 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.15/5.43 @ ( collect_Code_integer
% 5.15/5.43 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % subset_divisors_dvd
% 5.15/5.43 thf(fact_4158_subset__divisors__dvd,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ( ( ord_less_eq_set_nat
% 5.15/5.43 @ ( collect_nat
% 5.15/5.43 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.15/5.43 @ ( collect_nat
% 5.15/5.43 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.15/5.43
% 5.15/5.43 % subset_divisors_dvd
% 5.15/5.43 thf(fact_4159_case__prodE2,axiom,
% 5.15/5.43 ! [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] :
% 5.15/5.43 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.15/5.43 => ~ ! [X3: nat,Y3: nat] :
% 5.15/5.43 ( ( Z
% 5.15/5.43 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.15/5.43 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % case_prodE2
% 5.15/5.43 thf(fact_4160_case__prodE2,axiom,
% 5.15/5.43 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.15/5.43 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.15/5.43 => ~ ! [X3: nat,Y3: nat] :
% 5.15/5.43 ( ( Z
% 5.15/5.43 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.15/5.43 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % case_prodE2
% 5.15/5.43 thf(fact_4161_case__prodE2,axiom,
% 5.15/5.43 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.15/5.43 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.15/5.43 => ~ ! [X3: int,Y3: int] :
% 5.15/5.43 ( ( Z
% 5.15/5.43 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.15/5.43 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % case_prodE2
% 5.15/5.43 thf(fact_4162_case__prodE2,axiom,
% 5.15/5.43 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.15/5.43 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.15/5.43 => ~ ! [X3: int,Y3: int] :
% 5.15/5.43 ( ( Z
% 5.15/5.43 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.15/5.43 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % case_prodE2
% 5.15/5.43 thf(fact_4163_case__prodE2,axiom,
% 5.15/5.43 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.15/5.43 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.15/5.43 => ~ ! [X3: int,Y3: int] :
% 5.15/5.43 ( ( Z
% 5.15/5.43 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.15/5.43 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % case_prodE2
% 5.15/5.43 thf(fact_4164_case__prod__eta,axiom,
% 5.15/5.43 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.15/5.43 ( ( produc27273713700761075at_nat
% 5.15/5.43 @ ^ [X2: nat,Y2: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) )
% 5.15/5.43 = F ) ).
% 5.15/5.43
% 5.15/5.43 % case_prod_eta
% 5.15/5.43 thf(fact_4165_case__prod__eta,axiom,
% 5.15/5.43 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.15/5.43 ( ( produc8739625826339149834_nat_o
% 5.15/5.43 @ ^ [X2: nat,Y2: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) )
% 5.15/5.43 = F ) ).
% 5.15/5.43
% 5.15/5.43 % case_prod_eta
% 5.15/5.43 thf(fact_4166_case__prod__eta,axiom,
% 5.15/5.43 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.15/5.43 ( ( produc4245557441103728435nt_int
% 5.15/5.43 @ ^ [X2: int,Y2: int] : ( F @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 5.15/5.43 = F ) ).
% 5.15/5.43
% 5.15/5.43 % case_prod_eta
% 5.15/5.43 thf(fact_4167_case__prod__eta,axiom,
% 5.15/5.43 ! [F: product_prod_int_int > $o] :
% 5.15/5.43 ( ( produc4947309494688390418_int_o
% 5.15/5.43 @ ^ [X2: int,Y2: int] : ( F @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 5.15/5.43 = F ) ).
% 5.15/5.43
% 5.15/5.43 % case_prod_eta
% 5.15/5.43 thf(fact_4168_case__prod__eta,axiom,
% 5.15/5.43 ! [F: product_prod_int_int > int] :
% 5.15/5.43 ( ( produc8211389475949308722nt_int
% 5.15/5.43 @ ^ [X2: int,Y2: int] : ( F @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 5.15/5.43 = F ) ).
% 5.15/5.43
% 5.15/5.43 % case_prod_eta
% 5.15/5.43 thf(fact_4169_cond__case__prod__eta,axiom,
% 5.15/5.43 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.15/5.43 ( ! [X3: nat,Y3: nat] :
% 5.15/5.43 ( ( F @ X3 @ Y3 )
% 5.15/5.43 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.15/5.43 => ( ( produc27273713700761075at_nat @ F )
% 5.15/5.43 = G ) ) ).
% 5.15/5.43
% 5.15/5.43 % cond_case_prod_eta
% 5.15/5.43 thf(fact_4170_cond__case__prod__eta,axiom,
% 5.15/5.43 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.15/5.43 ( ! [X3: nat,Y3: nat] :
% 5.15/5.43 ( ( F @ X3 @ Y3 )
% 5.15/5.43 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.15/5.43 => ( ( produc8739625826339149834_nat_o @ F )
% 5.15/5.43 = G ) ) ).
% 5.15/5.43
% 5.15/5.43 % cond_case_prod_eta
% 5.15/5.43 thf(fact_4171_cond__case__prod__eta,axiom,
% 5.15/5.43 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.15/5.43 ( ! [X3: int,Y3: int] :
% 5.15/5.43 ( ( F @ X3 @ Y3 )
% 5.15/5.43 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.15/5.43 => ( ( produc4245557441103728435nt_int @ F )
% 5.15/5.43 = G ) ) ).
% 5.15/5.43
% 5.15/5.43 % cond_case_prod_eta
% 5.15/5.43 thf(fact_4172_cond__case__prod__eta,axiom,
% 5.15/5.43 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.15/5.43 ( ! [X3: int,Y3: int] :
% 5.15/5.43 ( ( F @ X3 @ Y3 )
% 5.15/5.43 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.15/5.43 => ( ( produc4947309494688390418_int_o @ F )
% 5.15/5.43 = G ) ) ).
% 5.15/5.43
% 5.15/5.43 % cond_case_prod_eta
% 5.15/5.43 thf(fact_4173_cond__case__prod__eta,axiom,
% 5.15/5.43 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.15/5.43 ( ! [X3: int,Y3: int] :
% 5.15/5.43 ( ( F @ X3 @ Y3 )
% 5.15/5.43 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.15/5.43 => ( ( produc8211389475949308722nt_int @ F )
% 5.15/5.43 = G ) ) ).
% 5.15/5.43
% 5.15/5.43 % cond_case_prod_eta
% 5.15/5.43 thf(fact_4174_strict__subset__divisors__dvd,axiom,
% 5.15/5.43 ! [A: complex,B: complex] :
% 5.15/5.43 ( ( ord_less_set_complex
% 5.15/5.43 @ ( collect_complex
% 5.15/5.43 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.15/5.43 @ ( collect_complex
% 5.15/5.43 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.15/5.43 = ( ( dvd_dvd_complex @ A @ B )
% 5.15/5.43 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % strict_subset_divisors_dvd
% 5.15/5.43 thf(fact_4175_strict__subset__divisors__dvd,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ( ( ord_less_set_nat
% 5.15/5.43 @ ( collect_nat
% 5.15/5.43 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.15/5.43 @ ( collect_nat
% 5.15/5.43 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.15/5.43 = ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % strict_subset_divisors_dvd
% 5.15/5.43 thf(fact_4176_strict__subset__divisors__dvd,axiom,
% 5.15/5.43 ! [A: int,B: int] :
% 5.15/5.43 ( ( ord_less_set_int
% 5.15/5.43 @ ( collect_int
% 5.15/5.43 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.15/5.43 @ ( collect_int
% 5.15/5.43 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.15/5.43 = ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % strict_subset_divisors_dvd
% 5.15/5.43 thf(fact_4177_strict__subset__divisors__dvd,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( ord_le1307284697595431911nteger
% 5.15/5.43 @ ( collect_Code_integer
% 5.15/5.43 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.15/5.43 @ ( collect_Code_integer
% 5.15/5.43 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.15/5.43 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % strict_subset_divisors_dvd
% 5.15/5.43 thf(fact_4178_even__signed__take__bit__iff,axiom,
% 5.15/5.43 ! [M: nat,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_signed_take_bit_iff
% 5.15/5.43 thf(fact_4179_even__signed__take__bit__iff,axiom,
% 5.15/5.43 ! [M: nat,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.15/5.43 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_signed_take_bit_iff
% 5.15/5.43 thf(fact_4180_not__is__unit__0,axiom,
% 5.15/5.43 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.15/5.43
% 5.15/5.43 % not_is_unit_0
% 5.15/5.43 thf(fact_4181_not__is__unit__0,axiom,
% 5.15/5.43 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.15/5.43
% 5.15/5.43 % not_is_unit_0
% 5.15/5.43 thf(fact_4182_not__is__unit__0,axiom,
% 5.15/5.43 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.15/5.43
% 5.15/5.43 % not_is_unit_0
% 5.15/5.43 thf(fact_4183_pinf_I9_J,axiom,
% 5.15/5.43 ! [D: code_integer,S: code_integer] :
% 5.15/5.43 ? [Z2: code_integer] :
% 5.15/5.43 ! [X5: code_integer] :
% 5.15/5.43 ( ( ord_le6747313008572928689nteger @ Z2 @ X5 )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(9)
% 5.15/5.43 thf(fact_4184_pinf_I9_J,axiom,
% 5.15/5.43 ! [D: real,S: real] :
% 5.15/5.43 ? [Z2: real] :
% 5.15/5.43 ! [X5: real] :
% 5.15/5.43 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.43 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(9)
% 5.15/5.43 thf(fact_4185_pinf_I9_J,axiom,
% 5.15/5.43 ! [D: rat,S: rat] :
% 5.15/5.43 ? [Z2: rat] :
% 5.15/5.43 ! [X5: rat] :
% 5.15/5.43 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.43 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(9)
% 5.15/5.43 thf(fact_4186_pinf_I9_J,axiom,
% 5.15/5.43 ! [D: nat,S: nat] :
% 5.15/5.43 ? [Z2: nat] :
% 5.15/5.43 ! [X5: nat] :
% 5.15/5.43 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.43 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(9)
% 5.15/5.43 thf(fact_4187_pinf_I9_J,axiom,
% 5.15/5.43 ! [D: int,S: int] :
% 5.15/5.43 ? [Z2: int] :
% 5.15/5.43 ! [X5: int] :
% 5.15/5.43 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.43 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(9)
% 5.15/5.43 thf(fact_4188_pinf_I10_J,axiom,
% 5.15/5.43 ! [D: code_integer,S: code_integer] :
% 5.15/5.43 ? [Z2: code_integer] :
% 5.15/5.43 ! [X5: code_integer] :
% 5.15/5.43 ( ( ord_le6747313008572928689nteger @ Z2 @ X5 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(10)
% 5.15/5.43 thf(fact_4189_pinf_I10_J,axiom,
% 5.15/5.43 ! [D: real,S: real] :
% 5.15/5.43 ? [Z2: real] :
% 5.15/5.43 ! [X5: real] :
% 5.15/5.43 ( ( ord_less_real @ Z2 @ X5 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(10)
% 5.15/5.43 thf(fact_4190_pinf_I10_J,axiom,
% 5.15/5.43 ! [D: rat,S: rat] :
% 5.15/5.43 ? [Z2: rat] :
% 5.15/5.43 ! [X5: rat] :
% 5.15/5.43 ( ( ord_less_rat @ Z2 @ X5 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(10)
% 5.15/5.43 thf(fact_4191_pinf_I10_J,axiom,
% 5.15/5.43 ! [D: nat,S: nat] :
% 5.15/5.43 ? [Z2: nat] :
% 5.15/5.43 ! [X5: nat] :
% 5.15/5.43 ( ( ord_less_nat @ Z2 @ X5 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(10)
% 5.15/5.43 thf(fact_4192_pinf_I10_J,axiom,
% 5.15/5.43 ! [D: int,S: int] :
% 5.15/5.43 ? [Z2: int] :
% 5.15/5.43 ! [X5: int] :
% 5.15/5.43 ( ( ord_less_int @ Z2 @ X5 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % pinf(10)
% 5.15/5.43 thf(fact_4193_minf_I9_J,axiom,
% 5.15/5.43 ! [D: code_integer,S: code_integer] :
% 5.15/5.43 ? [Z2: code_integer] :
% 5.15/5.43 ! [X5: code_integer] :
% 5.15/5.43 ( ( ord_le6747313008572928689nteger @ X5 @ Z2 )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(9)
% 5.15/5.43 thf(fact_4194_minf_I9_J,axiom,
% 5.15/5.43 ! [D: real,S: real] :
% 5.15/5.43 ? [Z2: real] :
% 5.15/5.43 ! [X5: real] :
% 5.15/5.43 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.43 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(9)
% 5.15/5.43 thf(fact_4195_minf_I9_J,axiom,
% 5.15/5.43 ! [D: rat,S: rat] :
% 5.15/5.43 ? [Z2: rat] :
% 5.15/5.43 ! [X5: rat] :
% 5.15/5.43 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.43 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(9)
% 5.15/5.43 thf(fact_4196_minf_I9_J,axiom,
% 5.15/5.43 ! [D: nat,S: nat] :
% 5.15/5.43 ? [Z2: nat] :
% 5.15/5.43 ! [X5: nat] :
% 5.15/5.43 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.43 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(9)
% 5.15/5.43 thf(fact_4197_minf_I9_J,axiom,
% 5.15/5.43 ! [D: int,S: int] :
% 5.15/5.43 ? [Z2: int] :
% 5.15/5.43 ! [X5: int] :
% 5.15/5.43 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.43 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) )
% 5.15/5.43 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(9)
% 5.15/5.43 thf(fact_4198_minf_I10_J,axiom,
% 5.15/5.43 ! [D: code_integer,S: code_integer] :
% 5.15/5.43 ? [Z2: code_integer] :
% 5.15/5.43 ! [X5: code_integer] :
% 5.15/5.43 ( ( ord_le6747313008572928689nteger @ X5 @ Z2 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(10)
% 5.15/5.43 thf(fact_4199_minf_I10_J,axiom,
% 5.15/5.43 ! [D: real,S: real] :
% 5.15/5.43 ? [Z2: real] :
% 5.15/5.43 ! [X5: real] :
% 5.15/5.43 ( ( ord_less_real @ X5 @ Z2 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(10)
% 5.15/5.43 thf(fact_4200_minf_I10_J,axiom,
% 5.15/5.43 ! [D: rat,S: rat] :
% 5.15/5.43 ? [Z2: rat] :
% 5.15/5.43 ! [X5: rat] :
% 5.15/5.43 ( ( ord_less_rat @ X5 @ Z2 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(10)
% 5.15/5.43 thf(fact_4201_minf_I10_J,axiom,
% 5.15/5.43 ! [D: nat,S: nat] :
% 5.15/5.43 ? [Z2: nat] :
% 5.15/5.43 ! [X5: nat] :
% 5.15/5.43 ( ( ord_less_nat @ X5 @ Z2 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(10)
% 5.15/5.43 thf(fact_4202_minf_I10_J,axiom,
% 5.15/5.43 ! [D: int,S: int] :
% 5.15/5.43 ? [Z2: int] :
% 5.15/5.43 ! [X5: int] :
% 5.15/5.43 ( ( ord_less_int @ X5 @ Z2 )
% 5.15/5.43 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % minf(10)
% 5.15/5.43 thf(fact_4203_dvd__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.43 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.15/5.43 = zero_z3403309356797280102nteger )
% 5.15/5.43 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_0_iff
% 5.15/5.43 thf(fact_4204_dvd__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: complex,A: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ B @ A )
% 5.15/5.43 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.15/5.43 = zero_zero_complex )
% 5.15/5.43 = ( A = zero_zero_complex ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_0_iff
% 5.15/5.43 thf(fact_4205_dvd__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: real,A: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ B @ A )
% 5.15/5.43 => ( ( ( divide_divide_real @ A @ B )
% 5.15/5.43 = zero_zero_real )
% 5.15/5.43 = ( A = zero_zero_real ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_0_iff
% 5.15/5.43 thf(fact_4206_dvd__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: rat,A: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ B @ A )
% 5.15/5.43 => ( ( ( divide_divide_rat @ A @ B )
% 5.15/5.43 = zero_zero_rat )
% 5.15/5.43 = ( A = zero_zero_rat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_0_iff
% 5.15/5.43 thf(fact_4207_dvd__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ A )
% 5.15/5.43 => ( ( ( divide_divide_nat @ A @ B )
% 5.15/5.43 = zero_zero_nat )
% 5.15/5.43 = ( A = zero_zero_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_0_iff
% 5.15/5.43 thf(fact_4208_dvd__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ A )
% 5.15/5.43 => ( ( ( divide_divide_int @ A @ B )
% 5.15/5.43 = zero_zero_int )
% 5.15/5.43 = ( A = zero_zero_int ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_0_iff
% 5.15/5.43 thf(fact_4209_unit__mult__right__cancel,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.43 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.15/5.43 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_mult_right_cancel
% 5.15/5.43 thf(fact_4210_unit__mult__right__cancel,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.43 => ( ( ( times_times_nat @ B @ A )
% 5.15/5.43 = ( times_times_nat @ C @ A ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_mult_right_cancel
% 5.15/5.43 thf(fact_4211_unit__mult__right__cancel,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.43 => ( ( ( times_times_int @ B @ A )
% 5.15/5.43 = ( times_times_int @ C @ A ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_mult_right_cancel
% 5.15/5.43 thf(fact_4212_unit__mult__left__cancel,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.43 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.15/5.43 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_mult_left_cancel
% 5.15/5.43 thf(fact_4213_unit__mult__left__cancel,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.43 => ( ( ( times_times_nat @ A @ B )
% 5.15/5.43 = ( times_times_nat @ A @ C ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_mult_left_cancel
% 5.15/5.43 thf(fact_4214_unit__mult__left__cancel,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.43 => ( ( ( times_times_int @ A @ B )
% 5.15/5.43 = ( times_times_int @ A @ C ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_mult_left_cancel
% 5.15/5.43 thf(fact_4215_mult__unit__dvd__iff_H,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_unit_dvd_iff'
% 5.15/5.43 thf(fact_4216_mult__unit__dvd__iff_H,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_unit_dvd_iff'
% 5.15/5.43 thf(fact_4217_mult__unit__dvd__iff_H,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_unit_dvd_iff'
% 5.15/5.43 thf(fact_4218_dvd__mult__unit__iff_H,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_unit_iff'
% 5.15/5.43 thf(fact_4219_dvd__mult__unit__iff_H,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_unit_iff'
% 5.15/5.43 thf(fact_4220_dvd__mult__unit__iff_H,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_unit_iff'
% 5.15/5.43 thf(fact_4221_mult__unit__dvd__iff,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_unit_dvd_iff
% 5.15/5.43 thf(fact_4222_mult__unit__dvd__iff,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_unit_dvd_iff
% 5.15/5.43 thf(fact_4223_mult__unit__dvd__iff,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mult_unit_dvd_iff
% 5.15/5.43 thf(fact_4224_dvd__mult__unit__iff,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_unit_iff
% 5.15/5.43 thf(fact_4225_dvd__mult__unit__iff,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_unit_iff
% 5.15/5.43 thf(fact_4226_dvd__mult__unit__iff,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.15/5.43 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_unit_iff
% 5.15/5.43 thf(fact_4227_is__unit__mult__iff,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.15/5.43 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.43 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_mult_iff
% 5.15/5.43 thf(fact_4228_is__unit__mult__iff,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.15/5.43 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.43 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_mult_iff
% 5.15/5.43 thf(fact_4229_is__unit__mult__iff,axiom,
% 5.15/5.43 ! [A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.15/5.43 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.43 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_mult_iff
% 5.15/5.43 thf(fact_4230_div__mult__div__if__dvd,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.15/5.43 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_div_if_dvd
% 5.15/5.43 thf(fact_4231_div__mult__div__if__dvd,axiom,
% 5.15/5.43 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ A )
% 5.15/5.43 => ( ( dvd_dvd_nat @ D @ C )
% 5.15/5.43 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.15/5.43 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_div_if_dvd
% 5.15/5.43 thf(fact_4232_div__mult__div__if__dvd,axiom,
% 5.15/5.43 ! [B: int,A: int,D: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ A )
% 5.15/5.43 => ( ( dvd_dvd_int @ D @ C )
% 5.15/5.43 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.15/5.43 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_div_if_dvd
% 5.15/5.43 thf(fact_4233_dvd__mult__imp__div,axiom,
% 5.15/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_imp_div
% 5.15/5.43 thf(fact_4234_dvd__mult__imp__div,axiom,
% 5.15/5.43 ! [A: nat,C: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.15/5.43 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_imp_div
% 5.15/5.43 thf(fact_4235_dvd__mult__imp__div,axiom,
% 5.15/5.43 ! [A: int,C: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.15/5.43 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_mult_imp_div
% 5.15/5.43 thf(fact_4236_dvd__div__mult2__eq,axiom,
% 5.15/5.43 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_mult2_eq
% 5.15/5.43 thf(fact_4237_dvd__div__mult2__eq,axiom,
% 5.15/5.43 ! [B: nat,C: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.15/5.43 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.15/5.43 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_mult2_eq
% 5.15/5.43 thf(fact_4238_dvd__div__mult2__eq,axiom,
% 5.15/5.43 ! [B: int,C: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.15/5.43 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.43 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_mult2_eq
% 5.15/5.43 thf(fact_4239_div__div__eq__right,axiom,
% 5.15/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.15/5.43 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_div_eq_right
% 5.15/5.43 thf(fact_4240_div__div__eq__right,axiom,
% 5.15/5.43 ! [C: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ B @ A )
% 5.15/5.43 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.15/5.43 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_div_eq_right
% 5.15/5.43 thf(fact_4241_div__div__eq__right,axiom,
% 5.15/5.43 ! [C: int,B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ B @ A )
% 5.15/5.43 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.15/5.43 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_div_eq_right
% 5.15/5.43 thf(fact_4242_div__mult__swap,axiom,
% 5.15/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_swap
% 5.15/5.43 thf(fact_4243_div__mult__swap,axiom,
% 5.15/5.43 ! [C: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.15/5.43 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_swap
% 5.15/5.43 thf(fact_4244_div__mult__swap,axiom,
% 5.15/5.43 ! [C: int,B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.15/5.43 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_swap
% 5.15/5.43 thf(fact_4245_dvd__div__mult,axiom,
% 5.15/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_mult
% 5.15/5.43 thf(fact_4246_dvd__div__mult,axiom,
% 5.15/5.43 ! [C: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.15/5.43 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_mult
% 5.15/5.43 thf(fact_4247_dvd__div__mult,axiom,
% 5.15/5.43 ! [C: int,B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.15/5.43 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_mult
% 5.15/5.43 thf(fact_4248_dvd__div__unit__iff,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_unit_iff
% 5.15/5.43 thf(fact_4249_dvd__div__unit__iff,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_unit_iff
% 5.15/5.43 thf(fact_4250_dvd__div__unit__iff,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.15/5.43 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_unit_iff
% 5.15/5.43 thf(fact_4251_div__unit__dvd__iff,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_unit_dvd_iff
% 5.15/5.43 thf(fact_4252_div__unit__dvd__iff,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_unit_dvd_iff
% 5.15/5.43 thf(fact_4253_div__unit__dvd__iff,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_unit_dvd_iff
% 5.15/5.43 thf(fact_4254_unit__div__cancel,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.43 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.15/5.43 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_cancel
% 5.15/5.43 thf(fact_4255_unit__div__cancel,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.43 => ( ( ( divide_divide_nat @ B @ A )
% 5.15/5.43 = ( divide_divide_nat @ C @ A ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_cancel
% 5.15/5.43 thf(fact_4256_unit__div__cancel,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.43 => ( ( ( divide_divide_int @ B @ A )
% 5.15/5.43 = ( divide_divide_int @ C @ A ) )
% 5.15/5.43 = ( B = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_cancel
% 5.15/5.43 thf(fact_4257_div__plus__div__distrib__dvd__right,axiom,
% 5.15/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.15/5.43 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_plus_div_distrib_dvd_right
% 5.15/5.43 thf(fact_4258_div__plus__div__distrib__dvd__right,axiom,
% 5.15/5.43 ! [C: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.43 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_plus_div_distrib_dvd_right
% 5.15/5.43 thf(fact_4259_div__plus__div__distrib__dvd__right,axiom,
% 5.15/5.43 ! [C: int,B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.43 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_plus_div_distrib_dvd_right
% 5.15/5.43 thf(fact_4260_div__plus__div__distrib__dvd__left,axiom,
% 5.15/5.43 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.15/5.43 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_plus_div_distrib_dvd_left
% 5.15/5.43 thf(fact_4261_div__plus__div__distrib__dvd__left,axiom,
% 5.15/5.43 ! [C: nat,A: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ A )
% 5.15/5.43 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.15/5.43 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_plus_div_distrib_dvd_left
% 5.15/5.43 thf(fact_4262_div__plus__div__distrib__dvd__left,axiom,
% 5.15/5.43 ! [C: int,A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ A )
% 5.15/5.43 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.15/5.43 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_plus_div_distrib_dvd_left
% 5.15/5.43 thf(fact_4263_div__power,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.43 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N2 )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_power
% 5.15/5.43 thf(fact_4264_div__power,axiom,
% 5.15/5.43 ! [B: nat,A: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ A )
% 5.15/5.43 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
% 5.15/5.43 = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_power
% 5.15/5.43 thf(fact_4265_div__power,axiom,
% 5.15/5.43 ! [B: int,A: int,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ A )
% 5.15/5.43 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N2 )
% 5.15/5.43 = ( divide_divide_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_power
% 5.15/5.43 thf(fact_4266_mod__eq__0__iff__dvd,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ( ( ( modulo_modulo_nat @ A @ B )
% 5.15/5.43 = zero_zero_nat )
% 5.15/5.43 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_eq_0_iff_dvd
% 5.15/5.43 thf(fact_4267_mod__eq__0__iff__dvd,axiom,
% 5.15/5.43 ! [A: int,B: int] :
% 5.15/5.43 ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.43 = zero_zero_int )
% 5.15/5.43 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_eq_0_iff_dvd
% 5.15/5.43 thf(fact_4268_mod__eq__0__iff__dvd,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.15/5.43 = zero_z3403309356797280102nteger )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_eq_0_iff_dvd
% 5.15/5.43 thf(fact_4269_dvd__eq__mod__eq__0,axiom,
% 5.15/5.43 ( dvd_dvd_nat
% 5.15/5.43 = ( ^ [A3: nat,B2: nat] :
% 5.15/5.43 ( ( modulo_modulo_nat @ B2 @ A3 )
% 5.15/5.43 = zero_zero_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_eq_mod_eq_0
% 5.15/5.43 thf(fact_4270_dvd__eq__mod__eq__0,axiom,
% 5.15/5.43 ( dvd_dvd_int
% 5.15/5.43 = ( ^ [A3: int,B2: int] :
% 5.15/5.43 ( ( modulo_modulo_int @ B2 @ A3 )
% 5.15/5.43 = zero_zero_int ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_eq_mod_eq_0
% 5.15/5.43 thf(fact_4271_dvd__eq__mod__eq__0,axiom,
% 5.15/5.43 ( dvd_dvd_Code_integer
% 5.15/5.43 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.15/5.43 ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 5.15/5.43 = zero_z3403309356797280102nteger ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_eq_mod_eq_0
% 5.15/5.43 thf(fact_4272_mod__0__imp__dvd,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ( ( ( modulo_modulo_nat @ A @ B )
% 5.15/5.43 = zero_zero_nat )
% 5.15/5.43 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_0_imp_dvd
% 5.15/5.43 thf(fact_4273_mod__0__imp__dvd,axiom,
% 5.15/5.43 ! [A: int,B: int] :
% 5.15/5.43 ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.43 = zero_zero_int )
% 5.15/5.43 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_0_imp_dvd
% 5.15/5.43 thf(fact_4274_mod__0__imp__dvd,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.15/5.43 = zero_z3403309356797280102nteger )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_0_imp_dvd
% 5.15/5.43 thf(fact_4275_dvd__power__le,axiom,
% 5.15/5.43 ! [X: code_integer,Y: code_integer,N2: nat,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.15/5.43 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_le
% 5.15/5.43 thf(fact_4276_dvd__power__le,axiom,
% 5.15/5.43 ! [X: nat,Y: nat,N2: nat,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ X @ Y )
% 5.15/5.43 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.43 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_le
% 5.15/5.43 thf(fact_4277_dvd__power__le,axiom,
% 5.15/5.43 ! [X: real,Y: real,N2: nat,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_real @ X @ Y )
% 5.15/5.43 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.43 => ( dvd_dvd_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_le
% 5.15/5.43 thf(fact_4278_dvd__power__le,axiom,
% 5.15/5.43 ! [X: complex,Y: complex,N2: nat,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_complex @ X @ Y )
% 5.15/5.43 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.43 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_le
% 5.15/5.43 thf(fact_4279_dvd__power__le,axiom,
% 5.15/5.43 ! [X: int,Y: int,N2: nat,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_int @ X @ Y )
% 5.15/5.43 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.43 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_power_le
% 5.15/5.43 thf(fact_4280_power__le__dvd,axiom,
% 5.15/5.43 ! [A: code_integer,N2: nat,B: code_integer,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ B )
% 5.15/5.43 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_le_dvd
% 5.15/5.43 thf(fact_4281_power__le__dvd,axiom,
% 5.15/5.43 ! [A: nat,N2: nat,B: nat,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 5.15/5.43 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_le_dvd
% 5.15/5.43 thf(fact_4282_power__le__dvd,axiom,
% 5.15/5.43 ! [A: real,N2: nat,B: real,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 5.15/5.43 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_le_dvd
% 5.15/5.43 thf(fact_4283_power__le__dvd,axiom,
% 5.15/5.43 ! [A: complex,N2: nat,B: complex,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 5.15/5.43 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_le_dvd
% 5.15/5.43 thf(fact_4284_power__le__dvd,axiom,
% 5.15/5.43 ! [A: int,N2: nat,B: int,M: nat] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 5.15/5.43 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % power_le_dvd
% 5.15/5.43 thf(fact_4285_le__imp__power__dvd,axiom,
% 5.15/5.43 ! [M: nat,N2: nat,A: code_integer] :
% 5.15/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % le_imp_power_dvd
% 5.15/5.43 thf(fact_4286_le__imp__power__dvd,axiom,
% 5.15/5.43 ! [M: nat,N2: nat,A: nat] :
% 5.15/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % le_imp_power_dvd
% 5.15/5.43 thf(fact_4287_le__imp__power__dvd,axiom,
% 5.15/5.43 ! [M: nat,N2: nat,A: real] :
% 5.15/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % le_imp_power_dvd
% 5.15/5.43 thf(fact_4288_le__imp__power__dvd,axiom,
% 5.15/5.43 ! [M: nat,N2: nat,A: complex] :
% 5.15/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % le_imp_power_dvd
% 5.15/5.43 thf(fact_4289_le__imp__power__dvd,axiom,
% 5.15/5.43 ! [M: nat,N2: nat,A: int] :
% 5.15/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % le_imp_power_dvd
% 5.15/5.43 thf(fact_4290_dvd__minus__mod,axiom,
% 5.15/5.43 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_minus_mod
% 5.15/5.43 thf(fact_4291_dvd__minus__mod,axiom,
% 5.15/5.43 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_minus_mod
% 5.15/5.43 thf(fact_4292_dvd__minus__mod,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_minus_mod
% 5.15/5.43 thf(fact_4293_mod__eq__dvd__iff,axiom,
% 5.15/5.43 ! [A: int,C: int,B: int] :
% 5.15/5.43 ( ( ( modulo_modulo_int @ A @ C )
% 5.15/5.43 = ( modulo_modulo_int @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_eq_dvd_iff
% 5.15/5.43 thf(fact_4294_mod__eq__dvd__iff,axiom,
% 5.15/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.15/5.43 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.15/5.43 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % mod_eq_dvd_iff
% 5.15/5.43 thf(fact_4295_dvd__pos__nat,axiom,
% 5.15/5.43 ! [N2: nat,M: nat] :
% 5.15/5.43 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.43 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.15/5.43 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_pos_nat
% 5.15/5.43 thf(fact_4296_nat__dvd__not__less,axiom,
% 5.15/5.43 ! [M: nat,N2: nat] :
% 5.15/5.43 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.43 => ( ( ord_less_nat @ M @ N2 )
% 5.15/5.43 => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % nat_dvd_not_less
% 5.15/5.43 thf(fact_4297_dvd__minus__self,axiom,
% 5.15/5.43 ! [M: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 5.15/5.43 = ( ( ord_less_nat @ N2 @ M )
% 5.15/5.43 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_minus_self
% 5.15/5.43 thf(fact_4298_dvd__diffD,axiom,
% 5.15/5.43 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.43 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.15/5.43 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.43 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diffD
% 5.15/5.43 thf(fact_4299_dvd__diffD1,axiom,
% 5.15/5.43 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.43 => ( ( dvd_dvd_nat @ K @ M )
% 5.15/5.43 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.43 => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_diffD1
% 5.15/5.43 thf(fact_4300_less__eq__dvd__minus,axiom,
% 5.15/5.43 ! [M: nat,N2: nat] :
% 5.15/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.43 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.15/5.43 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % less_eq_dvd_minus
% 5.15/5.43 thf(fact_4301_bezout__lemma__nat,axiom,
% 5.15/5.43 ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ D @ A )
% 5.15/5.43 => ( ( dvd_dvd_nat @ D @ B )
% 5.15/5.43 => ( ( ( ( times_times_nat @ A @ X )
% 5.15/5.43 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.15/5.43 | ( ( times_times_nat @ B @ X )
% 5.15/5.43 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.15/5.43 => ? [X3: nat,Y3: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ D @ A )
% 5.15/5.43 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.15/5.43 & ( ( ( times_times_nat @ A @ X3 )
% 5.15/5.43 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.15/5.43 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 5.15/5.43 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % bezout_lemma_nat
% 5.15/5.43 thf(fact_4302_bezout__add__nat,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ? [D3: nat,X3: nat,Y3: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ D3 @ A )
% 5.15/5.43 & ( dvd_dvd_nat @ D3 @ B )
% 5.15/5.43 & ( ( ( times_times_nat @ A @ X3 )
% 5.15/5.43 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.15/5.43 | ( ( times_times_nat @ B @ X3 )
% 5.15/5.43 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % bezout_add_nat
% 5.15/5.43 thf(fact_4303_zdvd__mult__cancel,axiom,
% 5.15/5.43 ! [K: int,M: int,N2: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N2 ) )
% 5.15/5.43 => ( ( K != zero_zero_int )
% 5.15/5.43 => ( dvd_dvd_int @ M @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zdvd_mult_cancel
% 5.15/5.43 thf(fact_4304_zdvd__mono,axiom,
% 5.15/5.43 ! [K: int,M: int,T: int] :
% 5.15/5.43 ( ( K != zero_zero_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ M @ T )
% 5.15/5.43 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zdvd_mono
% 5.15/5.43 thf(fact_4305_bezout1__nat,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ? [D3: nat,X3: nat,Y3: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ D3 @ A )
% 5.15/5.43 & ( dvd_dvd_nat @ D3 @ B )
% 5.15/5.43 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.15/5.43 = D3 )
% 5.15/5.43 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.15/5.43 = D3 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % bezout1_nat
% 5.15/5.43 thf(fact_4306_zdvd__period,axiom,
% 5.15/5.43 ! [A: int,D: int,X: int,T: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ D )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 5.15/5.43 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % zdvd_period
% 5.15/5.43 thf(fact_4307_zdvd__reduce,axiom,
% 5.15/5.43 ! [K: int,N2: int,M: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N2 @ ( times_times_int @ K @ M ) ) )
% 5.15/5.43 = ( dvd_dvd_int @ K @ N2 ) ) ).
% 5.15/5.43
% 5.15/5.43 % zdvd_reduce
% 5.15/5.43 thf(fact_4308_finite__divisors__int,axiom,
% 5.15/5.43 ! [I: int] :
% 5.15/5.43 ( ( I != zero_zero_int )
% 5.15/5.43 => ( finite_finite_int
% 5.15/5.43 @ ( collect_int
% 5.15/5.43 @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ I ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % finite_divisors_int
% 5.15/5.43 thf(fact_4309_unit__dvdE,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.43 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.43 => ! [C2: code_integer] :
% 5.15/5.43 ( B
% 5.15/5.43 != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_dvdE
% 5.15/5.43 thf(fact_4310_unit__dvdE,axiom,
% 5.15/5.43 ! [A: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.43 => ~ ( ( A != zero_zero_nat )
% 5.15/5.43 => ! [C2: nat] :
% 5.15/5.43 ( B
% 5.15/5.43 != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_dvdE
% 5.15/5.43 thf(fact_4311_unit__dvdE,axiom,
% 5.15/5.43 ! [A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.43 => ~ ( ( A != zero_zero_int )
% 5.15/5.43 => ! [C2: int] :
% 5.15/5.43 ( B
% 5.15/5.43 != ( times_times_int @ A @ C2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_dvdE
% 5.15/5.43 thf(fact_4312_unity__coeff__ex,axiom,
% 5.15/5.43 ! [P: code_integer > $o,L: code_integer] :
% 5.15/5.43 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X2 ) ) )
% 5.15/5.43 = ( ? [X2: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 5.15/5.43 & ( P @ X2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unity_coeff_ex
% 5.15/5.43 thf(fact_4313_unity__coeff__ex,axiom,
% 5.15/5.43 ! [P: complex > $o,L: complex] :
% 5.15/5.43 ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L @ X2 ) ) )
% 5.15/5.43 = ( ? [X2: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 5.15/5.43 & ( P @ X2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unity_coeff_ex
% 5.15/5.43 thf(fact_4314_unity__coeff__ex,axiom,
% 5.15/5.43 ! [P: real > $o,L: real] :
% 5.15/5.43 ( ( ? [X2: real] : ( P @ ( times_times_real @ L @ X2 ) ) )
% 5.15/5.43 = ( ? [X2: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 5.15/5.43 & ( P @ X2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unity_coeff_ex
% 5.15/5.43 thf(fact_4315_unity__coeff__ex,axiom,
% 5.15/5.43 ! [P: rat > $o,L: rat] :
% 5.15/5.43 ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L @ X2 ) ) )
% 5.15/5.43 = ( ? [X2: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 5.15/5.43 & ( P @ X2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unity_coeff_ex
% 5.15/5.43 thf(fact_4316_unity__coeff__ex,axiom,
% 5.15/5.43 ! [P: nat > $o,L: nat] :
% 5.15/5.43 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L @ X2 ) ) )
% 5.15/5.43 = ( ? [X2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 5.15/5.43 & ( P @ X2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unity_coeff_ex
% 5.15/5.43 thf(fact_4317_unity__coeff__ex,axiom,
% 5.15/5.43 ! [P: int > $o,L: int] :
% 5.15/5.43 ( ( ? [X2: int] : ( P @ ( times_times_int @ L @ X2 ) ) )
% 5.15/5.43 = ( ? [X2: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 5.15/5.43 & ( P @ X2 ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unity_coeff_ex
% 5.15/5.43 thf(fact_4318_dvd__div__eq__mult,axiom,
% 5.15/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.15/5.43 ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.15/5.43 = C )
% 5.15/5.43 = ( B
% 5.15/5.43 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_mult
% 5.15/5.43 thf(fact_4319_dvd__div__eq__mult,axiom,
% 5.15/5.43 ! [A: nat,B: nat,C: nat] :
% 5.15/5.43 ( ( A != zero_zero_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 => ( ( ( divide_divide_nat @ B @ A )
% 5.15/5.43 = C )
% 5.15/5.43 = ( B
% 5.15/5.43 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_mult
% 5.15/5.43 thf(fact_4320_dvd__div__eq__mult,axiom,
% 5.15/5.43 ! [A: int,B: int,C: int] :
% 5.15/5.43 ( ( A != zero_zero_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 => ( ( ( divide_divide_int @ B @ A )
% 5.15/5.43 = C )
% 5.15/5.43 = ( B
% 5.15/5.43 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_eq_mult
% 5.15/5.43 thf(fact_4321_div__dvd__iff__mult,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( B != zero_z3403309356797280102nteger )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_dvd_iff_mult
% 5.15/5.43 thf(fact_4322_div__dvd__iff__mult,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( B != zero_zero_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ B @ A )
% 5.15/5.43 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_dvd_iff_mult
% 5.15/5.43 thf(fact_4323_div__dvd__iff__mult,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( B != zero_zero_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ B @ A )
% 5.15/5.43 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.15/5.43 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_dvd_iff_mult
% 5.15/5.43 thf(fact_4324_dvd__div__iff__mult,axiom,
% 5.15/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( C != zero_z3403309356797280102nteger )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_iff_mult
% 5.15/5.43 thf(fact_4325_dvd__div__iff__mult,axiom,
% 5.15/5.43 ! [C: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( C != zero_zero_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_iff_mult
% 5.15/5.43 thf(fact_4326_dvd__div__iff__mult,axiom,
% 5.15/5.43 ! [C: int,B: int,A: int] :
% 5.15/5.43 ( ( C != zero_zero_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.15/5.43 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_iff_mult
% 5.15/5.43 thf(fact_4327_dvd__div__div__eq__mult,axiom,
% 5.15/5.43 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.15/5.43 ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.43 => ( ( C != zero_z3403309356797280102nteger )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.15/5.43 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.15/5.43 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.15/5.43 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.15/5.43 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_div_eq_mult
% 5.15/5.43 thf(fact_4328_dvd__div__div__eq__mult,axiom,
% 5.15/5.43 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.15/5.43 ( ( A != zero_zero_nat )
% 5.15/5.43 => ( ( C != zero_zero_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ D )
% 5.15/5.43 => ( ( ( divide_divide_nat @ B @ A )
% 5.15/5.43 = ( divide_divide_nat @ D @ C ) )
% 5.15/5.43 = ( ( times_times_nat @ B @ C )
% 5.15/5.43 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_div_eq_mult
% 5.15/5.43 thf(fact_4329_dvd__div__div__eq__mult,axiom,
% 5.15/5.43 ! [A: int,C: int,B: int,D: int] :
% 5.15/5.43 ( ( A != zero_zero_int )
% 5.15/5.43 => ( ( C != zero_zero_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ A @ B )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ D )
% 5.15/5.43 => ( ( ( divide_divide_int @ B @ A )
% 5.15/5.43 = ( divide_divide_int @ D @ C ) )
% 5.15/5.43 = ( ( times_times_int @ B @ C )
% 5.15/5.43 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % dvd_div_div_eq_mult
% 5.15/5.43 thf(fact_4330_unit__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.15/5.43 = zero_z3403309356797280102nteger )
% 5.15/5.43 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_eq_0_iff
% 5.15/5.43 thf(fact_4331_unit__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( ( divide_divide_nat @ A @ B )
% 5.15/5.43 = zero_zero_nat )
% 5.15/5.43 = ( A = zero_zero_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_eq_0_iff
% 5.15/5.43 thf(fact_4332_unit__div__eq__0__iff,axiom,
% 5.15/5.43 ! [B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( ( divide_divide_int @ A @ B )
% 5.15/5.43 = zero_zero_int )
% 5.15/5.43 = ( A = zero_zero_int ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_eq_0_iff
% 5.15/5.43 thf(fact_4333_even__numeral,axiom,
% 5.15/5.43 ! [N2: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_numeral
% 5.15/5.43 thf(fact_4334_even__numeral,axiom,
% 5.15/5.43 ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_numeral
% 5.15/5.43 thf(fact_4335_even__numeral,axiom,
% 5.15/5.43 ! [N2: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % even_numeral
% 5.15/5.43 thf(fact_4336_inf__period_I4_J,axiom,
% 5.15/5.43 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.15/5.43 => ! [X5: code_integer,K4: code_integer] :
% 5.15/5.43 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(4)
% 5.15/5.43 thf(fact_4337_inf__period_I4_J,axiom,
% 5.15/5.43 ! [D: complex,D4: complex,T: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ D @ D4 )
% 5.15/5.43 => ! [X5: complex,K4: complex] :
% 5.15/5.43 ( ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X5 @ T ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(4)
% 5.15/5.43 thf(fact_4338_inf__period_I4_J,axiom,
% 5.15/5.43 ! [D: real,D4: real,T: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ D @ D4 )
% 5.15/5.43 => ! [X5: real,K4: real] :
% 5.15/5.43 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(4)
% 5.15/5.43 thf(fact_4339_inf__period_I4_J,axiom,
% 5.15/5.43 ! [D: rat,D4: rat,T: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ D @ D4 )
% 5.15/5.43 => ! [X5: rat,K4: rat] :
% 5.15/5.43 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(4)
% 5.15/5.43 thf(fact_4340_inf__period_I4_J,axiom,
% 5.15/5.43 ! [D: int,D4: int,T: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ D @ D4 )
% 5.15/5.43 => ! [X5: int,K4: int] :
% 5.15/5.43 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 5.15/5.43 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(4)
% 5.15/5.43 thf(fact_4341_inf__period_I3_J,axiom,
% 5.15/5.43 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.15/5.43 => ! [X5: code_integer,K4: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 5.15/5.43 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(3)
% 5.15/5.43 thf(fact_4342_inf__period_I3_J,axiom,
% 5.15/5.43 ! [D: complex,D4: complex,T: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ D @ D4 )
% 5.15/5.43 => ! [X5: complex,K4: complex] :
% 5.15/5.43 ( ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X5 @ T ) )
% 5.15/5.43 = ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(3)
% 5.15/5.43 thf(fact_4343_inf__period_I3_J,axiom,
% 5.15/5.43 ! [D: real,D4: real,T: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ D @ D4 )
% 5.15/5.43 => ! [X5: real,K4: real] :
% 5.15/5.43 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 5.15/5.43 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(3)
% 5.15/5.43 thf(fact_4344_inf__period_I3_J,axiom,
% 5.15/5.43 ! [D: rat,D4: rat,T: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ D @ D4 )
% 5.15/5.43 => ! [X5: rat,K4: rat] :
% 5.15/5.43 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 5.15/5.43 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(3)
% 5.15/5.43 thf(fact_4345_inf__period_I3_J,axiom,
% 5.15/5.43 ! [D: int,D4: int,T: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ D @ D4 )
% 5.15/5.43 => ! [X5: int,K4: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.15/5.43 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % inf_period(3)
% 5.15/5.43 thf(fact_4346_is__unit__div__mult2__eq,axiom,
% 5.15/5.43 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_div_mult2_eq
% 5.15/5.43 thf(fact_4347_is__unit__div__mult2__eq,axiom,
% 5.15/5.43 ! [B: nat,C: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.15/5.43 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.15/5.43 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_div_mult2_eq
% 5.15/5.43 thf(fact_4348_is__unit__div__mult2__eq,axiom,
% 5.15/5.43 ! [B: int,C: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.15/5.43 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.43 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_div_mult2_eq
% 5.15/5.43 thf(fact_4349_unit__div__mult__swap,axiom,
% 5.15/5.43 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.15/5.43 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_mult_swap
% 5.15/5.43 thf(fact_4350_unit__div__mult__swap,axiom,
% 5.15/5.43 ! [C: nat,A: nat,B: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.15/5.43 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.15/5.43 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_mult_swap
% 5.15/5.43 thf(fact_4351_unit__div__mult__swap,axiom,
% 5.15/5.43 ! [C: int,A: int,B: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.15/5.43 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.15/5.43 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_mult_swap
% 5.15/5.43 thf(fact_4352_unit__div__commute,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_commute
% 5.15/5.43 thf(fact_4353_unit__div__commute,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.15/5.43 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_commute
% 5.15/5.43 thf(fact_4354_unit__div__commute,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.15/5.43 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_div_commute
% 5.15/5.43 thf(fact_4355_div__mult__unit2,axiom,
% 5.15/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.15/5.43 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.43 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.15/5.43 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_unit2
% 5.15/5.43 thf(fact_4356_div__mult__unit2,axiom,
% 5.15/5.43 ! [C: nat,B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.15/5.43 => ( ( dvd_dvd_nat @ B @ A )
% 5.15/5.43 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.15/5.43 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_unit2
% 5.15/5.43 thf(fact_4357_div__mult__unit2,axiom,
% 5.15/5.43 ! [C: int,B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.15/5.43 => ( ( dvd_dvd_int @ B @ A )
% 5.15/5.43 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.15/5.43 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % div_mult_unit2
% 5.15/5.43 thf(fact_4358_unit__eq__div2,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( A
% 5.15/5.43 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.15/5.43 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.15/5.43 = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_eq_div2
% 5.15/5.43 thf(fact_4359_unit__eq__div2,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( A
% 5.15/5.43 = ( divide_divide_nat @ C @ B ) )
% 5.15/5.43 = ( ( times_times_nat @ A @ B )
% 5.15/5.43 = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_eq_div2
% 5.15/5.43 thf(fact_4360_unit__eq__div2,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( A
% 5.15/5.43 = ( divide_divide_int @ C @ B ) )
% 5.15/5.43 = ( ( times_times_int @ A @ B )
% 5.15/5.43 = C ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_eq_div2
% 5.15/5.43 thf(fact_4361_unit__eq__div1,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.15/5.43 = C )
% 5.15/5.43 = ( A
% 5.15/5.43 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_eq_div1
% 5.15/5.43 thf(fact_4362_unit__eq__div1,axiom,
% 5.15/5.43 ! [B: nat,A: nat,C: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( ( divide_divide_nat @ A @ B )
% 5.15/5.43 = C )
% 5.15/5.43 = ( A
% 5.15/5.43 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_eq_div1
% 5.15/5.43 thf(fact_4363_unit__eq__div1,axiom,
% 5.15/5.43 ! [B: int,A: int,C: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( ( divide_divide_int @ A @ B )
% 5.15/5.43 = C )
% 5.15/5.43 = ( A
% 5.15/5.43 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_eq_div1
% 5.15/5.43 thf(fact_4364_is__unit__power__iff,axiom,
% 5.15/5.43 ! [A: code_integer,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 5.15/5.43 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.43 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_power_iff
% 5.15/5.43 thf(fact_4365_is__unit__power__iff,axiom,
% 5.15/5.43 ! [A: nat,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 5.15/5.43 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.43 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_power_iff
% 5.15/5.43 thf(fact_4366_is__unit__power__iff,axiom,
% 5.15/5.43 ! [A: int,N2: nat] :
% 5.15/5.43 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 5.15/5.43 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.43 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.43
% 5.15/5.43 % is_unit_power_iff
% 5.15/5.43 thf(fact_4367_unit__imp__mod__eq__0,axiom,
% 5.15/5.43 ! [B: nat,A: nat] :
% 5.15/5.43 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.43 => ( ( modulo_modulo_nat @ A @ B )
% 5.15/5.43 = zero_zero_nat ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_imp_mod_eq_0
% 5.15/5.43 thf(fact_4368_unit__imp__mod__eq__0,axiom,
% 5.15/5.43 ! [B: int,A: int] :
% 5.15/5.43 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.43 => ( ( modulo_modulo_int @ A @ B )
% 5.15/5.43 = zero_zero_int ) ) ).
% 5.15/5.43
% 5.15/5.43 % unit_imp_mod_eq_0
% 5.15/5.43 thf(fact_4369_unit__imp__mod__eq__0,axiom,
% 5.15/5.43 ! [B: code_integer,A: code_integer] :
% 5.15/5.43 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.43 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % unit_imp_mod_eq_0
% 5.15/5.44 thf(fact_4370_dvd__imp__le,axiom,
% 5.15/5.44 ! [K: nat,N2: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ K @ N2 )
% 5.15/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_imp_le
% 5.15/5.44 thf(fact_4371_nat__mult__dvd__cancel1,axiom,
% 5.15/5.44 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.44 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.44 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.44 = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % nat_mult_dvd_cancel1
% 5.15/5.44 thf(fact_4372_dvd__mult__cancel,axiom,
% 5.15/5.44 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.15/5.44 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.44 => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_mult_cancel
% 5.15/5.44 thf(fact_4373_bezout__add__strong__nat,axiom,
% 5.15/5.44 ! [A: nat,B: nat] :
% 5.15/5.44 ( ( A != zero_zero_nat )
% 5.15/5.44 => ? [D3: nat,X3: nat,Y3: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ D3 @ A )
% 5.15/5.44 & ( dvd_dvd_nat @ D3 @ B )
% 5.15/5.44 & ( ( times_times_nat @ A @ X3 )
% 5.15/5.44 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % bezout_add_strong_nat
% 5.15/5.44 thf(fact_4374_mod__greater__zero__iff__not__dvd,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.15/5.44 = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod_greater_zero_iff_not_dvd
% 5.15/5.44 thf(fact_4375_set__decode__def,axiom,
% 5.15/5.44 ( nat_set_decode
% 5.15/5.44 = ( ^ [X2: nat] :
% 5.15/5.44 ( collect_nat
% 5.15/5.44 @ ^ [N3: nat] :
% 5.15/5.44 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % set_decode_def
% 5.15/5.44 thf(fact_4376_mod__eq__dvd__iff__nat,axiom,
% 5.15/5.44 ! [N2: nat,M: nat,Q3: nat] :
% 5.15/5.44 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.44 => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.15/5.44 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 5.15/5.44 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod_eq_dvd_iff_nat
% 5.15/5.44 thf(fact_4377_finite__divisors__nat,axiom,
% 5.15/5.44 ! [M: nat] :
% 5.15/5.44 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.44 => ( finite_finite_nat
% 5.15/5.44 @ ( collect_nat
% 5.15/5.44 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % finite_divisors_nat
% 5.15/5.44 thf(fact_4378_even__zero,axiom,
% 5.15/5.44 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.15/5.44
% 5.15/5.44 % even_zero
% 5.15/5.44 thf(fact_4379_even__zero,axiom,
% 5.15/5.44 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.15/5.44
% 5.15/5.44 % even_zero
% 5.15/5.44 thf(fact_4380_even__zero,axiom,
% 5.15/5.44 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.15/5.44
% 5.15/5.44 % even_zero
% 5.15/5.44 thf(fact_4381_is__unit__div__mult__cancel__right,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.44 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.44 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.15/5.44 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unit_div_mult_cancel_right
% 5.15/5.44 thf(fact_4382_is__unit__div__mult__cancel__right,axiom,
% 5.15/5.44 ! [A: nat,B: nat] :
% 5.15/5.44 ( ( A != zero_zero_nat )
% 5.15/5.44 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.44 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.15/5.44 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unit_div_mult_cancel_right
% 5.15/5.44 thf(fact_4383_is__unit__div__mult__cancel__right,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( A != zero_zero_int )
% 5.15/5.44 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.44 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.15/5.44 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unit_div_mult_cancel_right
% 5.15/5.44 thf(fact_4384_is__unit__div__mult__cancel__left,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.44 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.15/5.44 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.15/5.44 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unit_div_mult_cancel_left
% 5.15/5.44 thf(fact_4385_is__unit__div__mult__cancel__left,axiom,
% 5.15/5.44 ! [A: nat,B: nat] :
% 5.15/5.44 ( ( A != zero_zero_nat )
% 5.15/5.44 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.15/5.44 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.15/5.44 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unit_div_mult_cancel_left
% 5.15/5.44 thf(fact_4386_is__unit__div__mult__cancel__left,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( A != zero_zero_int )
% 5.15/5.44 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.15/5.44 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.15/5.44 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unit_div_mult_cancel_left
% 5.15/5.44 thf(fact_4387_is__unitE,axiom,
% 5.15/5.44 ! [A: code_integer,C: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.15/5.44 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.44 => ! [B6: code_integer] :
% 5.15/5.44 ( ( B6 != zero_z3403309356797280102nteger )
% 5.15/5.44 => ( ( dvd_dvd_Code_integer @ B6 @ one_one_Code_integer )
% 5.15/5.44 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.15/5.44 = B6 )
% 5.15/5.44 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B6 )
% 5.15/5.44 = A )
% 5.15/5.44 => ( ( ( times_3573771949741848930nteger @ A @ B6 )
% 5.15/5.44 = one_one_Code_integer )
% 5.15/5.44 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.15/5.44 != ( times_3573771949741848930nteger @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unitE
% 5.15/5.44 thf(fact_4388_is__unitE,axiom,
% 5.15/5.44 ! [A: nat,C: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.15/5.44 => ~ ( ( A != zero_zero_nat )
% 5.15/5.44 => ! [B6: nat] :
% 5.15/5.44 ( ( B6 != zero_zero_nat )
% 5.15/5.44 => ( ( dvd_dvd_nat @ B6 @ one_one_nat )
% 5.15/5.44 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.15/5.44 = B6 )
% 5.15/5.44 => ( ( ( divide_divide_nat @ one_one_nat @ B6 )
% 5.15/5.44 = A )
% 5.15/5.44 => ( ( ( times_times_nat @ A @ B6 )
% 5.15/5.44 = one_one_nat )
% 5.15/5.44 => ( ( divide_divide_nat @ C @ A )
% 5.15/5.44 != ( times_times_nat @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unitE
% 5.15/5.44 thf(fact_4389_is__unitE,axiom,
% 5.15/5.44 ! [A: int,C: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.15/5.44 => ~ ( ( A != zero_zero_int )
% 5.15/5.44 => ! [B6: int] :
% 5.15/5.44 ( ( B6 != zero_zero_int )
% 5.15/5.44 => ( ( dvd_dvd_int @ B6 @ one_one_int )
% 5.15/5.44 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.15/5.44 = B6 )
% 5.15/5.44 => ( ( ( divide_divide_int @ one_one_int @ B6 )
% 5.15/5.44 = A )
% 5.15/5.44 => ( ( ( times_times_int @ A @ B6 )
% 5.15/5.44 = one_one_int )
% 5.15/5.44 => ( ( divide_divide_int @ C @ A )
% 5.15/5.44 != ( times_times_int @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % is_unitE
% 5.15/5.44 thf(fact_4390_evenE,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ~ ! [B6: code_integer] :
% 5.15/5.44 ( A
% 5.15/5.44 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % evenE
% 5.15/5.44 thf(fact_4391_evenE,axiom,
% 5.15/5.44 ! [A: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ~ ! [B6: nat] :
% 5.15/5.44 ( A
% 5.15/5.44 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % evenE
% 5.15/5.44 thf(fact_4392_evenE,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ~ ! [B6: int] :
% 5.15/5.44 ( A
% 5.15/5.44 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % evenE
% 5.15/5.44 thf(fact_4393_odd__one,axiom,
% 5.15/5.44 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.15/5.44
% 5.15/5.44 % odd_one
% 5.15/5.44 thf(fact_4394_odd__one,axiom,
% 5.15/5.44 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.15/5.44
% 5.15/5.44 % odd_one
% 5.15/5.44 thf(fact_4395_odd__one,axiom,
% 5.15/5.44 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.15/5.44
% 5.15/5.44 % odd_one
% 5.15/5.44 thf(fact_4396_odd__even__add,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.15/5.44 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_even_add
% 5.15/5.44 thf(fact_4397_odd__even__add,axiom,
% 5.15/5.44 ! [A: nat,B: nat] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.15/5.44 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_even_add
% 5.15/5.44 thf(fact_4398_odd__even__add,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.15/5.44 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_even_add
% 5.15/5.44 thf(fact_4399_bit__eq__rec,axiom,
% 5.15/5.44 ( ( ^ [Y5: code_integer,Z5: code_integer] : ( Y5 = Z5 ) )
% 5.15/5.44 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.15/5.44 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 5.15/5.44 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 5.15/5.44 & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.44 = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % bit_eq_rec
% 5.15/5.44 thf(fact_4400_bit__eq__rec,axiom,
% 5.15/5.44 ( ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 ) )
% 5.15/5.44 = ( ^ [A3: nat,B2: nat] :
% 5.15/5.44 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 5.15/5.44 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 5.15/5.44 & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.44 = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % bit_eq_rec
% 5.15/5.44 thf(fact_4401_bit__eq__rec,axiom,
% 5.15/5.44 ( ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 ) )
% 5.15/5.44 = ( ^ [A3: int,B2: int] :
% 5.15/5.44 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 5.15/5.44 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 5.15/5.44 & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.44 = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % bit_eq_rec
% 5.15/5.44 thf(fact_4402_dvd__power__iff,axiom,
% 5.15/5.44 ! [X: code_integer,M: nat,N2: nat] :
% 5.15/5.44 ( ( X != zero_z3403309356797280102nteger )
% 5.15/5.44 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 5.15/5.44 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.15/5.44 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power_iff
% 5.15/5.44 thf(fact_4403_dvd__power__iff,axiom,
% 5.15/5.44 ! [X: nat,M: nat,N2: nat] :
% 5.15/5.44 ( ( X != zero_zero_nat )
% 5.15/5.44 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N2 ) )
% 5.15/5.44 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.15/5.44 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power_iff
% 5.15/5.44 thf(fact_4404_dvd__power__iff,axiom,
% 5.15/5.44 ! [X: int,M: nat,N2: nat] :
% 5.15/5.44 ( ( X != zero_zero_int )
% 5.15/5.44 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N2 ) )
% 5.15/5.44 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.15/5.44 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power_iff
% 5.15/5.44 thf(fact_4405_odd__numeral,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_numeral
% 5.15/5.44 thf(fact_4406_odd__numeral,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_numeral
% 5.15/5.44 thf(fact_4407_odd__numeral,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_numeral
% 5.15/5.44 thf(fact_4408_subset__decode__imp__le,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 5.15/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % subset_decode_imp_le
% 5.15/5.44 thf(fact_4409_dvd__power,axiom,
% 5.15/5.44 ! [N2: nat,X: code_integer] :
% 5.15/5.44 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 | ( X = one_one_Code_integer ) )
% 5.15/5.44 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power
% 5.15/5.44 thf(fact_4410_dvd__power,axiom,
% 5.15/5.44 ! [N2: nat,X: rat] :
% 5.15/5.44 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 | ( X = one_one_rat ) )
% 5.15/5.44 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power
% 5.15/5.44 thf(fact_4411_dvd__power,axiom,
% 5.15/5.44 ! [N2: nat,X: nat] :
% 5.15/5.44 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 | ( X = one_one_nat ) )
% 5.15/5.44 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power
% 5.15/5.44 thf(fact_4412_dvd__power,axiom,
% 5.15/5.44 ! [N2: nat,X: real] :
% 5.15/5.44 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 | ( X = one_one_real ) )
% 5.15/5.44 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power
% 5.15/5.44 thf(fact_4413_dvd__power,axiom,
% 5.15/5.44 ! [N2: nat,X: complex] :
% 5.15/5.44 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 | ( X = one_one_complex ) )
% 5.15/5.44 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power
% 5.15/5.44 thf(fact_4414_dvd__power,axiom,
% 5.15/5.44 ! [N2: nat,X: int] :
% 5.15/5.44 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 | ( X = one_one_int ) )
% 5.15/5.44 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power
% 5.15/5.44 thf(fact_4415_div2__even__ext__nat,axiom,
% 5.15/5.44 ! [X: nat,Y: nat] :
% 5.15/5.44 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.44 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.44 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.15/5.44 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.15/5.44 => ( X = Y ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % div2_even_ext_nat
% 5.15/5.44 thf(fact_4416_even__even__mod__4__iff,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_even_mod_4_iff
% 5.15/5.44 thf(fact_4417_dvd__mult__cancel2,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.44 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 5.15/5.44 = ( N2 = one_one_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_mult_cancel2
% 5.15/5.44 thf(fact_4418_dvd__mult__cancel1,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.44 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 5.15/5.44 = ( N2 = one_one_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_mult_cancel1
% 5.15/5.44 thf(fact_4419_odd__numeral__BitM,axiom,
% 5.15/5.44 ! [W: num] :
% 5.15/5.44 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_numeral_BitM
% 5.15/5.44 thf(fact_4420_odd__numeral__BitM,axiom,
% 5.15/5.44 ! [W: num] :
% 5.15/5.44 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_numeral_BitM
% 5.15/5.44 thf(fact_4421_odd__numeral__BitM,axiom,
% 5.15/5.44 ! [W: num] :
% 5.15/5.44 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_numeral_BitM
% 5.15/5.44 thf(fact_4422_dvd__minus__add,axiom,
% 5.15/5.44 ! [Q3: nat,N2: nat,R2: nat,M: nat] :
% 5.15/5.44 ( ( ord_less_eq_nat @ Q3 @ N2 )
% 5.15/5.44 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M ) )
% 5.15/5.44 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q3 ) )
% 5.15/5.44 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q3 ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_minus_add
% 5.15/5.44 thf(fact_4423_power__dvd__imp__le,axiom,
% 5.15/5.44 ! [I: nat,M: nat,N2: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N2 ) )
% 5.15/5.44 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.15/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % power_dvd_imp_le
% 5.15/5.44 thf(fact_4424_mod__nat__eqI,axiom,
% 5.15/5.44 ! [R2: nat,N2: nat,M: nat] :
% 5.15/5.44 ( ( ord_less_nat @ R2 @ N2 )
% 5.15/5.44 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.15/5.44 => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R2 ) )
% 5.15/5.44 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.15/5.44 = R2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod_nat_eqI
% 5.15/5.44 thf(fact_4425_mod__int__pos__iff,axiom,
% 5.15/5.44 ! [K: int,L: int] :
% 5.15/5.44 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.15/5.44 = ( ( dvd_dvd_int @ L @ K )
% 5.15/5.44 | ( ( L = zero_zero_int )
% 5.15/5.44 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.15/5.44 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod_int_pos_iff
% 5.15/5.44 thf(fact_4426_even__two__times__div__two,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.15/5.44 = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_two_times_div_two
% 5.15/5.44 thf(fact_4427_even__two__times__div__two,axiom,
% 5.15/5.44 ! [A: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.44 = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_two_times_div_two
% 5.15/5.44 thf(fact_4428_even__two__times__div__two,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.15/5.44 = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_two_times_div_two
% 5.15/5.44 thf(fact_4429_even__iff__mod__2__eq__zero,axiom,
% 5.15/5.44 ! [A: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.44 = zero_zero_nat ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_iff_mod_2_eq_zero
% 5.15/5.44 thf(fact_4430_even__iff__mod__2__eq__zero,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.44 = zero_zero_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_iff_mod_2_eq_zero
% 5.15/5.44 thf(fact_4431_even__iff__mod__2__eq__zero,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_iff_mod_2_eq_zero
% 5.15/5.44 thf(fact_4432_odd__iff__mod__2__eq__one,axiom,
% 5.15/5.44 ! [A: nat] :
% 5.15/5.44 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.44 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.44 = one_one_nat ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_iff_mod_2_eq_one
% 5.15/5.44 thf(fact_4433_odd__iff__mod__2__eq__one,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.44 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.44 = one_one_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_iff_mod_2_eq_one
% 5.15/5.44 thf(fact_4434_odd__iff__mod__2__eq__one,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.44 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.44 = one_one_Code_integer ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_iff_mod_2_eq_one
% 5.15/5.44 thf(fact_4435_power__mono__odd,axiom,
% 5.15/5.44 ! [N2: nat,A: real,B: real] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ( ord_less_eq_real @ A @ B )
% 5.15/5.44 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % power_mono_odd
% 5.15/5.44 thf(fact_4436_power__mono__odd,axiom,
% 5.15/5.44 ! [N2: nat,A: rat,B: rat] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.44 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % power_mono_odd
% 5.15/5.44 thf(fact_4437_power__mono__odd,axiom,
% 5.15/5.44 ! [N2: nat,A: int,B: int] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ( ord_less_eq_int @ A @ B )
% 5.15/5.44 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % power_mono_odd
% 5.15/5.44 thf(fact_4438_odd__pos,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_pos
% 5.15/5.44 thf(fact_4439_dvd__power__iff__le,axiom,
% 5.15/5.44 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.15/5.44 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 5.15/5.44 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_power_iff_le
% 5.15/5.44 thf(fact_4440_signed__take__bit__int__less__exp,axiom,
% 5.15/5.44 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_int_less_exp
% 5.15/5.44 thf(fact_4441_even__unset__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 | ( M = zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_unset_bit_iff
% 5.15/5.44 thf(fact_4442_even__unset__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 | ( M = zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_unset_bit_iff
% 5.15/5.44 thf(fact_4443_even__unset__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 | ( M = zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_unset_bit_iff
% 5.15/5.44 thf(fact_4444_even__set__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 & ( M != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_set_bit_iff
% 5.15/5.44 thf(fact_4445_even__set__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 & ( M != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_set_bit_iff
% 5.15/5.44 thf(fact_4446_even__set__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 & ( M != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_set_bit_iff
% 5.15/5.44 thf(fact_4447_even__flip__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 != ( M = zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_flip_bit_iff
% 5.15/5.44 thf(fact_4448_even__flip__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 != ( M = zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_flip_bit_iff
% 5.15/5.44 thf(fact_4449_even__flip__bit__iff,axiom,
% 5.15/5.44 ! [M: nat,A: nat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.15/5.44 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 != ( M = zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_flip_bit_iff
% 5.15/5.44 thf(fact_4450_even__diff__iff,axiom,
% 5.15/5.44 ! [K: int,L: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 5.15/5.44 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_diff_iff
% 5.15/5.44 thf(fact_4451_oddE,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ~ ! [B6: code_integer] :
% 5.15/5.44 ( A
% 5.15/5.44 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B6 ) @ one_one_Code_integer ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % oddE
% 5.15/5.44 thf(fact_4452_oddE,axiom,
% 5.15/5.44 ! [A: nat] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ~ ! [B6: nat] :
% 5.15/5.44 ( A
% 5.15/5.44 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B6 ) @ one_one_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % oddE
% 5.15/5.44 thf(fact_4453_oddE,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ~ ! [B6: int] :
% 5.15/5.44 ( A
% 5.15/5.44 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B6 ) @ one_one_int ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % oddE
% 5.15/5.44 thf(fact_4454_parity__cases,axiom,
% 5.15/5.44 ! [A: nat] :
% 5.15/5.44 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.44 != zero_zero_nat ) )
% 5.15/5.44 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.44 != one_one_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % parity_cases
% 5.15/5.44 thf(fact_4455_parity__cases,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.44 != zero_zero_int ) )
% 5.15/5.44 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.44 != one_one_int ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % parity_cases
% 5.15/5.44 thf(fact_4456_parity__cases,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.44 != zero_z3403309356797280102nteger ) )
% 5.15/5.44 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.44 != one_one_Code_integer ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % parity_cases
% 5.15/5.44 thf(fact_4457_mod2__eq__if,axiom,
% 5.15/5.44 ! [A: nat] :
% 5.15/5.44 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.44 = zero_zero_nat ) )
% 5.15/5.44 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.44 = one_one_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod2_eq_if
% 5.15/5.44 thf(fact_4458_mod2__eq__if,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.44 = zero_zero_int ) )
% 5.15/5.44 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.44 = one_one_int ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod2_eq_if
% 5.15/5.44 thf(fact_4459_mod2__eq__if,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.44 = zero_z3403309356797280102nteger ) )
% 5.15/5.44 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.44 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.44 = one_one_Code_integer ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod2_eq_if
% 5.15/5.44 thf(fact_4460_zero__le__even__power,axiom,
% 5.15/5.44 ! [N2: nat,A: real] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_even_power
% 5.15/5.44 thf(fact_4461_zero__le__even__power,axiom,
% 5.15/5.44 ! [N2: nat,A: rat] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_even_power
% 5.15/5.44 thf(fact_4462_zero__le__even__power,axiom,
% 5.15/5.44 ! [N2: nat,A: int] :
% 5.15/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_even_power
% 5.15/5.44 thf(fact_4463_zero__le__odd__power,axiom,
% 5.15/5.44 ! [N2: nat,A: real] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.15/5.44 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_odd_power
% 5.15/5.44 thf(fact_4464_zero__le__odd__power,axiom,
% 5.15/5.44 ! [N2: nat,A: rat] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.15/5.44 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_odd_power
% 5.15/5.44 thf(fact_4465_zero__le__odd__power,axiom,
% 5.15/5.44 ! [N2: nat,A: int] :
% 5.15/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.15/5.44 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_odd_power
% 5.15/5.44 thf(fact_4466_zero__le__power__eq,axiom,
% 5.15/5.44 ! [A: real,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.15/5.44 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_power_eq
% 5.15/5.44 thf(fact_4467_zero__le__power__eq,axiom,
% 5.15/5.44 ! [A: rat,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.15/5.44 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_power_eq
% 5.15/5.44 thf(fact_4468_zero__le__power__eq,axiom,
% 5.15/5.44 ! [A: int,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.15/5.44 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_le_power_eq
% 5.15/5.44 thf(fact_4469_signed__take__bit__int__less__self__iff,axiom,
% 5.15/5.44 ! [N2: nat,K: int] :
% 5.15/5.44 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.15/5.44 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_int_less_self_iff
% 5.15/5.44 thf(fact_4470_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.15/5.44 ! [K: int,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.15/5.44 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_int_greater_eq_self_iff
% 5.15/5.44 thf(fact_4471_zero__less__power__eq,axiom,
% 5.15/5.44 ! [A: real,N2: nat] :
% 5.15/5.44 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.15/5.44 = ( ( N2 = zero_zero_nat )
% 5.15/5.44 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( A != zero_zero_real ) )
% 5.15/5.44 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_less_power_eq
% 5.15/5.44 thf(fact_4472_zero__less__power__eq,axiom,
% 5.15/5.44 ! [A: rat,N2: nat] :
% 5.15/5.44 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.15/5.44 = ( ( N2 = zero_zero_nat )
% 5.15/5.44 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( A != zero_zero_rat ) )
% 5.15/5.44 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_less_power_eq
% 5.15/5.44 thf(fact_4473_zero__less__power__eq,axiom,
% 5.15/5.44 ! [A: int,N2: nat] :
% 5.15/5.44 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.15/5.44 = ( ( N2 = zero_zero_nat )
% 5.15/5.44 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( A != zero_zero_int ) )
% 5.15/5.44 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % zero_less_power_eq
% 5.15/5.44 thf(fact_4474_signed__take__bit__int__less__eq,axiom,
% 5.15/5.44 ! [N2: nat,K: int] :
% 5.15/5.44 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.15/5.44 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_int_less_eq
% 5.15/5.44 thf(fact_4475_even__mask__div__iff_H,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( 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 ) ) )
% 5.15/5.44 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mask_div_iff'
% 5.15/5.44 thf(fact_4476_even__mask__div__iff_H,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( 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 ) ) )
% 5.15/5.44 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mask_div_iff'
% 5.15/5.44 thf(fact_4477_even__mask__div__iff_H,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( 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 ) ) )
% 5.15/5.44 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mask_div_iff'
% 5.15/5.44 thf(fact_4478_power__le__zero__eq,axiom,
% 5.15/5.44 ! [A: real,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.15/5.44 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.15/5.44 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % power_le_zero_eq
% 5.15/5.44 thf(fact_4479_power__le__zero__eq,axiom,
% 5.15/5.44 ! [A: rat,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.15/5.44 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.15/5.44 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % power_le_zero_eq
% 5.15/5.44 thf(fact_4480_power__le__zero__eq,axiom,
% 5.15/5.44 ! [A: int,N2: nat] :
% 5.15/5.44 ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.15/5.44 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.44 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.15/5.44 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % power_le_zero_eq
% 5.15/5.44 thf(fact_4481_option_Osize__gen_I1_J,axiom,
% 5.15/5.44 ! [X: product_prod_nat_nat > nat] :
% 5.15/5.44 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 5.15/5.44 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.44
% 5.15/5.44 % option.size_gen(1)
% 5.15/5.44 thf(fact_4482_option_Osize__gen_I1_J,axiom,
% 5.15/5.44 ! [X: nat > nat] :
% 5.15/5.44 ( ( size_option_nat @ X @ none_nat )
% 5.15/5.44 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.44
% 5.15/5.44 % option.size_gen(1)
% 5.15/5.44 thf(fact_4483_option_Osize__gen_I1_J,axiom,
% 5.15/5.44 ! [X: num > nat] :
% 5.15/5.44 ( ( size_option_num @ X @ none_num )
% 5.15/5.44 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.44
% 5.15/5.44 % option.size_gen(1)
% 5.15/5.44 thf(fact_4484_even__mod__4__div__2,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.44 = ( suc @ zero_zero_nat ) )
% 5.15/5.44 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mod_4_div_2
% 5.15/5.44 thf(fact_4485_divmod__step__nat__def,axiom,
% 5.15/5.44 ( unique5026877609467782581ep_nat
% 5.15/5.44 = ( ^ [L2: num] :
% 5.15/5.44 ( produc2626176000494625587at_nat
% 5.15/5.44 @ ^ [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 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % divmod_step_nat_def
% 5.15/5.44 thf(fact_4486_even__mask__div__iff,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( 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 ) ) )
% 5.15/5.44 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 = zero_z3403309356797280102nteger )
% 5.15/5.44 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mask_div_iff
% 5.15/5.44 thf(fact_4487_even__mask__div__iff,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( 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 ) ) )
% 5.15/5.44 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 = zero_zero_nat )
% 5.15/5.44 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mask_div_iff
% 5.15/5.44 thf(fact_4488_even__mask__div__iff,axiom,
% 5.15/5.44 ! [M: nat,N2: nat] :
% 5.15/5.44 ( ( 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 ) ) )
% 5.15/5.44 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 = zero_zero_int )
% 5.15/5.44 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mask_div_iff
% 5.15/5.44 thf(fact_4489_divmod__step__int__def,axiom,
% 5.15/5.44 ( unique5024387138958732305ep_int
% 5.15/5.44 = ( ^ [L2: num] :
% 5.15/5.44 ( produc4245557441103728435nt_int
% 5.15/5.44 @ ^ [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 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % divmod_step_int_def
% 5.15/5.44 thf(fact_4490_odd__mod__4__div__2,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.44 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.15/5.44 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % odd_mod_4_div_2
% 5.15/5.44 thf(fact_4491_even__mult__exp__div__exp__iff,axiom,
% 5.15/5.44 ! [A: code_integer,M: nat,N2: nat] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.44 = ( ( ord_less_nat @ N2 @ M )
% 5.15/5.44 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 = zero_z3403309356797280102nteger )
% 5.15/5.44 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.44 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mult_exp_div_exp_iff
% 5.15/5.44 thf(fact_4492_even__mult__exp__div__exp__iff,axiom,
% 5.15/5.44 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.44 ( ( 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 ) ) )
% 5.15/5.44 = ( ( ord_less_nat @ N2 @ M )
% 5.15/5.44 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 = zero_zero_nat )
% 5.15/5.44 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.44 & ( 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 ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mult_exp_div_exp_iff
% 5.15/5.44 thf(fact_4493_even__mult__exp__div__exp__iff,axiom,
% 5.15/5.44 ! [A: int,M: nat,N2: nat] :
% 5.15/5.44 ( ( 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 ) ) )
% 5.15/5.44 = ( ( ord_less_nat @ N2 @ M )
% 5.15/5.44 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.44 = zero_zero_int )
% 5.15/5.44 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.44 & ( 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 ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % even_mult_exp_div_exp_iff
% 5.15/5.44 thf(fact_4494_divmod__step__def,axiom,
% 5.15/5.44 ( unique5026877609467782581ep_nat
% 5.15/5.44 = ( ^ [L2: num] :
% 5.15/5.44 ( produc2626176000494625587at_nat
% 5.15/5.44 @ ^ [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 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % divmod_step_def
% 5.15/5.44 thf(fact_4495_divmod__step__def,axiom,
% 5.15/5.44 ( unique5024387138958732305ep_int
% 5.15/5.44 = ( ^ [L2: num] :
% 5.15/5.44 ( produc4245557441103728435nt_int
% 5.15/5.44 @ ^ [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 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % divmod_step_def
% 5.15/5.44 thf(fact_4496_divmod__step__def,axiom,
% 5.15/5.44 ( unique4921790084139445826nteger
% 5.15/5.44 = ( ^ [L2: num] :
% 5.15/5.44 ( produc6916734918728496179nteger
% 5.15/5.44 @ ^ [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 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % divmod_step_def
% 5.15/5.44 thf(fact_4497_infinite__growing,axiom,
% 5.15/5.44 ! [X8: set_real] :
% 5.15/5.44 ( ( X8 != bot_bot_set_real )
% 5.15/5.44 => ( ! [X3: real] :
% 5.15/5.44 ( ( member_real @ X3 @ X8 )
% 5.15/5.44 => ? [Xa: real] :
% 5.15/5.44 ( ( member_real @ Xa @ X8 )
% 5.15/5.44 & ( ord_less_real @ X3 @ Xa ) ) )
% 5.15/5.44 => ~ ( finite_finite_real @ X8 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % infinite_growing
% 5.15/5.44 thf(fact_4498_infinite__growing,axiom,
% 5.15/5.44 ! [X8: set_rat] :
% 5.15/5.44 ( ( X8 != bot_bot_set_rat )
% 5.15/5.44 => ( ! [X3: rat] :
% 5.15/5.44 ( ( member_rat @ X3 @ X8 )
% 5.15/5.44 => ? [Xa: rat] :
% 5.15/5.44 ( ( member_rat @ Xa @ X8 )
% 5.15/5.44 & ( ord_less_rat @ X3 @ Xa ) ) )
% 5.15/5.44 => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % infinite_growing
% 5.15/5.44 thf(fact_4499_infinite__growing,axiom,
% 5.15/5.44 ! [X8: set_num] :
% 5.15/5.44 ( ( X8 != bot_bot_set_num )
% 5.15/5.44 => ( ! [X3: num] :
% 5.15/5.44 ( ( member_num @ X3 @ X8 )
% 5.15/5.44 => ? [Xa: num] :
% 5.15/5.44 ( ( member_num @ Xa @ X8 )
% 5.15/5.44 & ( ord_less_num @ X3 @ Xa ) ) )
% 5.15/5.44 => ~ ( finite_finite_num @ X8 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % infinite_growing
% 5.15/5.44 thf(fact_4500_infinite__growing,axiom,
% 5.15/5.44 ! [X8: set_nat] :
% 5.15/5.44 ( ( X8 != bot_bot_set_nat )
% 5.15/5.44 => ( ! [X3: nat] :
% 5.15/5.44 ( ( member_nat @ X3 @ X8 )
% 5.15/5.44 => ? [Xa: nat] :
% 5.15/5.44 ( ( member_nat @ Xa @ X8 )
% 5.15/5.44 & ( ord_less_nat @ X3 @ Xa ) ) )
% 5.15/5.44 => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % infinite_growing
% 5.15/5.44 thf(fact_4501_infinite__growing,axiom,
% 5.15/5.44 ! [X8: set_int] :
% 5.15/5.44 ( ( X8 != bot_bot_set_int )
% 5.15/5.44 => ( ! [X3: int] :
% 5.15/5.44 ( ( member_int @ X3 @ X8 )
% 5.15/5.44 => ? [Xa: int] :
% 5.15/5.44 ( ( member_int @ Xa @ X8 )
% 5.15/5.44 & ( ord_less_int @ X3 @ Xa ) ) )
% 5.15/5.44 => ~ ( finite_finite_int @ X8 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % infinite_growing
% 5.15/5.44 thf(fact_4502_ex__min__if__finite,axiom,
% 5.15/5.44 ! [S3: set_real] :
% 5.15/5.44 ( ( finite_finite_real @ S3 )
% 5.15/5.44 => ( ( S3 != bot_bot_set_real )
% 5.15/5.44 => ? [X3: real] :
% 5.15/5.44 ( ( member_real @ X3 @ S3 )
% 5.15/5.44 & ~ ? [Xa: real] :
% 5.15/5.44 ( ( member_real @ Xa @ S3 )
% 5.15/5.44 & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % ex_min_if_finite
% 5.15/5.44 thf(fact_4503_ex__min__if__finite,axiom,
% 5.15/5.44 ! [S3: set_rat] :
% 5.15/5.44 ( ( finite_finite_rat @ S3 )
% 5.15/5.44 => ( ( S3 != bot_bot_set_rat )
% 5.15/5.44 => ? [X3: rat] :
% 5.15/5.44 ( ( member_rat @ X3 @ S3 )
% 5.15/5.44 & ~ ? [Xa: rat] :
% 5.15/5.44 ( ( member_rat @ Xa @ S3 )
% 5.15/5.44 & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % ex_min_if_finite
% 5.15/5.44 thf(fact_4504_ex__min__if__finite,axiom,
% 5.15/5.44 ! [S3: set_num] :
% 5.15/5.44 ( ( finite_finite_num @ S3 )
% 5.15/5.44 => ( ( S3 != bot_bot_set_num )
% 5.15/5.44 => ? [X3: num] :
% 5.15/5.44 ( ( member_num @ X3 @ S3 )
% 5.15/5.44 & ~ ? [Xa: num] :
% 5.15/5.44 ( ( member_num @ Xa @ S3 )
% 5.15/5.44 & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % ex_min_if_finite
% 5.15/5.44 thf(fact_4505_ex__min__if__finite,axiom,
% 5.15/5.44 ! [S3: set_nat] :
% 5.15/5.44 ( ( finite_finite_nat @ S3 )
% 5.15/5.44 => ( ( S3 != bot_bot_set_nat )
% 5.15/5.44 => ? [X3: nat] :
% 5.15/5.44 ( ( member_nat @ X3 @ S3 )
% 5.15/5.44 & ~ ? [Xa: nat] :
% 5.15/5.44 ( ( member_nat @ Xa @ S3 )
% 5.15/5.44 & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % ex_min_if_finite
% 5.15/5.44 thf(fact_4506_ex__min__if__finite,axiom,
% 5.15/5.44 ! [S3: set_int] :
% 5.15/5.44 ( ( finite_finite_int @ S3 )
% 5.15/5.44 => ( ( S3 != bot_bot_set_int )
% 5.15/5.44 => ? [X3: int] :
% 5.15/5.44 ( ( member_int @ X3 @ S3 )
% 5.15/5.44 & ~ ? [Xa: int] :
% 5.15/5.44 ( ( member_int @ Xa @ S3 )
% 5.15/5.44 & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % ex_min_if_finite
% 5.15/5.44 thf(fact_4507_vebt__buildup_Oelims,axiom,
% 5.15/5.44 ! [X: nat,Y: vEBT_VEBT] :
% 5.15/5.44 ( ( ( vEBT_vebt_buildup @ X )
% 5.15/5.44 = Y )
% 5.15/5.44 => ( ( ( X = zero_zero_nat )
% 5.15/5.44 => ( Y
% 5.15/5.44 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.15/5.44 => ( ( ( X
% 5.15/5.44 = ( suc @ zero_zero_nat ) )
% 5.15/5.44 => ( Y
% 5.15/5.44 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.15/5.44 => ~ ! [Va3: nat] :
% 5.15/5.44 ( ( X
% 5.15/5.44 = ( suc @ ( suc @ Va3 ) ) )
% 5.15/5.44 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.15/5.44 => ( Y
% 5.15/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.15/5.44 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.15/5.44 => ( Y
% 5.15/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % vebt_buildup.elims
% 5.15/5.44 thf(fact_4508_divmod__nat__if,axiom,
% 5.15/5.44 ( divmod_nat
% 5.15/5.44 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.44 ( if_Pro6206227464963214023at_nat
% 5.15/5.44 @ ( ( N3 = zero_zero_nat )
% 5.15/5.44 | ( ord_less_nat @ M5 @ N3 ) )
% 5.15/5.44 @ ( product_Pair_nat_nat @ zero_zero_nat @ M5 )
% 5.15/5.44 @ ( produc2626176000494625587at_nat
% 5.15/5.44 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.15/5.44 @ ( divmod_nat @ ( minus_minus_nat @ M5 @ N3 ) @ N3 ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % divmod_nat_if
% 5.15/5.44 thf(fact_4509_signed__take__bit__Suc__minus__bit1,axiom,
% 5.15/5.44 ! [N2: nat,K: num] :
% 5.15/5.44 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.15/5.44 = ( 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 ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_Suc_minus_bit1
% 5.15/5.44 thf(fact_4510_signed__take__bit__rec,axiom,
% 5.15/5.44 ( bit_ri6519982836138164636nteger
% 5.15/5.44 = ( ^ [N3: nat,A3: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_rec
% 5.15/5.44 thf(fact_4511_signed__take__bit__rec,axiom,
% 5.15/5.44 ( bit_ri631733984087533419it_int
% 5.15/5.44 = ( ^ [N3: nat,A3: int] : ( if_int @ ( N3 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_rec
% 5.15/5.44 thf(fact_4512_signed__take__bit__numeral__bit1,axiom,
% 5.15/5.44 ! [L: num,K: num] :
% 5.15/5.44 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.15/5.44 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_numeral_bit1
% 5.15/5.44 thf(fact_4513_flip__bit__0,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.15/5.44 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % flip_bit_0
% 5.15/5.44 thf(fact_4514_flip__bit__0,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.15/5.44 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % flip_bit_0
% 5.15/5.44 thf(fact_4515_flip__bit__0,axiom,
% 5.15/5.44 ! [A: nat] :
% 5.15/5.44 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.15/5.44 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % flip_bit_0
% 5.15/5.44 thf(fact_4516_diff__shunt__var,axiom,
% 5.15/5.44 ! [X: set_int,Y: set_int] :
% 5.15/5.44 ( ( ( minus_minus_set_int @ X @ Y )
% 5.15/5.44 = bot_bot_set_int )
% 5.15/5.44 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_shunt_var
% 5.15/5.44 thf(fact_4517_diff__shunt__var,axiom,
% 5.15/5.44 ! [X: set_real,Y: set_real] :
% 5.15/5.44 ( ( ( minus_minus_set_real @ X @ Y )
% 5.15/5.44 = bot_bot_set_real )
% 5.15/5.44 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_shunt_var
% 5.15/5.44 thf(fact_4518_diff__shunt__var,axiom,
% 5.15/5.44 ! [X: set_nat,Y: set_nat] :
% 5.15/5.44 ( ( ( minus_minus_set_nat @ X @ Y )
% 5.15/5.44 = bot_bot_set_nat )
% 5.15/5.44 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_shunt_var
% 5.15/5.44 thf(fact_4519_intind,axiom,
% 5.15/5.44 ! [I: nat,N2: nat,P: int > $o,X: int] :
% 5.15/5.44 ( ( ord_less_nat @ I @ N2 )
% 5.15/5.44 => ( ( P @ X )
% 5.15/5.44 => ( P @ ( nth_int @ ( replicate_int @ N2 @ X ) @ I ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % intind
% 5.15/5.44 thf(fact_4520_intind,axiom,
% 5.15/5.44 ! [I: nat,N2: nat,P: nat > $o,X: nat] :
% 5.15/5.44 ( ( ord_less_nat @ I @ N2 )
% 5.15/5.44 => ( ( P @ X )
% 5.15/5.44 => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X ) @ I ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % intind
% 5.15/5.44 thf(fact_4521_intind,axiom,
% 5.15/5.44 ! [I: nat,N2: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.15/5.44 ( ( ord_less_nat @ I @ N2 )
% 5.15/5.44 => ( ( P @ X )
% 5.15/5.44 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) @ I ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % intind
% 5.15/5.44 thf(fact_4522_add_Oinverse__inverse,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_inverse
% 5.15/5.44 thf(fact_4523_add_Oinverse__inverse,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_inverse
% 5.15/5.44 thf(fact_4524_add_Oinverse__inverse,axiom,
% 5.15/5.44 ! [A: complex] :
% 5.15/5.44 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_inverse
% 5.15/5.44 thf(fact_4525_add_Oinverse__inverse,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_inverse
% 5.15/5.44 thf(fact_4526_add_Oinverse__inverse,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_inverse
% 5.15/5.44 thf(fact_4527_neg__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( ( uminus_uminus_int @ A )
% 5.15/5.44 = ( uminus_uminus_int @ B ) )
% 5.15/5.44 = ( A = B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_iff_equal
% 5.15/5.44 thf(fact_4528_neg__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( ( uminus_uminus_real @ A )
% 5.15/5.44 = ( uminus_uminus_real @ B ) )
% 5.15/5.44 = ( A = B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_iff_equal
% 5.15/5.44 thf(fact_4529_neg__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( ( uminus1482373934393186551omplex @ A )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.44 = ( A = B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_iff_equal
% 5.15/5.44 thf(fact_4530_neg__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( ( uminus_uminus_rat @ A )
% 5.15/5.44 = ( uminus_uminus_rat @ B ) )
% 5.15/5.44 = ( A = B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_iff_equal
% 5.15/5.44 thf(fact_4531_neg__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( ( uminus1351360451143612070nteger @ A )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.44 = ( A = B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_iff_equal
% 5.15/5.44 thf(fact_4532_case__prodI2,axiom,
% 5.15/5.44 ! [P2: produc6271795597528267376eger_o,C: code_integer > $o > $o] :
% 5.15/5.44 ( ! [A5: code_integer,B6: $o] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( produc6677183202524767010eger_o @ A5 @ B6 ) )
% 5.15/5.44 => ( C @ A5 @ B6 ) )
% 5.15/5.44 => ( produc7828578312038201481er_o_o @ C @ P2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI2
% 5.15/5.44 thf(fact_4533_case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_num_num,C: num > num > $o] :
% 5.15/5.44 ( ! [A5: num,B6: num] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_num_num @ A5 @ B6 ) )
% 5.15/5.44 => ( C @ A5 @ B6 ) )
% 5.15/5.44 => ( produc5703948589228662326_num_o @ C @ P2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI2
% 5.15/5.44 thf(fact_4534_case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_nat_num,C: nat > num > $o] :
% 5.15/5.44 ( ! [A5: nat,B6: num] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_nat_num @ A5 @ B6 ) )
% 5.15/5.44 => ( C @ A5 @ B6 ) )
% 5.15/5.44 => ( produc4927758841916487424_num_o @ C @ P2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI2
% 5.15/5.44 thf(fact_4535_case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_nat_nat,C: nat > nat > $o] :
% 5.15/5.44 ( ! [A5: nat,B6: nat] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_nat_nat @ A5 @ B6 ) )
% 5.15/5.44 => ( C @ A5 @ B6 ) )
% 5.15/5.44 => ( produc6081775807080527818_nat_o @ C @ P2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI2
% 5.15/5.44 thf(fact_4536_case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_int_int,C: int > int > $o] :
% 5.15/5.44 ( ! [A5: int,B6: int] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_int_int @ A5 @ B6 ) )
% 5.15/5.44 => ( C @ A5 @ B6 ) )
% 5.15/5.44 => ( produc4947309494688390418_int_o @ C @ P2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI2
% 5.15/5.44 thf(fact_4537_case__prodI,axiom,
% 5.15/5.44 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.15/5.44 ( ( F @ A @ B )
% 5.15/5.44 => ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI
% 5.15/5.44 thf(fact_4538_case__prodI,axiom,
% 5.15/5.44 ! [F: num > num > $o,A: num,B: num] :
% 5.15/5.44 ( ( F @ A @ B )
% 5.15/5.44 => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI
% 5.15/5.44 thf(fact_4539_case__prodI,axiom,
% 5.15/5.44 ! [F: nat > num > $o,A: nat,B: num] :
% 5.15/5.44 ( ( F @ A @ B )
% 5.15/5.44 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI
% 5.15/5.44 thf(fact_4540_case__prodI,axiom,
% 5.15/5.44 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.15/5.44 ( ( F @ A @ B )
% 5.15/5.44 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI
% 5.15/5.44 thf(fact_4541_case__prodI,axiom,
% 5.15/5.44 ! [F: int > int > $o,A: int,B: int] :
% 5.15/5.44 ( ( F @ A @ B )
% 5.15/5.44 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI
% 5.15/5.44 thf(fact_4542_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: produc6271795597528267376eger_o,Z: complex,C: code_integer > $o > set_complex] :
% 5.15/5.44 ( ! [A5: code_integer,B6: $o] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( produc6677183202524767010eger_o @ A5 @ B6 ) )
% 5.15/5.44 => ( member_complex @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4543_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: produc6271795597528267376eger_o,Z: real,C: code_integer > $o > set_real] :
% 5.15/5.44 ( ! [A5: code_integer,B6: $o] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( produc6677183202524767010eger_o @ A5 @ B6 ) )
% 5.15/5.44 => ( member_real @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4544_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: produc6271795597528267376eger_o,Z: nat,C: code_integer > $o > set_nat] :
% 5.15/5.44 ( ! [A5: code_integer,B6: $o] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( produc6677183202524767010eger_o @ A5 @ B6 ) )
% 5.15/5.44 => ( member_nat @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4545_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: produc6271795597528267376eger_o,Z: int,C: code_integer > $o > set_int] :
% 5.15/5.44 ( ! [A5: code_integer,B6: $o] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( produc6677183202524767010eger_o @ A5 @ B6 ) )
% 5.15/5.44 => ( member_int @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4546_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_num_num,Z: complex,C: num > num > set_complex] :
% 5.15/5.44 ( ! [A5: num,B6: num] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_num_num @ A5 @ B6 ) )
% 5.15/5.44 => ( member_complex @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4547_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_num_num,Z: real,C: num > num > set_real] :
% 5.15/5.44 ( ! [A5: num,B6: num] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_num_num @ A5 @ B6 ) )
% 5.15/5.44 => ( member_real @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4548_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 5.15/5.44 ( ! [A5: num,B6: num] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_num_num @ A5 @ B6 ) )
% 5.15/5.44 => ( member_nat @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4549_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_num_num,Z: int,C: num > num > set_int] :
% 5.15/5.44 ( ! [A5: num,B6: num] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_num_num @ A5 @ B6 ) )
% 5.15/5.44 => ( member_int @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4550_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_nat_num,Z: complex,C: nat > num > set_complex] :
% 5.15/5.44 ( ! [A5: nat,B6: num] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_nat_num @ A5 @ B6 ) )
% 5.15/5.44 => ( member_complex @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4551_mem__case__prodI2,axiom,
% 5.15/5.44 ! [P2: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 5.15/5.44 ( ! [A5: nat,B6: num] :
% 5.15/5.44 ( ( P2
% 5.15/5.44 = ( product_Pair_nat_num @ A5 @ B6 ) )
% 5.15/5.44 => ( member_real @ Z @ ( C @ A5 @ B6 ) ) )
% 5.15/5.44 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI2
% 5.15/5.44 thf(fact_4552_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: complex,C: code_integer > $o > set_complex,A: code_integer,B: $o] :
% 5.15/5.44 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4553_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: real,C: code_integer > $o > set_real,A: code_integer,B: $o] :
% 5.15/5.44 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4554_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: nat,C: code_integer > $o > set_nat,A: code_integer,B: $o] :
% 5.15/5.44 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4555_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: int,C: code_integer > $o > set_int,A: code_integer,B: $o] :
% 5.15/5.44 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4556_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: complex,C: num > num > set_complex,A: num,B: num] :
% 5.15/5.44 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4557_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 5.15/5.44 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4558_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 5.15/5.44 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4559_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 5.15/5.44 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4560_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: complex,C: nat > num > set_complex,A: nat,B: num] :
% 5.15/5.44 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4561_mem__case__prodI,axiom,
% 5.15/5.44 ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 5.15/5.44 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.15/5.44 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mem_case_prodI
% 5.15/5.44 thf(fact_4562_case__prodI2_H,axiom,
% 5.15/5.44 ! [P2: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.15/5.44 ( ! [A5: nat,B6: nat] :
% 5.15/5.44 ( ( ( product_Pair_nat_nat @ A5 @ B6 )
% 5.15/5.44 = P2 )
% 5.15/5.44 => ( C @ A5 @ B6 @ X ) )
% 5.15/5.44 => ( produc8739625826339149834_nat_o @ C @ P2 @ X ) ) ).
% 5.15/5.44
% 5.15/5.44 % case_prodI2'
% 5.15/5.44 thf(fact_4563_compl__le__compl__iff,axiom,
% 5.15/5.44 ! [X: set_nat,Y: set_nat] :
% 5.15/5.44 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 5.15/5.44 = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 5.15/5.44
% 5.15/5.44 % compl_le_compl_iff
% 5.15/5.44 thf(fact_4564_neg__le__iff__le,axiom,
% 5.15/5.44 ! [B: real,A: real] :
% 5.15/5.44 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_le_iff_le
% 5.15/5.44 thf(fact_4565_neg__le__iff__le,axiom,
% 5.15/5.44 ! [B: code_integer,A: code_integer] :
% 5.15/5.44 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_le_iff_le
% 5.15/5.44 thf(fact_4566_neg__le__iff__le,axiom,
% 5.15/5.44 ! [B: rat,A: rat] :
% 5.15/5.44 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_le_iff_le
% 5.15/5.44 thf(fact_4567_neg__le__iff__le,axiom,
% 5.15/5.44 ! [B: int,A: int] :
% 5.15/5.44 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.15/5.44 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_le_iff_le
% 5.15/5.44 thf(fact_4568_add_Oinverse__neutral,axiom,
% 5.15/5.44 ( ( uminus_uminus_int @ zero_zero_int )
% 5.15/5.44 = zero_zero_int ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_neutral
% 5.15/5.44 thf(fact_4569_add_Oinverse__neutral,axiom,
% 5.15/5.44 ( ( uminus_uminus_real @ zero_zero_real )
% 5.15/5.44 = zero_zero_real ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_neutral
% 5.15/5.44 thf(fact_4570_add_Oinverse__neutral,axiom,
% 5.15/5.44 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.15/5.44 = zero_zero_complex ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_neutral
% 5.15/5.44 thf(fact_4571_add_Oinverse__neutral,axiom,
% 5.15/5.44 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.15/5.44 = zero_zero_rat ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_neutral
% 5.15/5.44 thf(fact_4572_add_Oinverse__neutral,axiom,
% 5.15/5.44 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ).
% 5.15/5.44
% 5.15/5.44 % add.inverse_neutral
% 5.15/5.44 thf(fact_4573_neg__0__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( zero_zero_int
% 5.15/5.44 = ( uminus_uminus_int @ A ) )
% 5.15/5.44 = ( zero_zero_int = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_equal_iff_equal
% 5.15/5.44 thf(fact_4574_neg__0__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( zero_zero_real
% 5.15/5.44 = ( uminus_uminus_real @ A ) )
% 5.15/5.44 = ( zero_zero_real = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_equal_iff_equal
% 5.15/5.44 thf(fact_4575_neg__0__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: complex] :
% 5.15/5.44 ( ( zero_zero_complex
% 5.15/5.44 = ( uminus1482373934393186551omplex @ A ) )
% 5.15/5.44 = ( zero_zero_complex = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_equal_iff_equal
% 5.15/5.44 thf(fact_4576_neg__0__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( zero_zero_rat
% 5.15/5.44 = ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = ( zero_zero_rat = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_equal_iff_equal
% 5.15/5.44 thf(fact_4577_neg__0__equal__iff__equal,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( zero_z3403309356797280102nteger
% 5.15/5.44 = ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_equal_iff_equal
% 5.15/5.44 thf(fact_4578_neg__equal__0__iff__equal,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ( uminus_uminus_int @ A )
% 5.15/5.44 = zero_zero_int )
% 5.15/5.44 = ( A = zero_zero_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_0_iff_equal
% 5.15/5.44 thf(fact_4579_neg__equal__0__iff__equal,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ( uminus_uminus_real @ A )
% 5.15/5.44 = zero_zero_real )
% 5.15/5.44 = ( A = zero_zero_real ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_0_iff_equal
% 5.15/5.44 thf(fact_4580_neg__equal__0__iff__equal,axiom,
% 5.15/5.44 ! [A: complex] :
% 5.15/5.44 ( ( ( uminus1482373934393186551omplex @ A )
% 5.15/5.44 = zero_zero_complex )
% 5.15/5.44 = ( A = zero_zero_complex ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_0_iff_equal
% 5.15/5.44 thf(fact_4581_neg__equal__0__iff__equal,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ( uminus_uminus_rat @ A )
% 5.15/5.44 = zero_zero_rat )
% 5.15/5.44 = ( A = zero_zero_rat ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_0_iff_equal
% 5.15/5.44 thf(fact_4582_neg__equal__0__iff__equal,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ( uminus1351360451143612070nteger @ A )
% 5.15/5.44 = zero_z3403309356797280102nteger )
% 5.15/5.44 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_0_iff_equal
% 5.15/5.44 thf(fact_4583_equal__neg__zero,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( A
% 5.15/5.44 = ( uminus_uminus_int @ A ) )
% 5.15/5.44 = ( A = zero_zero_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % equal_neg_zero
% 5.15/5.44 thf(fact_4584_equal__neg__zero,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( A
% 5.15/5.44 = ( uminus_uminus_real @ A ) )
% 5.15/5.44 = ( A = zero_zero_real ) ) ).
% 5.15/5.44
% 5.15/5.44 % equal_neg_zero
% 5.15/5.44 thf(fact_4585_equal__neg__zero,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( A
% 5.15/5.44 = ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = ( A = zero_zero_rat ) ) ).
% 5.15/5.44
% 5.15/5.44 % equal_neg_zero
% 5.15/5.44 thf(fact_4586_equal__neg__zero,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( A
% 5.15/5.44 = ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % equal_neg_zero
% 5.15/5.44 thf(fact_4587_neg__equal__zero,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ( uminus_uminus_int @ A )
% 5.15/5.44 = A )
% 5.15/5.44 = ( A = zero_zero_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_zero
% 5.15/5.44 thf(fact_4588_neg__equal__zero,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ( uminus_uminus_real @ A )
% 5.15/5.44 = A )
% 5.15/5.44 = ( A = zero_zero_real ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_zero
% 5.15/5.44 thf(fact_4589_neg__equal__zero,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ( uminus_uminus_rat @ A )
% 5.15/5.44 = A )
% 5.15/5.44 = ( A = zero_zero_rat ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_zero
% 5.15/5.44 thf(fact_4590_neg__equal__zero,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ( uminus1351360451143612070nteger @ A )
% 5.15/5.44 = A )
% 5.15/5.44 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_equal_zero
% 5.15/5.44 thf(fact_4591_neg__less__iff__less,axiom,
% 5.15/5.44 ! [B: int,A: int] :
% 5.15/5.44 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.15/5.44 = ( ord_less_int @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_iff_less
% 5.15/5.44 thf(fact_4592_neg__less__iff__less,axiom,
% 5.15/5.44 ! [B: real,A: real] :
% 5.15/5.44 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = ( ord_less_real @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_iff_less
% 5.15/5.44 thf(fact_4593_neg__less__iff__less,axiom,
% 5.15/5.44 ! [B: rat,A: rat] :
% 5.15/5.44 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = ( ord_less_rat @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_iff_less
% 5.15/5.44 thf(fact_4594_neg__less__iff__less,axiom,
% 5.15/5.44 ! [B: code_integer,A: code_integer] :
% 5.15/5.44 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_iff_less
% 5.15/5.44 thf(fact_4595_neg__numeral__eq__iff,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.44 = ( M = N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_numeral_eq_iff
% 5.15/5.44 thf(fact_4596_neg__numeral__eq__iff,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.44 = ( M = N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_numeral_eq_iff
% 5.15/5.44 thf(fact_4597_neg__numeral__eq__iff,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.15/5.44 = ( M = N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_numeral_eq_iff
% 5.15/5.44 thf(fact_4598_neg__numeral__eq__iff,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.44 = ( M = N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_numeral_eq_iff
% 5.15/5.44 thf(fact_4599_neg__numeral__eq__iff,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.44 = ( M = N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_numeral_eq_iff
% 5.15/5.44 thf(fact_4600_mult__minus__left,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.44 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_left
% 5.15/5.44 thf(fact_4601_mult__minus__left,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.15/5.44 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_left
% 5.15/5.44 thf(fact_4602_mult__minus__left,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_left
% 5.15/5.44 thf(fact_4603_mult__minus__left,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.15/5.44 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_left
% 5.15/5.44 thf(fact_4604_mult__minus__left,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_left
% 5.15/5.44 thf(fact_4605_minus__mult__minus,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.15/5.44 = ( times_times_int @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_mult_minus
% 5.15/5.44 thf(fact_4606_minus__mult__minus,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.15/5.44 = ( times_times_real @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_mult_minus
% 5.15/5.44 thf(fact_4607_minus__mult__minus,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.44 = ( times_times_complex @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_mult_minus
% 5.15/5.44 thf(fact_4608_minus__mult__minus,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.15/5.44 = ( times_times_rat @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_mult_minus
% 5.15/5.44 thf(fact_4609_minus__mult__minus,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.44 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_mult_minus
% 5.15/5.44 thf(fact_4610_mult__minus__right,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_right
% 5.15/5.44 thf(fact_4611_mult__minus__right,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_right
% 5.15/5.44 thf(fact_4612_mult__minus__right,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_right
% 5.15/5.44 thf(fact_4613_mult__minus__right,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_right
% 5.15/5.44 thf(fact_4614_mult__minus__right,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus_right
% 5.15/5.44 thf(fact_4615_add__minus__cancel,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % add_minus_cancel
% 5.15/5.44 thf(fact_4616_add__minus__cancel,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % add_minus_cancel
% 5.15/5.44 thf(fact_4617_add__minus__cancel,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % add_minus_cancel
% 5.15/5.44 thf(fact_4618_add__minus__cancel,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % add_minus_cancel
% 5.15/5.44 thf(fact_4619_add__minus__cancel,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % add_minus_cancel
% 5.15/5.44 thf(fact_4620_minus__add__cancel,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_cancel
% 5.15/5.44 thf(fact_4621_minus__add__cancel,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_cancel
% 5.15/5.44 thf(fact_4622_minus__add__cancel,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_cancel
% 5.15/5.44 thf(fact_4623_minus__add__cancel,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_cancel
% 5.15/5.44 thf(fact_4624_minus__add__cancel,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.15/5.44 = B ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_cancel
% 5.15/5.44 thf(fact_4625_minus__add__distrib,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.15/5.44 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_distrib
% 5.15/5.44 thf(fact_4626_minus__add__distrib,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.15/5.44 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_distrib
% 5.15/5.44 thf(fact_4627_minus__add__distrib,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.15/5.44 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_distrib
% 5.15/5.44 thf(fact_4628_minus__add__distrib,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.15/5.44 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_distrib
% 5.15/5.44 thf(fact_4629_minus__add__distrib,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.15/5.44 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_add_distrib
% 5.15/5.44 thf(fact_4630_minus__diff__eq,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.15/5.44 = ( minus_minus_int @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_diff_eq
% 5.15/5.44 thf(fact_4631_minus__diff__eq,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.15/5.44 = ( minus_minus_real @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_diff_eq
% 5.15/5.44 thf(fact_4632_minus__diff__eq,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.15/5.44 = ( minus_minus_complex @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_diff_eq
% 5.15/5.44 thf(fact_4633_minus__diff__eq,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.15/5.44 = ( minus_minus_rat @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_diff_eq
% 5.15/5.44 thf(fact_4634_minus__diff__eq,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.15/5.44 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_diff_eq
% 5.15/5.44 thf(fact_4635_div__minus__minus,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.15/5.44 = ( divide_divide_int @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % div_minus_minus
% 5.15/5.44 thf(fact_4636_div__minus__minus,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.44 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % div_minus_minus
% 5.15/5.44 thf(fact_4637_dvd__minus__iff,axiom,
% 5.15/5.44 ! [X: int,Y: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 5.15/5.44 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_minus_iff
% 5.15/5.44 thf(fact_4638_dvd__minus__iff,axiom,
% 5.15/5.44 ! [X: real,Y: real] :
% 5.15/5.44 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 5.15/5.44 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_minus_iff
% 5.15/5.44 thf(fact_4639_dvd__minus__iff,axiom,
% 5.15/5.44 ! [X: complex,Y: complex] :
% 5.15/5.44 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 5.15/5.44 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_minus_iff
% 5.15/5.44 thf(fact_4640_dvd__minus__iff,axiom,
% 5.15/5.44 ! [X: rat,Y: rat] :
% 5.15/5.44 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 5.15/5.44 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_minus_iff
% 5.15/5.44 thf(fact_4641_dvd__minus__iff,axiom,
% 5.15/5.44 ! [X: code_integer,Y: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 5.15/5.44 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % dvd_minus_iff
% 5.15/5.44 thf(fact_4642_minus__dvd__iff,axiom,
% 5.15/5.44 ! [X: int,Y: int] :
% 5.15/5.44 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 5.15/5.44 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_dvd_iff
% 5.15/5.44 thf(fact_4643_minus__dvd__iff,axiom,
% 5.15/5.44 ! [X: real,Y: real] :
% 5.15/5.44 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 5.15/5.44 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_dvd_iff
% 5.15/5.44 thf(fact_4644_minus__dvd__iff,axiom,
% 5.15/5.44 ! [X: complex,Y: complex] :
% 5.15/5.44 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 5.15/5.44 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_dvd_iff
% 5.15/5.44 thf(fact_4645_minus__dvd__iff,axiom,
% 5.15/5.44 ! [X: rat,Y: rat] :
% 5.15/5.44 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 5.15/5.44 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_dvd_iff
% 5.15/5.44 thf(fact_4646_minus__dvd__iff,axiom,
% 5.15/5.44 ! [X: code_integer,Y: code_integer] :
% 5.15/5.44 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 5.15/5.44 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_dvd_iff
% 5.15/5.44 thf(fact_4647_mod__minus__minus,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod_minus_minus
% 5.15/5.44 thf(fact_4648_mod__minus__minus,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % mod_minus_minus
% 5.15/5.44 thf(fact_4649_of__bool__less__eq__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.15/5.44 = ( P
% 5.15/5.44 => Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_eq_iff
% 5.15/5.44 thf(fact_4650_of__bool__less__eq__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.15/5.44 = ( P
% 5.15/5.44 => Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_eq_iff
% 5.15/5.44 thf(fact_4651_of__bool__less__eq__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.15/5.44 = ( P
% 5.15/5.44 => Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_eq_iff
% 5.15/5.44 thf(fact_4652_of__bool__less__eq__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.15/5.44 = ( P
% 5.15/5.44 => Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_eq_iff
% 5.15/5.44 thf(fact_4653_of__bool__eq_I1_J,axiom,
% 5.15/5.44 ( ( zero_n1201886186963655149omplex @ $false )
% 5.15/5.44 = zero_zero_complex ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(1)
% 5.15/5.44 thf(fact_4654_of__bool__eq_I1_J,axiom,
% 5.15/5.44 ( ( zero_n3304061248610475627l_real @ $false )
% 5.15/5.44 = zero_zero_real ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(1)
% 5.15/5.44 thf(fact_4655_of__bool__eq_I1_J,axiom,
% 5.15/5.44 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.15/5.44 = zero_zero_rat ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(1)
% 5.15/5.44 thf(fact_4656_of__bool__eq_I1_J,axiom,
% 5.15/5.44 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.15/5.44 = zero_zero_nat ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(1)
% 5.15/5.44 thf(fact_4657_of__bool__eq_I1_J,axiom,
% 5.15/5.44 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.15/5.44 = zero_zero_int ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(1)
% 5.15/5.44 thf(fact_4658_of__bool__eq_I1_J,axiom,
% 5.15/5.44 ( ( zero_n356916108424825756nteger @ $false )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(1)
% 5.15/5.44 thf(fact_4659_of__bool__eq__0__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.15/5.44 = zero_zero_complex )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_0_iff
% 5.15/5.44 thf(fact_4660_of__bool__eq__0__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.15/5.44 = zero_zero_real )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_0_iff
% 5.15/5.44 thf(fact_4661_of__bool__eq__0__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.15/5.44 = zero_zero_rat )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_0_iff
% 5.15/5.44 thf(fact_4662_of__bool__eq__0__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.15/5.44 = zero_zero_nat )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_0_iff
% 5.15/5.44 thf(fact_4663_of__bool__eq__0__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.15/5.44 = zero_zero_int )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_0_iff
% 5.15/5.44 thf(fact_4664_of__bool__eq__0__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n356916108424825756nteger @ P )
% 5.15/5.44 = zero_z3403309356797280102nteger )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_0_iff
% 5.15/5.44 thf(fact_4665_real__add__minus__iff,axiom,
% 5.15/5.44 ! [X: real,A: real] :
% 5.15/5.44 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = zero_zero_real )
% 5.15/5.44 = ( X = A ) ) ).
% 5.15/5.44
% 5.15/5.44 % real_add_minus_iff
% 5.15/5.44 thf(fact_4666_of__bool__less__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.15/5.44 = ( ~ P
% 5.15/5.44 & Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_iff
% 5.15/5.44 thf(fact_4667_of__bool__less__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.15/5.44 = ( ~ P
% 5.15/5.44 & Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_iff
% 5.15/5.44 thf(fact_4668_of__bool__less__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.15/5.44 = ( ~ P
% 5.15/5.44 & Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_iff
% 5.15/5.44 thf(fact_4669_of__bool__less__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.15/5.44 = ( ~ P
% 5.15/5.44 & Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_iff
% 5.15/5.44 thf(fact_4670_of__bool__less__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.15/5.44 = ( ~ P
% 5.15/5.44 & Q ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_iff
% 5.15/5.44 thf(fact_4671_of__bool__eq_I2_J,axiom,
% 5.15/5.44 ( ( zero_n1201886186963655149omplex @ $true )
% 5.15/5.44 = one_one_complex ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(2)
% 5.15/5.44 thf(fact_4672_of__bool__eq_I2_J,axiom,
% 5.15/5.44 ( ( zero_n3304061248610475627l_real @ $true )
% 5.15/5.44 = one_one_real ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(2)
% 5.15/5.44 thf(fact_4673_of__bool__eq_I2_J,axiom,
% 5.15/5.44 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.15/5.44 = one_one_rat ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(2)
% 5.15/5.44 thf(fact_4674_of__bool__eq_I2_J,axiom,
% 5.15/5.44 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.15/5.44 = one_one_nat ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(2)
% 5.15/5.44 thf(fact_4675_of__bool__eq_I2_J,axiom,
% 5.15/5.44 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.15/5.44 = one_one_int ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(2)
% 5.15/5.44 thf(fact_4676_of__bool__eq_I2_J,axiom,
% 5.15/5.44 ( ( zero_n356916108424825756nteger @ $true )
% 5.15/5.44 = one_one_Code_integer ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq(2)
% 5.15/5.44 thf(fact_4677_of__bool__eq__1__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.15/5.44 = one_one_complex )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_1_iff
% 5.15/5.44 thf(fact_4678_of__bool__eq__1__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.15/5.44 = one_one_real )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_1_iff
% 5.15/5.44 thf(fact_4679_of__bool__eq__1__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.15/5.44 = one_one_rat )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_1_iff
% 5.15/5.44 thf(fact_4680_of__bool__eq__1__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.15/5.44 = one_one_nat )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_1_iff
% 5.15/5.44 thf(fact_4681_of__bool__eq__1__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.15/5.44 = one_one_int )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_1_iff
% 5.15/5.44 thf(fact_4682_of__bool__eq__1__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ( zero_n356916108424825756nteger @ P )
% 5.15/5.44 = one_one_Code_integer )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_eq_1_iff
% 5.15/5.44 thf(fact_4683_replicate__eq__replicate,axiom,
% 5.15/5.44 ! [M: nat,X: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.15/5.44 ( ( ( replicate_VEBT_VEBT @ M @ X )
% 5.15/5.44 = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 5.15/5.44 = ( ( M = N2 )
% 5.15/5.44 & ( ( M != zero_zero_nat )
% 5.15/5.44 => ( X = Y ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % replicate_eq_replicate
% 5.15/5.44 thf(fact_4684_length__replicate,axiom,
% 5.15/5.44 ! [N2: nat,X: vEBT_VEBT] :
% 5.15/5.44 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.15/5.44 = N2 ) ).
% 5.15/5.44
% 5.15/5.44 % length_replicate
% 5.15/5.44 thf(fact_4685_length__replicate,axiom,
% 5.15/5.44 ! [N2: nat,X: $o] :
% 5.15/5.44 ( ( size_size_list_o @ ( replicate_o @ N2 @ X ) )
% 5.15/5.44 = N2 ) ).
% 5.15/5.44
% 5.15/5.44 % length_replicate
% 5.15/5.44 thf(fact_4686_length__replicate,axiom,
% 5.15/5.44 ! [N2: nat,X: int] :
% 5.15/5.44 ( ( size_size_list_int @ ( replicate_int @ N2 @ X ) )
% 5.15/5.44 = N2 ) ).
% 5.15/5.44
% 5.15/5.44 % length_replicate
% 5.15/5.44 thf(fact_4687_of__bool__or__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( zero_n2687167440665602831ol_nat
% 5.15/5.44 @ ( P
% 5.15/5.44 | Q ) )
% 5.15/5.44 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_or_iff
% 5.15/5.44 thf(fact_4688_of__bool__or__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( zero_n2684676970156552555ol_int
% 5.15/5.44 @ ( P
% 5.15/5.44 | Q ) )
% 5.15/5.44 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_or_iff
% 5.15/5.44 thf(fact_4689_of__bool__or__iff,axiom,
% 5.15/5.44 ! [P: $o,Q: $o] :
% 5.15/5.44 ( ( zero_n356916108424825756nteger
% 5.15/5.44 @ ( P
% 5.15/5.44 | Q ) )
% 5.15/5.44 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_or_iff
% 5.15/5.44 thf(fact_4690_neg__0__le__iff__le,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_le_iff_le
% 5.15/5.44 thf(fact_4691_neg__0__le__iff__le,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_le_iff_le
% 5.15/5.44 thf(fact_4692_neg__0__le__iff__le,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_le_iff_le
% 5.15/5.44 thf(fact_4693_neg__0__le__iff__le,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.15/5.44 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_le_iff_le
% 5.15/5.44 thf(fact_4694_neg__le__0__iff__le,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.15/5.44 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_le_0_iff_le
% 5.15/5.44 thf(fact_4695_neg__le__0__iff__le,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.15/5.44 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_le_0_iff_le
% 5.15/5.44 thf(fact_4696_neg__le__0__iff__le,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.15/5.44 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_le_0_iff_le
% 5.15/5.44 thf(fact_4697_neg__le__0__iff__le,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.15/5.44 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_le_0_iff_le
% 5.15/5.44 thf(fact_4698_less__eq__neg__nonpos,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.15/5.44
% 5.15/5.44 % less_eq_neg_nonpos
% 5.15/5.44 thf(fact_4699_less__eq__neg__nonpos,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % less_eq_neg_nonpos
% 5.15/5.44 thf(fact_4700_less__eq__neg__nonpos,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.44
% 5.15/5.44 % less_eq_neg_nonpos
% 5.15/5.44 thf(fact_4701_less__eq__neg__nonpos,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.15/5.44 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % less_eq_neg_nonpos
% 5.15/5.44 thf(fact_4702_neg__less__eq__nonneg,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.15/5.44 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_eq_nonneg
% 5.15/5.44 thf(fact_4703_neg__less__eq__nonneg,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.15/5.44 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_eq_nonneg
% 5.15/5.44 thf(fact_4704_neg__less__eq__nonneg,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.15/5.44 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_eq_nonneg
% 5.15/5.44 thf(fact_4705_neg__less__eq__nonneg,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.15/5.44 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_eq_nonneg
% 5.15/5.44 thf(fact_4706_less__neg__neg,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.15/5.44 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % less_neg_neg
% 5.15/5.44 thf(fact_4707_less__neg__neg,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.15/5.44
% 5.15/5.44 % less_neg_neg
% 5.15/5.44 thf(fact_4708_less__neg__neg,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.44
% 5.15/5.44 % less_neg_neg
% 5.15/5.44 thf(fact_4709_less__neg__neg,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % less_neg_neg
% 5.15/5.44 thf(fact_4710_neg__less__pos,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.15/5.44 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_pos
% 5.15/5.44 thf(fact_4711_neg__less__pos,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.15/5.44 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_pos
% 5.15/5.44 thf(fact_4712_neg__less__pos,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.15/5.44 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_pos
% 5.15/5.44 thf(fact_4713_neg__less__pos,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.15/5.44 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_pos
% 5.15/5.44 thf(fact_4714_neg__0__less__iff__less,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.15/5.44 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_less_iff_less
% 5.15/5.44 thf(fact_4715_neg__0__less__iff__less,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_less_iff_less
% 5.15/5.44 thf(fact_4716_neg__0__less__iff__less,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_less_iff_less
% 5.15/5.44 thf(fact_4717_neg__0__less__iff__less,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_0_less_iff_less
% 5.15/5.44 thf(fact_4718_neg__less__0__iff__less,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.15/5.44 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_0_iff_less
% 5.15/5.44 thf(fact_4719_neg__less__0__iff__less,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.15/5.44 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_0_iff_less
% 5.15/5.44 thf(fact_4720_neg__less__0__iff__less,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.15/5.44 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_0_iff_less
% 5.15/5.44 thf(fact_4721_neg__less__0__iff__less,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.15/5.44 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_less_0_iff_less
% 5.15/5.44 thf(fact_4722_add_Oright__inverse,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.15/5.44 = zero_zero_int ) ).
% 5.15/5.44
% 5.15/5.44 % add.right_inverse
% 5.15/5.44 thf(fact_4723_add_Oright__inverse,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.15/5.44 = zero_zero_real ) ).
% 5.15/5.44
% 5.15/5.44 % add.right_inverse
% 5.15/5.44 thf(fact_4724_add_Oright__inverse,axiom,
% 5.15/5.44 ! [A: complex] :
% 5.15/5.44 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.15/5.44 = zero_zero_complex ) ).
% 5.15/5.44
% 5.15/5.44 % add.right_inverse
% 5.15/5.44 thf(fact_4725_add_Oright__inverse,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.15/5.44 = zero_zero_rat ) ).
% 5.15/5.44
% 5.15/5.44 % add.right_inverse
% 5.15/5.44 thf(fact_4726_add_Oright__inverse,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ).
% 5.15/5.44
% 5.15/5.44 % add.right_inverse
% 5.15/5.44 thf(fact_4727_ab__left__minus,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.15/5.44 = zero_zero_int ) ).
% 5.15/5.44
% 5.15/5.44 % ab_left_minus
% 5.15/5.44 thf(fact_4728_ab__left__minus,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.15/5.44 = zero_zero_real ) ).
% 5.15/5.44
% 5.15/5.44 % ab_left_minus
% 5.15/5.44 thf(fact_4729_ab__left__minus,axiom,
% 5.15/5.44 ! [A: complex] :
% 5.15/5.44 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.15/5.44 = zero_zero_complex ) ).
% 5.15/5.44
% 5.15/5.44 % ab_left_minus
% 5.15/5.44 thf(fact_4730_ab__left__minus,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.15/5.44 = zero_zero_rat ) ).
% 5.15/5.44
% 5.15/5.44 % ab_left_minus
% 5.15/5.44 thf(fact_4731_ab__left__minus,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ).
% 5.15/5.44
% 5.15/5.44 % ab_left_minus
% 5.15/5.44 thf(fact_4732_verit__minus__simplify_I3_J,axiom,
% 5.15/5.44 ! [B: int] :
% 5.15/5.44 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.15/5.44 = ( uminus_uminus_int @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % verit_minus_simplify(3)
% 5.15/5.44 thf(fact_4733_verit__minus__simplify_I3_J,axiom,
% 5.15/5.44 ! [B: real] :
% 5.15/5.44 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.15/5.44 = ( uminus_uminus_real @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % verit_minus_simplify(3)
% 5.15/5.44 thf(fact_4734_verit__minus__simplify_I3_J,axiom,
% 5.15/5.44 ! [B: complex] :
% 5.15/5.44 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % verit_minus_simplify(3)
% 5.15/5.44 thf(fact_4735_verit__minus__simplify_I3_J,axiom,
% 5.15/5.44 ! [B: rat] :
% 5.15/5.44 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.15/5.44 = ( uminus_uminus_rat @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % verit_minus_simplify(3)
% 5.15/5.44 thf(fact_4736_verit__minus__simplify_I3_J,axiom,
% 5.15/5.44 ! [B: code_integer] :
% 5.15/5.44 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % verit_minus_simplify(3)
% 5.15/5.44 thf(fact_4737_diff__0,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.15/5.44 = ( uminus_uminus_int @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_0
% 5.15/5.44 thf(fact_4738_diff__0,axiom,
% 5.15/5.44 ! [A: real] :
% 5.15/5.44 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.15/5.44 = ( uminus_uminus_real @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_0
% 5.15/5.44 thf(fact_4739_diff__0,axiom,
% 5.15/5.44 ! [A: complex] :
% 5.15/5.44 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_0
% 5.15/5.44 thf(fact_4740_diff__0,axiom,
% 5.15/5.44 ! [A: rat] :
% 5.15/5.44 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.15/5.44 = ( uminus_uminus_rat @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_0
% 5.15/5.44 thf(fact_4741_diff__0,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_0
% 5.15/5.44 thf(fact_4742_add__neg__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_simps(3)
% 5.15/5.44 thf(fact_4743_add__neg__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_simps(3)
% 5.15/5.44 thf(fact_4744_add__neg__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_simps(3)
% 5.15/5.44 thf(fact_4745_add__neg__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_simps(3)
% 5.15/5.44 thf(fact_4746_add__neg__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_simps(3)
% 5.15/5.44 thf(fact_4747_mult__minus1__right,axiom,
% 5.15/5.44 ! [Z: int] :
% 5.15/5.44 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.44 = ( uminus_uminus_int @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1_right
% 5.15/5.44 thf(fact_4748_mult__minus1__right,axiom,
% 5.15/5.44 ! [Z: real] :
% 5.15/5.44 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.44 = ( uminus_uminus_real @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1_right
% 5.15/5.44 thf(fact_4749_mult__minus1__right,axiom,
% 5.15/5.44 ! [Z: complex] :
% 5.15/5.44 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1_right
% 5.15/5.44 thf(fact_4750_mult__minus1__right,axiom,
% 5.15/5.44 ! [Z: rat] :
% 5.15/5.44 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.44 = ( uminus_uminus_rat @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1_right
% 5.15/5.44 thf(fact_4751_mult__minus1__right,axiom,
% 5.15/5.44 ! [Z: code_integer] :
% 5.15/5.44 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1_right
% 5.15/5.44 thf(fact_4752_mult__minus1,axiom,
% 5.15/5.44 ! [Z: int] :
% 5.15/5.44 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.15/5.44 = ( uminus_uminus_int @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1
% 5.15/5.44 thf(fact_4753_mult__minus1,axiom,
% 5.15/5.44 ! [Z: real] :
% 5.15/5.44 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.15/5.44 = ( uminus_uminus_real @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1
% 5.15/5.44 thf(fact_4754_mult__minus1,axiom,
% 5.15/5.44 ! [Z: complex] :
% 5.15/5.44 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1
% 5.15/5.44 thf(fact_4755_mult__minus1,axiom,
% 5.15/5.44 ! [Z: rat] :
% 5.15/5.44 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.15/5.44 = ( uminus_uminus_rat @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1
% 5.15/5.44 thf(fact_4756_mult__minus1,axiom,
% 5.15/5.44 ! [Z: code_integer] :
% 5.15/5.44 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.15/5.44
% 5.15/5.44 % mult_minus1
% 5.15/5.44 thf(fact_4757_diff__minus__eq__add,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.44 = ( plus_plus_int @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_minus_eq_add
% 5.15/5.44 thf(fact_4758_diff__minus__eq__add,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.15/5.44 = ( plus_plus_real @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_minus_eq_add
% 5.15/5.44 thf(fact_4759_diff__minus__eq__add,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.44 = ( plus_plus_complex @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_minus_eq_add
% 5.15/5.44 thf(fact_4760_diff__minus__eq__add,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.15/5.44 = ( plus_plus_rat @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_minus_eq_add
% 5.15/5.44 thf(fact_4761_diff__minus__eq__add,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.44 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_minus_eq_add
% 5.15/5.44 thf(fact_4762_uminus__add__conv__diff,axiom,
% 5.15/5.44 ! [A: int,B: int] :
% 5.15/5.44 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.44 = ( minus_minus_int @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % uminus_add_conv_diff
% 5.15/5.44 thf(fact_4763_uminus__add__conv__diff,axiom,
% 5.15/5.44 ! [A: real,B: real] :
% 5.15/5.44 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.15/5.44 = ( minus_minus_real @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % uminus_add_conv_diff
% 5.15/5.44 thf(fact_4764_uminus__add__conv__diff,axiom,
% 5.15/5.44 ! [A: complex,B: complex] :
% 5.15/5.44 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.15/5.44 = ( minus_minus_complex @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % uminus_add_conv_diff
% 5.15/5.44 thf(fact_4765_uminus__add__conv__diff,axiom,
% 5.15/5.44 ! [A: rat,B: rat] :
% 5.15/5.44 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.15/5.44 = ( minus_minus_rat @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % uminus_add_conv_diff
% 5.15/5.44 thf(fact_4766_uminus__add__conv__diff,axiom,
% 5.15/5.44 ! [A: code_integer,B: code_integer] :
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.15/5.44 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % uminus_add_conv_diff
% 5.15/5.44 thf(fact_4767_div__minus1__right,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.44 = ( uminus_uminus_int @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % div_minus1_right
% 5.15/5.44 thf(fact_4768_div__minus1__right,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.15/5.44
% 5.15/5.44 % div_minus1_right
% 5.15/5.44 thf(fact_4769_divide__minus1,axiom,
% 5.15/5.44 ! [X: real] :
% 5.15/5.44 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.44 = ( uminus_uminus_real @ X ) ) ).
% 5.15/5.44
% 5.15/5.44 % divide_minus1
% 5.15/5.44 thf(fact_4770_divide__minus1,axiom,
% 5.15/5.44 ! [X: complex] :
% 5.15/5.44 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.15/5.44
% 5.15/5.44 % divide_minus1
% 5.15/5.44 thf(fact_4771_divide__minus1,axiom,
% 5.15/5.44 ! [X: rat] :
% 5.15/5.44 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.44 = ( uminus_uminus_rat @ X ) ) ).
% 5.15/5.44
% 5.15/5.44 % divide_minus1
% 5.15/5.44 thf(fact_4772_minus__mod__self1,axiom,
% 5.15/5.44 ! [B: int,A: int] :
% 5.15/5.44 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.15/5.44 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_mod_self1
% 5.15/5.44 thf(fact_4773_minus__mod__self1,axiom,
% 5.15/5.44 ! [B: code_integer,A: code_integer] :
% 5.15/5.44 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.15/5.44 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.15/5.44
% 5.15/5.44 % minus_mod_self1
% 5.15/5.44 thf(fact_4774_zero__less__of__bool__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % zero_less_of_bool_iff
% 5.15/5.44 thf(fact_4775_zero__less__of__bool__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % zero_less_of_bool_iff
% 5.15/5.44 thf(fact_4776_zero__less__of__bool__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % zero_less_of_bool_iff
% 5.15/5.44 thf(fact_4777_zero__less__of__bool__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % zero_less_of_bool_iff
% 5.15/5.44 thf(fact_4778_zero__less__of__bool__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.15/5.44 = P ) ).
% 5.15/5.44
% 5.15/5.44 % zero_less_of_bool_iff
% 5.15/5.44 thf(fact_4779_of__bool__less__one__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_one_iff
% 5.15/5.44 thf(fact_4780_of__bool__less__one__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_one_iff
% 5.15/5.44 thf(fact_4781_of__bool__less__one__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_one_iff
% 5.15/5.44 thf(fact_4782_of__bool__less__one__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_one_iff
% 5.15/5.44 thf(fact_4783_of__bool__less__one__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.15/5.44 = ~ P ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_less_one_iff
% 5.15/5.44 thf(fact_4784_of__bool__not__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.15/5.44 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_not_iff
% 5.15/5.44 thf(fact_4785_of__bool__not__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.15/5.44 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_not_iff
% 5.15/5.44 thf(fact_4786_of__bool__not__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.15/5.44 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_not_iff
% 5.15/5.44 thf(fact_4787_of__bool__not__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.15/5.44 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_not_iff
% 5.15/5.44 thf(fact_4788_of__bool__not__iff,axiom,
% 5.15/5.44 ! [P: $o] :
% 5.15/5.44 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.15/5.44 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % of_bool_not_iff
% 5.15/5.44 thf(fact_4789_Suc__0__mod__eq,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.44 = ( zero_n2687167440665602831ol_nat
% 5.15/5.44 @ ( N2
% 5.15/5.44 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % Suc_0_mod_eq
% 5.15/5.44 thf(fact_4790_signed__take__bit__of__minus__1,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_of_minus_1
% 5.15/5.44 thf(fact_4791_signed__take__bit__of__minus__1,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.44 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % signed_take_bit_of_minus_1
% 5.15/5.44 thf(fact_4792_Ball__set__replicate,axiom,
% 5.15/5.44 ! [N2: nat,A: int,P: int > $o] :
% 5.15/5.44 ( ( ! [X2: int] :
% 5.15/5.44 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.15/5.44 => ( P @ X2 ) ) )
% 5.15/5.44 = ( ( P @ A )
% 5.15/5.44 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % Ball_set_replicate
% 5.15/5.44 thf(fact_4793_Ball__set__replicate,axiom,
% 5.15/5.44 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.15/5.44 ( ( ! [X2: vEBT_VEBT] :
% 5.15/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.15/5.44 => ( P @ X2 ) ) )
% 5.15/5.44 = ( ( P @ A )
% 5.15/5.44 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % Ball_set_replicate
% 5.15/5.44 thf(fact_4794_Bex__set__replicate,axiom,
% 5.15/5.44 ! [N2: nat,A: int,P: int > $o] :
% 5.15/5.44 ( ( ? [X2: int] :
% 5.15/5.44 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.15/5.44 & ( P @ X2 ) ) )
% 5.15/5.44 = ( ( P @ A )
% 5.15/5.44 & ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % Bex_set_replicate
% 5.15/5.44 thf(fact_4795_Bex__set__replicate,axiom,
% 5.15/5.44 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.15/5.44 ( ( ? [X2: vEBT_VEBT] :
% 5.15/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.15/5.44 & ( P @ X2 ) ) )
% 5.15/5.44 = ( ( P @ A )
% 5.15/5.44 & ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % Bex_set_replicate
% 5.15/5.44 thf(fact_4796_in__set__replicate,axiom,
% 5.15/5.44 ! [X: complex,N2: nat,Y: complex] :
% 5.15/5.44 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N2 @ Y ) ) )
% 5.15/5.44 = ( ( X = Y )
% 5.15/5.44 & ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % in_set_replicate
% 5.15/5.44 thf(fact_4797_in__set__replicate,axiom,
% 5.15/5.44 ! [X: real,N2: nat,Y: real] :
% 5.15/5.44 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 5.15/5.44 = ( ( X = Y )
% 5.15/5.44 & ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % in_set_replicate
% 5.15/5.44 thf(fact_4798_in__set__replicate,axiom,
% 5.15/5.44 ! [X: set_nat,N2: nat,Y: set_nat] :
% 5.15/5.44 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N2 @ Y ) ) )
% 5.15/5.44 = ( ( X = Y )
% 5.15/5.44 & ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % in_set_replicate
% 5.15/5.44 thf(fact_4799_in__set__replicate,axiom,
% 5.15/5.44 ! [X: nat,N2: nat,Y: nat] :
% 5.15/5.44 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 5.15/5.44 = ( ( X = Y )
% 5.15/5.44 & ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % in_set_replicate
% 5.15/5.44 thf(fact_4800_in__set__replicate,axiom,
% 5.15/5.44 ! [X: int,N2: nat,Y: int] :
% 5.15/5.44 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 5.15/5.44 = ( ( X = Y )
% 5.15/5.44 & ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % in_set_replicate
% 5.15/5.44 thf(fact_4801_in__set__replicate,axiom,
% 5.15/5.44 ! [X: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.15/5.44 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 5.15/5.44 = ( ( X = Y )
% 5.15/5.44 & ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % in_set_replicate
% 5.15/5.44 thf(fact_4802_pred__numeral__simps_I1_J,axiom,
% 5.15/5.44 ( ( pred_numeral @ one )
% 5.15/5.44 = zero_zero_nat ) ).
% 5.15/5.44
% 5.15/5.44 % pred_numeral_simps(1)
% 5.15/5.44 thf(fact_4803_Suc__eq__numeral,axiom,
% 5.15/5.44 ! [N2: nat,K: num] :
% 5.15/5.44 ( ( ( suc @ N2 )
% 5.15/5.44 = ( numeral_numeral_nat @ K ) )
% 5.15/5.44 = ( N2
% 5.15/5.44 = ( pred_numeral @ K ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % Suc_eq_numeral
% 5.15/5.44 thf(fact_4804_eq__numeral__Suc,axiom,
% 5.15/5.44 ! [K: num,N2: nat] :
% 5.15/5.44 ( ( ( numeral_numeral_nat @ K )
% 5.15/5.44 = ( suc @ N2 ) )
% 5.15/5.44 = ( ( pred_numeral @ K )
% 5.15/5.44 = N2 ) ) ).
% 5.15/5.44
% 5.15/5.44 % eq_numeral_Suc
% 5.15/5.44 thf(fact_4805_nth__replicate,axiom,
% 5.15/5.44 ! [I: nat,N2: nat,X: int] :
% 5.15/5.44 ( ( ord_less_nat @ I @ N2 )
% 5.15/5.44 => ( ( nth_int @ ( replicate_int @ N2 @ X ) @ I )
% 5.15/5.44 = X ) ) ).
% 5.15/5.44
% 5.15/5.44 % nth_replicate
% 5.15/5.44 thf(fact_4806_nth__replicate,axiom,
% 5.15/5.44 ! [I: nat,N2: nat,X: nat] :
% 5.15/5.44 ( ( ord_less_nat @ I @ N2 )
% 5.15/5.44 => ( ( nth_nat @ ( replicate_nat @ N2 @ X ) @ I )
% 5.15/5.44 = X ) ) ).
% 5.15/5.44
% 5.15/5.44 % nth_replicate
% 5.15/5.44 thf(fact_4807_nth__replicate,axiom,
% 5.15/5.44 ! [I: nat,N2: nat,X: vEBT_VEBT] :
% 5.15/5.44 ( ( ord_less_nat @ I @ N2 )
% 5.15/5.44 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) @ I )
% 5.15/5.44 = X ) ) ).
% 5.15/5.44
% 5.15/5.44 % nth_replicate
% 5.15/5.44 thf(fact_4808_dbl__simps_I1_J,axiom,
% 5.15/5.44 ! [K: num] :
% 5.15/5.44 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_simps(1)
% 5.15/5.44 thf(fact_4809_dbl__simps_I1_J,axiom,
% 5.15/5.44 ! [K: num] :
% 5.15/5.44 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_simps(1)
% 5.15/5.44 thf(fact_4810_dbl__simps_I1_J,axiom,
% 5.15/5.44 ! [K: num] :
% 5.15/5.44 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_simps(1)
% 5.15/5.44 thf(fact_4811_dbl__simps_I1_J,axiom,
% 5.15/5.44 ! [K: num] :
% 5.15/5.44 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_simps(1)
% 5.15/5.44 thf(fact_4812_dbl__simps_I1_J,axiom,
% 5.15/5.44 ! [K: num] :
% 5.15/5.44 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_simps(1)
% 5.15/5.44 thf(fact_4813_dbl__inc__simps_I4_J,axiom,
% 5.15/5.44 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.44 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_inc_simps(4)
% 5.15/5.44 thf(fact_4814_dbl__inc__simps_I4_J,axiom,
% 5.15/5.44 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.44 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_inc_simps(4)
% 5.15/5.44 thf(fact_4815_dbl__inc__simps_I4_J,axiom,
% 5.15/5.44 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_inc_simps(4)
% 5.15/5.44 thf(fact_4816_dbl__inc__simps_I4_J,axiom,
% 5.15/5.44 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.44 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_inc_simps(4)
% 5.15/5.44 thf(fact_4817_dbl__inc__simps_I4_J,axiom,
% 5.15/5.44 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.44
% 5.15/5.44 % dbl_inc_simps(4)
% 5.15/5.44 thf(fact_4818_add__neg__numeral__special_I8_J,axiom,
% 5.15/5.44 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.15/5.44 = zero_zero_int ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(8)
% 5.15/5.44 thf(fact_4819_add__neg__numeral__special_I8_J,axiom,
% 5.15/5.44 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.15/5.44 = zero_zero_real ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(8)
% 5.15/5.44 thf(fact_4820_add__neg__numeral__special_I8_J,axiom,
% 5.15/5.44 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.15/5.44 = zero_zero_complex ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(8)
% 5.15/5.44 thf(fact_4821_add__neg__numeral__special_I8_J,axiom,
% 5.15/5.44 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.15/5.44 = zero_zero_rat ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(8)
% 5.15/5.44 thf(fact_4822_add__neg__numeral__special_I8_J,axiom,
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(8)
% 5.15/5.44 thf(fact_4823_add__neg__numeral__special_I7_J,axiom,
% 5.15/5.44 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.44 = zero_zero_int ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(7)
% 5.15/5.44 thf(fact_4824_add__neg__numeral__special_I7_J,axiom,
% 5.15/5.44 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.44 = zero_zero_real ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(7)
% 5.15/5.44 thf(fact_4825_add__neg__numeral__special_I7_J,axiom,
% 5.15/5.44 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.44 = zero_zero_complex ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(7)
% 5.15/5.44 thf(fact_4826_add__neg__numeral__special_I7_J,axiom,
% 5.15/5.44 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.44 = zero_zero_rat ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(7)
% 5.15/5.44 thf(fact_4827_add__neg__numeral__special_I7_J,axiom,
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ).
% 5.15/5.44
% 5.15/5.44 % add_neg_numeral_special(7)
% 5.15/5.44 thf(fact_4828_diff__numeral__special_I12_J,axiom,
% 5.15/5.44 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.44 = zero_zero_int ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_special(12)
% 5.15/5.44 thf(fact_4829_diff__numeral__special_I12_J,axiom,
% 5.15/5.44 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.44 = zero_zero_real ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_special(12)
% 5.15/5.44 thf(fact_4830_diff__numeral__special_I12_J,axiom,
% 5.15/5.44 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.44 = zero_zero_complex ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_special(12)
% 5.15/5.44 thf(fact_4831_diff__numeral__special_I12_J,axiom,
% 5.15/5.44 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.44 = zero_zero_rat ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_special(12)
% 5.15/5.44 thf(fact_4832_diff__numeral__special_I12_J,axiom,
% 5.15/5.44 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_special(12)
% 5.15/5.44 thf(fact_4833_neg__one__eq__numeral__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_int @ one_one_int )
% 5.15/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_one_eq_numeral_iff
% 5.15/5.44 thf(fact_4834_neg__one__eq__numeral__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_real @ one_one_real )
% 5.15/5.44 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_one_eq_numeral_iff
% 5.15/5.44 thf(fact_4835_neg__one__eq__numeral__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_one_eq_numeral_iff
% 5.15/5.44 thf(fact_4836_neg__one__eq__numeral__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.15/5.44 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_one_eq_numeral_iff
% 5.15/5.44 thf(fact_4837_neg__one__eq__numeral__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % neg_one_eq_numeral_iff
% 5.15/5.44 thf(fact_4838_numeral__eq__neg__one__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.44 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % numeral_eq_neg_one_iff
% 5.15/5.44 thf(fact_4839_numeral__eq__neg__one__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.44 = ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % numeral_eq_neg_one_iff
% 5.15/5.44 thf(fact_4840_numeral__eq__neg__one__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % numeral_eq_neg_one_iff
% 5.15/5.44 thf(fact_4841_numeral__eq__neg__one__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.44 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % numeral_eq_neg_one_iff
% 5.15/5.44 thf(fact_4842_numeral__eq__neg__one__iff,axiom,
% 5.15/5.44 ! [N2: num] :
% 5.15/5.44 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.44 = ( N2 = one ) ) ).
% 5.15/5.44
% 5.15/5.44 % numeral_eq_neg_one_iff
% 5.15/5.44 thf(fact_4843_left__minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat,A: int] :
% 5.15/5.44 ( ( 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 ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % left_minus_one_mult_self
% 5.15/5.44 thf(fact_4844_left__minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat,A: real] :
% 5.15/5.44 ( ( 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 ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % left_minus_one_mult_self
% 5.15/5.44 thf(fact_4845_left__minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat,A: complex] :
% 5.15/5.44 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ A ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % left_minus_one_mult_self
% 5.15/5.44 thf(fact_4846_left__minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat,A: rat] :
% 5.15/5.44 ( ( 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 ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % left_minus_one_mult_self
% 5.15/5.44 thf(fact_4847_left__minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat,A: code_integer] :
% 5.15/5.44 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 5.15/5.44 = A ) ).
% 5.15/5.44
% 5.15/5.44 % left_minus_one_mult_self
% 5.15/5.44 thf(fact_4848_minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 5.15/5.44 = one_one_int ) ).
% 5.15/5.44
% 5.15/5.44 % minus_one_mult_self
% 5.15/5.44 thf(fact_4849_minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) )
% 5.15/5.44 = one_one_real ) ).
% 5.15/5.44
% 5.15/5.44 % minus_one_mult_self
% 5.15/5.44 thf(fact_4850_minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) )
% 5.15/5.44 = one_one_complex ) ).
% 5.15/5.44
% 5.15/5.44 % minus_one_mult_self
% 5.15/5.44 thf(fact_4851_minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 5.15/5.44 = one_one_rat ) ).
% 5.15/5.44
% 5.15/5.44 % minus_one_mult_self
% 5.15/5.44 thf(fact_4852_minus__one__mult__self,axiom,
% 5.15/5.44 ! [N2: nat] :
% 5.15/5.44 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 5.15/5.44 = one_one_Code_integer ) ).
% 5.15/5.44
% 5.15/5.44 % minus_one_mult_self
% 5.15/5.44 thf(fact_4853_mod__minus1__right,axiom,
% 5.15/5.44 ! [A: int] :
% 5.15/5.44 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.44 = zero_zero_int ) ).
% 5.15/5.44
% 5.15/5.44 % mod_minus1_right
% 5.15/5.44 thf(fact_4854_mod__minus1__right,axiom,
% 5.15/5.44 ! [A: code_integer] :
% 5.15/5.44 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.44 = zero_z3403309356797280102nteger ) ).
% 5.15/5.44
% 5.15/5.44 % mod_minus1_right
% 5.15/5.44 thf(fact_4855_max__number__of_I2_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(2)
% 5.15/5.44 thf(fact_4856_max__number__of_I2_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.15/5.44 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(2)
% 5.15/5.44 thf(fact_4857_max__number__of_I2_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(2)
% 5.15/5.44 thf(fact_4858_max__number__of_I2_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(2)
% 5.15/5.44 thf(fact_4859_max__number__of_I3_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.44 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.44 = ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.44 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(3)
% 5.15/5.44 thf(fact_4860_max__number__of_I3_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.15/5.44 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.15/5.44 = ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.15/5.44 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(3)
% 5.15/5.44 thf(fact_4861_max__number__of_I3_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.44 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.44 = ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.44 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(3)
% 5.15/5.44 thf(fact_4862_max__number__of_I3_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.44 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.44 = ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.44 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(3)
% 5.15/5.44 thf(fact_4863_max__number__of_I4_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(4)
% 5.15/5.44 thf(fact_4864_max__number__of_I4_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.15/5.44 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(4)
% 5.15/5.44 thf(fact_4865_max__number__of_I4_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(4)
% 5.15/5.44 thf(fact_4866_max__number__of_I4_J,axiom,
% 5.15/5.44 ! [U: num,V: num] :
% 5.15/5.44 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.15/5.44 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % max_number_of(4)
% 5.15/5.44 thf(fact_4867_semiring__norm_I168_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: int] :
% 5.15/5.44 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.15/5.44 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(168)
% 5.15/5.44 thf(fact_4868_semiring__norm_I168_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: real] :
% 5.15/5.44 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.15/5.44 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(168)
% 5.15/5.44 thf(fact_4869_semiring__norm_I168_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: complex] :
% 5.15/5.44 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.15/5.44 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(168)
% 5.15/5.44 thf(fact_4870_semiring__norm_I168_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: rat] :
% 5.15/5.44 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.15/5.44 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(168)
% 5.15/5.44 thf(fact_4871_semiring__norm_I168_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: code_integer] :
% 5.15/5.44 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.15/5.44 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(168)
% 5.15/5.44 thf(fact_4872_diff__numeral__simps_I2_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.44 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(2)
% 5.15/5.44 thf(fact_4873_diff__numeral__simps_I2_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.44 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(2)
% 5.15/5.44 thf(fact_4874_diff__numeral__simps_I2_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.15/5.44 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(2)
% 5.15/5.44 thf(fact_4875_diff__numeral__simps_I2_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.44 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(2)
% 5.15/5.44 thf(fact_4876_diff__numeral__simps_I2_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.44 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(2)
% 5.15/5.44 thf(fact_4877_diff__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(3)
% 5.15/5.44 thf(fact_4878_diff__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.44 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(3)
% 5.15/5.44 thf(fact_4879_diff__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.44 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(3)
% 5.15/5.44 thf(fact_4880_diff__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.44 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(3)
% 5.15/5.44 thf(fact_4881_diff__numeral__simps_I3_J,axiom,
% 5.15/5.44 ! [M: num,N2: num] :
% 5.15/5.44 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.15/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.15/5.44
% 5.15/5.44 % diff_numeral_simps(3)
% 5.15/5.44 thf(fact_4882_semiring__norm_I172_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: int] :
% 5.15/5.44 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.15/5.44 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(172)
% 5.15/5.44 thf(fact_4883_semiring__norm_I172_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: real] :
% 5.15/5.44 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.15/5.44 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(172)
% 5.15/5.44 thf(fact_4884_semiring__norm_I172_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: complex] :
% 5.15/5.44 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.15/5.44 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(172)
% 5.15/5.44 thf(fact_4885_semiring__norm_I172_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: rat] :
% 5.15/5.44 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.15/5.44 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.15/5.44
% 5.15/5.44 % semiring_norm(172)
% 5.15/5.44 thf(fact_4886_semiring__norm_I172_J,axiom,
% 5.15/5.44 ! [V: num,W: num,Y: code_integer] :
% 5.15/5.44 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.15/5.45 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(172)
% 5.15/5.45 thf(fact_4887_semiring__norm_I171_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: int] :
% 5.15/5.45 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.15/5.45 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(171)
% 5.15/5.45 thf(fact_4888_semiring__norm_I171_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: real] :
% 5.15/5.45 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.15/5.45 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(171)
% 5.15/5.45 thf(fact_4889_semiring__norm_I171_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: complex] :
% 5.15/5.45 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.15/5.45 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(171)
% 5.15/5.45 thf(fact_4890_semiring__norm_I171_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: rat] :
% 5.15/5.45 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.15/5.45 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(171)
% 5.15/5.45 thf(fact_4891_semiring__norm_I171_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: code_integer] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.15/5.45 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(171)
% 5.15/5.45 thf(fact_4892_semiring__norm_I170_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: int] :
% 5.15/5.45 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 5.15/5.45 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(170)
% 5.15/5.45 thf(fact_4893_semiring__norm_I170_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: real] :
% 5.15/5.45 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 5.15/5.45 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(170)
% 5.15/5.45 thf(fact_4894_semiring__norm_I170_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: complex] :
% 5.15/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 5.15/5.45 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(170)
% 5.15/5.45 thf(fact_4895_semiring__norm_I170_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: rat] :
% 5.15/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 5.15/5.45 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(170)
% 5.15/5.45 thf(fact_4896_semiring__norm_I170_J,axiom,
% 5.15/5.45 ! [V: num,W: num,Y: code_integer] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 5.15/5.45 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % semiring_norm(170)
% 5.15/5.45 thf(fact_4897_mult__neg__numeral__simps_I3_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(3)
% 5.15/5.45 thf(fact_4898_mult__neg__numeral__simps_I3_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(3)
% 5.15/5.45 thf(fact_4899_mult__neg__numeral__simps_I3_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(3)
% 5.15/5.45 thf(fact_4900_mult__neg__numeral__simps_I3_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(3)
% 5.15/5.45 thf(fact_4901_mult__neg__numeral__simps_I3_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(3)
% 5.15/5.45 thf(fact_4902_mult__neg__numeral__simps_I2_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(2)
% 5.15/5.45 thf(fact_4903_mult__neg__numeral__simps_I2_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(2)
% 5.15/5.45 thf(fact_4904_mult__neg__numeral__simps_I2_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(2)
% 5.15/5.45 thf(fact_4905_mult__neg__numeral__simps_I2_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(2)
% 5.15/5.45 thf(fact_4906_mult__neg__numeral__simps_I2_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(2)
% 5.15/5.45 thf(fact_4907_mult__neg__numeral__simps_I1_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.45 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(1)
% 5.15/5.45 thf(fact_4908_mult__neg__numeral__simps_I1_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.45 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(1)
% 5.15/5.45 thf(fact_4909_mult__neg__numeral__simps_I1_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.15/5.45 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(1)
% 5.15/5.45 thf(fact_4910_mult__neg__numeral__simps_I1_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.45 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(1)
% 5.15/5.45 thf(fact_4911_mult__neg__numeral__simps_I1_J,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.45 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_neg_numeral_simps(1)
% 5.15/5.45 thf(fact_4912_less__Suc__numeral,axiom,
% 5.15/5.45 ! [N2: nat,K: num] :
% 5.15/5.45 ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.15/5.45 = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_Suc_numeral
% 5.15/5.45 thf(fact_4913_less__numeral__Suc,axiom,
% 5.15/5.45 ! [K: num,N2: nat] :
% 5.15/5.45 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.15/5.45 = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_numeral_Suc
% 5.15/5.45 thf(fact_4914_pred__numeral__simps_I3_J,axiom,
% 5.15/5.45 ! [K: num] :
% 5.15/5.45 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.15/5.45 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pred_numeral_simps(3)
% 5.15/5.45 thf(fact_4915_le__numeral__Suc,axiom,
% 5.15/5.45 ! [K: num,N2: nat] :
% 5.15/5.45 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.15/5.45 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_numeral_Suc
% 5.15/5.45 thf(fact_4916_le__Suc__numeral,axiom,
% 5.15/5.45 ! [N2: nat,K: num] :
% 5.15/5.45 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.15/5.45 = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_Suc_numeral
% 5.15/5.45 thf(fact_4917_neg__numeral__le__iff,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.45 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_iff
% 5.15/5.45 thf(fact_4918_neg__numeral__le__iff,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.45 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_iff
% 5.15/5.45 thf(fact_4919_neg__numeral__le__iff,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.45 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_iff
% 5.15/5.45 thf(fact_4920_neg__numeral__le__iff,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.45 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_iff
% 5.15/5.45 thf(fact_4921_diff__Suc__numeral,axiom,
% 5.15/5.45 ! [N2: nat,K: num] :
% 5.15/5.45 ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.15/5.45 = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_Suc_numeral
% 5.15/5.45 thf(fact_4922_diff__numeral__Suc,axiom,
% 5.15/5.45 ! [K: num,N2: nat] :
% 5.15/5.45 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.15/5.45 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_Suc
% 5.15/5.45 thf(fact_4923_neg__numeral__less__iff,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.45 = ( ord_less_num @ N2 @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_iff
% 5.15/5.45 thf(fact_4924_neg__numeral__less__iff,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.45 = ( ord_less_num @ N2 @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_iff
% 5.15/5.45 thf(fact_4925_neg__numeral__less__iff,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.45 = ( ord_less_num @ N2 @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_iff
% 5.15/5.45 thf(fact_4926_neg__numeral__less__iff,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.45 = ( ord_less_num @ N2 @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_iff
% 5.15/5.45 thf(fact_4927_max__numeral__Suc,axiom,
% 5.15/5.45 ! [K: num,N2: nat] :
% 5.15/5.45 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.15/5.45 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % max_numeral_Suc
% 5.15/5.45 thf(fact_4928_max__Suc__numeral,axiom,
% 5.15/5.45 ! [N2: nat,K: num] :
% 5.15/5.45 ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.15/5.45 = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % max_Suc_numeral
% 5.15/5.45 thf(fact_4929_pred__numeral__simps_I2_J,axiom,
% 5.15/5.45 ! [K: num] :
% 5.15/5.45 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.15/5.45 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pred_numeral_simps(2)
% 5.15/5.45 thf(fact_4930_not__neg__one__le__neg__numeral__iff,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.15/5.45 = ( M != one ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_neg_one_le_neg_numeral_iff
% 5.15/5.45 thf(fact_4931_not__neg__one__le__neg__numeral__iff,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.15/5.45 = ( M != one ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_neg_one_le_neg_numeral_iff
% 5.15/5.45 thf(fact_4932_not__neg__one__le__neg__numeral__iff,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.15/5.45 = ( M != one ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_neg_one_le_neg_numeral_iff
% 5.15/5.45 thf(fact_4933_not__neg__one__le__neg__numeral__iff,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.15/5.45 = ( M != one ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_neg_one_le_neg_numeral_iff
% 5.15/5.45 thf(fact_4934_neg__numeral__less__neg__one__iff,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.45 = ( M != one ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_neg_one_iff
% 5.15/5.45 thf(fact_4935_neg__numeral__less__neg__one__iff,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.45 = ( M != one ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_neg_one_iff
% 5.15/5.45 thf(fact_4936_neg__numeral__less__neg__one__iff,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.45 = ( M != one ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_neg_one_iff
% 5.15/5.45 thf(fact_4937_neg__numeral__less__neg__one__iff,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.45 = ( M != one ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_neg_one_iff
% 5.15/5.45 thf(fact_4938_divide__le__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [B: real,W: num,A: real] :
% 5.15/5.45 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.15/5.45 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_le_eq_numeral1(2)
% 5.15/5.45 thf(fact_4939_divide__le__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [B: rat,W: num,A: rat] :
% 5.15/5.45 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.15/5.45 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_le_eq_numeral1(2)
% 5.15/5.45 thf(fact_4940_le__divide__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [A: real,B: real,W: num] :
% 5.15/5.45 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.15/5.45 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_divide_eq_numeral1(2)
% 5.15/5.45 thf(fact_4941_le__divide__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [A: rat,B: rat,W: num] :
% 5.15/5.45 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.15/5.45 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_divide_eq_numeral1(2)
% 5.15/5.45 thf(fact_4942_divide__eq__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [B: real,W: num,A: real] :
% 5.15/5.45 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.45 = A )
% 5.15/5.45 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.45 != zero_zero_real )
% 5.15/5.45 => ( B
% 5.15/5.45 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.15/5.45 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.45 = zero_zero_real )
% 5.15/5.45 => ( A = zero_zero_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_eq_numeral1(2)
% 5.15/5.45 thf(fact_4943_divide__eq__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [B: complex,W: num,A: complex] :
% 5.15/5.45 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.45 = A )
% 5.15/5.45 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.45 != zero_zero_complex )
% 5.15/5.45 => ( B
% 5.15/5.45 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.15/5.45 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.45 = zero_zero_complex )
% 5.15/5.45 => ( A = zero_zero_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_eq_numeral1(2)
% 5.15/5.45 thf(fact_4944_divide__eq__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [B: rat,W: num,A: rat] :
% 5.15/5.45 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.15/5.45 = A )
% 5.15/5.45 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.15/5.45 != zero_zero_rat )
% 5.15/5.45 => ( B
% 5.15/5.45 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.15/5.45 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.15/5.45 = zero_zero_rat )
% 5.15/5.45 => ( A = zero_zero_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_eq_numeral1(2)
% 5.15/5.45 thf(fact_4945_eq__divide__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [A: real,B: real,W: num] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.15/5.45 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.45 != zero_zero_real )
% 5.15/5.45 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.45 = zero_zero_real )
% 5.15/5.45 => ( A = zero_zero_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_divide_eq_numeral1(2)
% 5.15/5.45 thf(fact_4946_eq__divide__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [A: complex,B: complex,W: num] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.15/5.45 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.45 != zero_zero_complex )
% 5.15/5.45 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.45 = zero_zero_complex )
% 5.15/5.45 => ( A = zero_zero_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_divide_eq_numeral1(2)
% 5.15/5.45 thf(fact_4947_eq__divide__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [A: rat,B: rat,W: num] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.15/5.45 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.15/5.45 != zero_zero_rat )
% 5.15/5.45 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.15/5.45 = zero_zero_rat )
% 5.15/5.45 => ( A = zero_zero_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_divide_eq_numeral1(2)
% 5.15/5.45 thf(fact_4948_divide__less__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [B: real,W: num,A: real] :
% 5.15/5.45 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.15/5.45 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_less_eq_numeral1(2)
% 5.15/5.45 thf(fact_4949_divide__less__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [B: rat,W: num,A: rat] :
% 5.15/5.45 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.15/5.45 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_less_eq_numeral1(2)
% 5.15/5.45 thf(fact_4950_less__divide__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [A: real,B: real,W: num] :
% 5.15/5.45 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.15/5.45 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_divide_eq_numeral1(2)
% 5.15/5.45 thf(fact_4951_less__divide__eq__numeral1_I2_J,axiom,
% 5.15/5.45 ! [A: rat,B: rat,W: num] :
% 5.15/5.45 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.15/5.45 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_divide_eq_numeral1(2)
% 5.15/5.45 thf(fact_4952_power2__minus,axiom,
% 5.15/5.45 ! [A: int] :
% 5.15/5.45 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_minus
% 5.15/5.45 thf(fact_4953_power2__minus,axiom,
% 5.15/5.45 ! [A: real] :
% 5.15/5.45 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_minus
% 5.15/5.45 thf(fact_4954_power2__minus,axiom,
% 5.15/5.45 ! [A: complex] :
% 5.15/5.45 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_minus
% 5.15/5.45 thf(fact_4955_power2__minus,axiom,
% 5.15/5.45 ! [A: rat] :
% 5.15/5.45 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_minus
% 5.15/5.45 thf(fact_4956_power2__minus,axiom,
% 5.15/5.45 ! [A: code_integer] :
% 5.15/5.45 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_minus
% 5.15/5.45 thf(fact_4957_odd__of__bool__self,axiom,
% 5.15/5.45 ! [P2: $o] :
% 5.15/5.45 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 5.15/5.45 = P2 ) ).
% 5.15/5.45
% 5.15/5.45 % odd_of_bool_self
% 5.15/5.45 thf(fact_4958_odd__of__bool__self,axiom,
% 5.15/5.45 ! [P2: $o] :
% 5.15/5.45 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 5.15/5.45 = P2 ) ).
% 5.15/5.45
% 5.15/5.45 % odd_of_bool_self
% 5.15/5.45 thf(fact_4959_odd__of__bool__self,axiom,
% 5.15/5.45 ! [P2: $o] :
% 5.15/5.45 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 5.15/5.45 = P2 ) ).
% 5.15/5.45
% 5.15/5.45 % odd_of_bool_self
% 5.15/5.45 thf(fact_4960_add__neg__numeral__special_I9_J,axiom,
% 5.15/5.45 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_neg_numeral_special(9)
% 5.15/5.45 thf(fact_4961_add__neg__numeral__special_I9_J,axiom,
% 5.15/5.45 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_neg_numeral_special(9)
% 5.15/5.45 thf(fact_4962_add__neg__numeral__special_I9_J,axiom,
% 5.15/5.45 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_neg_numeral_special(9)
% 5.15/5.45 thf(fact_4963_add__neg__numeral__special_I9_J,axiom,
% 5.15/5.45 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_neg_numeral_special(9)
% 5.15/5.45 thf(fact_4964_add__neg__numeral__special_I9_J,axiom,
% 5.15/5.45 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_neg_numeral_special(9)
% 5.15/5.45 thf(fact_4965_diff__numeral__special_I11_J,axiom,
% 5.15/5.45 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.45 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(11)
% 5.15/5.45 thf(fact_4966_diff__numeral__special_I11_J,axiom,
% 5.15/5.45 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.45 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(11)
% 5.15/5.45 thf(fact_4967_diff__numeral__special_I11_J,axiom,
% 5.15/5.45 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.45 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(11)
% 5.15/5.45 thf(fact_4968_diff__numeral__special_I11_J,axiom,
% 5.15/5.45 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.45 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(11)
% 5.15/5.45 thf(fact_4969_diff__numeral__special_I11_J,axiom,
% 5.15/5.45 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.45 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(11)
% 5.15/5.45 thf(fact_4970_diff__numeral__special_I10_J,axiom,
% 5.15/5.45 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.15/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(10)
% 5.15/5.45 thf(fact_4971_diff__numeral__special_I10_J,axiom,
% 5.15/5.45 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.15/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(10)
% 5.15/5.45 thf(fact_4972_diff__numeral__special_I10_J,axiom,
% 5.15/5.45 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(10)
% 5.15/5.45 thf(fact_4973_diff__numeral__special_I10_J,axiom,
% 5.15/5.45 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.15/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(10)
% 5.15/5.45 thf(fact_4974_diff__numeral__special_I10_J,axiom,
% 5.15/5.45 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(10)
% 5.15/5.45 thf(fact_4975_minus__1__div__2__eq,axiom,
% 5.15/5.45 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_1_div_2_eq
% 5.15/5.45 thf(fact_4976_minus__1__div__2__eq,axiom,
% 5.15/5.45 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_1_div_2_eq
% 5.15/5.45 thf(fact_4977_minus__1__mod__2__eq,axiom,
% 5.15/5.45 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_int ) ).
% 5.15/5.45
% 5.15/5.45 % minus_1_mod_2_eq
% 5.15/5.45 thf(fact_4978_minus__1__mod__2__eq,axiom,
% 5.15/5.45 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_Code_integer ) ).
% 5.15/5.45
% 5.15/5.45 % minus_1_mod_2_eq
% 5.15/5.45 thf(fact_4979_bits__minus__1__mod__2__eq,axiom,
% 5.15/5.45 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_int ) ).
% 5.15/5.45
% 5.15/5.45 % bits_minus_1_mod_2_eq
% 5.15/5.45 thf(fact_4980_bits__minus__1__mod__2__eq,axiom,
% 5.15/5.45 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_Code_integer ) ).
% 5.15/5.45
% 5.15/5.45 % bits_minus_1_mod_2_eq
% 5.15/5.45 thf(fact_4981_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [A: int,N2: nat] :
% 5.15/5.45 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Power.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4982_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [A: real,N2: nat] :
% 5.15/5.45 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Power.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4983_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [A: complex,N2: nat] :
% 5.15/5.45 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Power.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4984_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [A: rat,N2: nat] :
% 5.15/5.45 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Power.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4985_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [A: code_integer,N2: nat] :
% 5.15/5.45 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Power.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4986_of__bool__half__eq__0,axiom,
% 5.15/5.45 ! [B: $o] :
% 5.15/5.45 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = zero_zero_nat ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_half_eq_0
% 5.15/5.45 thf(fact_4987_of__bool__half__eq__0,axiom,
% 5.15/5.45 ! [B: $o] :
% 5.15/5.45 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.45 = zero_zero_int ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_half_eq_0
% 5.15/5.45 thf(fact_4988_of__bool__half__eq__0,axiom,
% 5.15/5.45 ! [B: $o] :
% 5.15/5.45 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.45 = zero_z3403309356797280102nteger ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_half_eq_0
% 5.15/5.45 thf(fact_4989_power__minus__odd,axiom,
% 5.15/5.45 ! [N2: nat,A: int] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_odd
% 5.15/5.45 thf(fact_4990_power__minus__odd,axiom,
% 5.15/5.45 ! [N2: nat,A: real] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_odd
% 5.15/5.45 thf(fact_4991_power__minus__odd,axiom,
% 5.15/5.45 ! [N2: nat,A: complex] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_odd
% 5.15/5.45 thf(fact_4992_power__minus__odd,axiom,
% 5.15/5.45 ! [N2: nat,A: rat] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_odd
% 5.15/5.45 thf(fact_4993_power__minus__odd,axiom,
% 5.15/5.45 ! [N2: nat,A: code_integer] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_odd
% 5.15/5.45 thf(fact_4994_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [N2: nat,A: int] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.15/5.45 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Parity.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4995_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [N2: nat,A: real] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.15/5.45 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Parity.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4996_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [N2: nat,A: complex] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.15/5.45 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Parity.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4997_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [N2: nat,A: rat] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.15/5.45 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Parity.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4998_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.15/5.45 ! [N2: nat,A: code_integer] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.15/5.45 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % Parity.ring_1_class.power_minus_even
% 5.15/5.45 thf(fact_4999_diff__numeral__special_I4_J,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.15/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(4)
% 5.15/5.45 thf(fact_5000_diff__numeral__special_I4_J,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.15/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(4)
% 5.15/5.45 thf(fact_5001_diff__numeral__special_I4_J,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(4)
% 5.15/5.45 thf(fact_5002_diff__numeral__special_I4_J,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.15/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(4)
% 5.15/5.45 thf(fact_5003_diff__numeral__special_I4_J,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(4)
% 5.15/5.45 thf(fact_5004_diff__numeral__special_I3_J,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.45 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(3)
% 5.15/5.45 thf(fact_5005_diff__numeral__special_I3_J,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.45 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(3)
% 5.15/5.45 thf(fact_5006_diff__numeral__special_I3_J,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.15/5.45 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(3)
% 5.15/5.45 thf(fact_5007_diff__numeral__special_I3_J,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.45 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(3)
% 5.15/5.45 thf(fact_5008_diff__numeral__special_I3_J,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.45 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_numeral_special(3)
% 5.15/5.45 thf(fact_5009_dbl__simps_I4_J,axiom,
% 5.15/5.45 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dbl_simps(4)
% 5.15/5.45 thf(fact_5010_dbl__simps_I4_J,axiom,
% 5.15/5.45 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dbl_simps(4)
% 5.15/5.45 thf(fact_5011_dbl__simps_I4_J,axiom,
% 5.15/5.45 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dbl_simps(4)
% 5.15/5.45 thf(fact_5012_dbl__simps_I4_J,axiom,
% 5.15/5.45 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dbl_simps(4)
% 5.15/5.45 thf(fact_5013_dbl__simps_I4_J,axiom,
% 5.15/5.45 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dbl_simps(4)
% 5.15/5.45 thf(fact_5014_power__minus1__even,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = one_one_int ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus1_even
% 5.15/5.45 thf(fact_5015_power__minus1__even,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = one_one_real ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus1_even
% 5.15/5.45 thf(fact_5016_power__minus1__even,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = one_one_complex ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus1_even
% 5.15/5.45 thf(fact_5017_power__minus1__even,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = one_one_rat ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus1_even
% 5.15/5.45 thf(fact_5018_power__minus1__even,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = one_one_Code_integer ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus1_even
% 5.15/5.45 thf(fact_5019_neg__one__odd__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_odd_power
% 5.15/5.45 thf(fact_5020_neg__one__odd__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_odd_power
% 5.15/5.45 thf(fact_5021_neg__one__odd__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_odd_power
% 5.15/5.45 thf(fact_5022_neg__one__odd__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_odd_power
% 5.15/5.45 thf(fact_5023_neg__one__odd__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_odd_power
% 5.15/5.45 thf(fact_5024_neg__one__even__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.15/5.45 = one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_even_power
% 5.15/5.45 thf(fact_5025_neg__one__even__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.15/5.45 = one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_even_power
% 5.15/5.45 thf(fact_5026_neg__one__even__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.15/5.45 = one_one_complex ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_even_power
% 5.15/5.45 thf(fact_5027_neg__one__even__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.15/5.45 = one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_even_power
% 5.15/5.45 thf(fact_5028_neg__one__even__power,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.15/5.45 = one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_even_power
% 5.15/5.45 thf(fact_5029_signed__take__bit__0,axiom,
% 5.15/5.45 ! [A: code_integer] :
% 5.15/5.45 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_0
% 5.15/5.45 thf(fact_5030_signed__take__bit__0,axiom,
% 5.15/5.45 ! [A: int] :
% 5.15/5.45 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.15/5.45 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_0
% 5.15/5.45 thf(fact_5031_signed__take__bit__Suc__minus__bit0,axiom,
% 5.15/5.45 ! [N2: nat,K: num] :
% 5.15/5.45 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.15/5.45 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_Suc_minus_bit0
% 5.15/5.45 thf(fact_5032_signed__take__bit__numeral__bit0,axiom,
% 5.15/5.45 ! [L: num,K: num] :
% 5.15/5.45 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.15/5.45 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_numeral_bit0
% 5.15/5.45 thf(fact_5033_one__div__2__pow__eq,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_div_2_pow_eq
% 5.15/5.45 thf(fact_5034_one__div__2__pow__eq,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_div_2_pow_eq
% 5.15/5.45 thf(fact_5035_one__div__2__pow__eq,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_div_2_pow_eq
% 5.15/5.45 thf(fact_5036_bits__1__div__exp,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % bits_1_div_exp
% 5.15/5.45 thf(fact_5037_bits__1__div__exp,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % bits_1_div_exp
% 5.15/5.45 thf(fact_5038_bits__1__div__exp,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % bits_1_div_exp
% 5.15/5.45 thf(fact_5039_signed__take__bit__numeral__minus__bit0,axiom,
% 5.15/5.45 ! [L: num,K: num] :
% 5.15/5.45 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.15/5.45 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_numeral_minus_bit0
% 5.15/5.45 thf(fact_5040_one__mod__2__pow__eq,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_mod_2_pow_eq
% 5.15/5.45 thf(fact_5041_one__mod__2__pow__eq,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_mod_2_pow_eq
% 5.15/5.45 thf(fact_5042_one__mod__2__pow__eq,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.45 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_mod_2_pow_eq
% 5.15/5.45 thf(fact_5043_signed__take__bit__numeral__minus__bit1,axiom,
% 5.15/5.45 ! [L: num,K: num] :
% 5.15/5.45 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.15/5.45 = ( 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 ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_numeral_minus_bit1
% 5.15/5.45 thf(fact_5044_dvd__antisym,axiom,
% 5.15/5.45 ! [M: nat,N2: nat] :
% 5.15/5.45 ( ( dvd_dvd_nat @ M @ N2 )
% 5.15/5.45 => ( ( dvd_dvd_nat @ N2 @ M )
% 5.15/5.45 => ( M = N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_antisym
% 5.15/5.45 thf(fact_5045_signed__take__bit__minus,axiom,
% 5.15/5.45 ! [N2: nat,K: int] :
% 5.15/5.45 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) )
% 5.15/5.45 = ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_minus
% 5.15/5.45 thf(fact_5046_of__bool__eq__iff,axiom,
% 5.15/5.45 ! [P2: $o,Q3: $o] :
% 5.15/5.45 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 5.15/5.45 = ( zero_n2687167440665602831ol_nat @ Q3 ) )
% 5.15/5.45 = ( P2 = Q3 ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_eq_iff
% 5.15/5.45 thf(fact_5047_of__bool__eq__iff,axiom,
% 5.15/5.45 ! [P2: $o,Q3: $o] :
% 5.15/5.45 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 5.15/5.45 = ( zero_n2684676970156552555ol_int @ Q3 ) )
% 5.15/5.45 = ( P2 = Q3 ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_eq_iff
% 5.15/5.45 thf(fact_5048_of__bool__eq__iff,axiom,
% 5.15/5.45 ! [P2: $o,Q3: $o] :
% 5.15/5.45 ( ( ( zero_n356916108424825756nteger @ P2 )
% 5.15/5.45 = ( zero_n356916108424825756nteger @ Q3 ) )
% 5.15/5.45 = ( P2 = Q3 ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_eq_iff
% 5.15/5.45 thf(fact_5049_equation__minus__iff,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % equation_minus_iff
% 5.15/5.45 thf(fact_5050_equation__minus__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus_uminus_real @ B ) )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % equation_minus_iff
% 5.15/5.45 thf(fact_5051_equation__minus__iff,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % equation_minus_iff
% 5.15/5.45 thf(fact_5052_equation__minus__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus_uminus_rat @ B ) )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % equation_minus_iff
% 5.15/5.45 thf(fact_5053_equation__minus__iff,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % equation_minus_iff
% 5.15/5.45 thf(fact_5054_minus__equation__iff,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ( uminus_uminus_int @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( uminus_uminus_int @ B )
% 5.15/5.45 = A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_equation_iff
% 5.15/5.45 thf(fact_5055_minus__equation__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ( uminus_uminus_real @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( uminus_uminus_real @ B )
% 5.15/5.45 = A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_equation_iff
% 5.15/5.45 thf(fact_5056_minus__equation__iff,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( ( uminus1482373934393186551omplex @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( uminus1482373934393186551omplex @ B )
% 5.15/5.45 = A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_equation_iff
% 5.15/5.45 thf(fact_5057_minus__equation__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ( uminus_uminus_rat @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( uminus_uminus_rat @ B )
% 5.15/5.45 = A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_equation_iff
% 5.15/5.45 thf(fact_5058_minus__equation__iff,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ( uminus1351360451143612070nteger @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( uminus1351360451143612070nteger @ B )
% 5.15/5.45 = A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_equation_iff
% 5.15/5.45 thf(fact_5059_compl__mono,axiom,
% 5.15/5.45 ! [X: set_nat,Y: set_nat] :
% 5.15/5.45 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.15/5.45 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % compl_mono
% 5.15/5.45 thf(fact_5060_compl__le__swap1,axiom,
% 5.15/5.45 ! [Y: set_nat,X: set_nat] :
% 5.15/5.45 ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 5.15/5.45 => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % compl_le_swap1
% 5.15/5.45 thf(fact_5061_compl__le__swap2,axiom,
% 5.15/5.45 ! [Y: set_nat,X: set_nat] :
% 5.15/5.45 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 5.15/5.45 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % compl_le_swap2
% 5.15/5.45 thf(fact_5062_of__bool__conj,axiom,
% 5.15/5.45 ! [P: $o,Q: $o] :
% 5.15/5.45 ( ( zero_n3304061248610475627l_real
% 5.15/5.45 @ ( P
% 5.15/5.45 & Q ) )
% 5.15/5.45 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_conj
% 5.15/5.45 thf(fact_5063_of__bool__conj,axiom,
% 5.15/5.45 ! [P: $o,Q: $o] :
% 5.15/5.45 ( ( zero_n2052037380579107095ol_rat
% 5.15/5.45 @ ( P
% 5.15/5.45 & Q ) )
% 5.15/5.45 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_conj
% 5.15/5.45 thf(fact_5064_of__bool__conj,axiom,
% 5.15/5.45 ! [P: $o,Q: $o] :
% 5.15/5.45 ( ( zero_n2687167440665602831ol_nat
% 5.15/5.45 @ ( P
% 5.15/5.45 & Q ) )
% 5.15/5.45 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_conj
% 5.15/5.45 thf(fact_5065_of__bool__conj,axiom,
% 5.15/5.45 ! [P: $o,Q: $o] :
% 5.15/5.45 ( ( zero_n2684676970156552555ol_int
% 5.15/5.45 @ ( P
% 5.15/5.45 & Q ) )
% 5.15/5.45 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_conj
% 5.15/5.45 thf(fact_5066_of__bool__conj,axiom,
% 5.15/5.45 ! [P: $o,Q: $o] :
% 5.15/5.45 ( ( zero_n356916108424825756nteger
% 5.15/5.45 @ ( P
% 5.15/5.45 & Q ) )
% 5.15/5.45 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_conj
% 5.15/5.45 thf(fact_5067_bot__nat__def,axiom,
% 5.15/5.45 bot_bot_nat = zero_zero_nat ).
% 5.15/5.45
% 5.15/5.45 % bot_nat_def
% 5.15/5.45 thf(fact_5068_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: complex,C: code_integer > $o > set_complex,P2: produc6271795597528267376eger_o] :
% 5.15/5.45 ( ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: code_integer,Y3: $o] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5069_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: real,C: code_integer > $o > set_real,P2: produc6271795597528267376eger_o] :
% 5.15/5.45 ( ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: code_integer,Y3: $o] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5070_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: nat,C: code_integer > $o > set_nat,P2: produc6271795597528267376eger_o] :
% 5.15/5.45 ( ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: code_integer,Y3: $o] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5071_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: int,C: code_integer > $o > set_int,P2: produc6271795597528267376eger_o] :
% 5.15/5.45 ( ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: code_integer,Y3: $o] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5072_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: complex,C: num > num > set_complex,P2: product_prod_num_num] :
% 5.15/5.45 ( ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: num,Y3: num] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5073_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: real,C: num > num > set_real,P2: product_prod_num_num] :
% 5.15/5.45 ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: num,Y3: num] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5074_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: nat,C: num > num > set_nat,P2: product_prod_num_num] :
% 5.15/5.45 ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: num,Y3: num] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5075_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: int,C: num > num > set_int,P2: product_prod_num_num] :
% 5.15/5.45 ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: num,Y3: num] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5076_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: complex,C: nat > num > set_complex,P2: product_prod_nat_num] :
% 5.15/5.45 ( ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: nat,Y3: num] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_complex @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5077_mem__case__prodE,axiom,
% 5.15/5.45 ! [Z: real,C: nat > num > set_real,P2: product_prod_nat_num] :
% 5.15/5.45 ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P2 ) )
% 5.15/5.45 => ~ ! [X3: nat,Y3: num] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( member_real @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mem_case_prodE
% 5.15/5.45 thf(fact_5078_le__imp__neg__le,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.45 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_imp_neg_le
% 5.15/5.45 thf(fact_5079_le__imp__neg__le,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.15/5.45 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_imp_neg_le
% 5.15/5.45 thf(fact_5080_le__imp__neg__le,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.45 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_imp_neg_le
% 5.15/5.45 thf(fact_5081_le__imp__neg__le,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.45 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_imp_neg_le
% 5.15/5.45 thf(fact_5082_minus__le__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.15/5.45 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_le_iff
% 5.15/5.45 thf(fact_5083_minus__le__iff,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.15/5.45 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_le_iff
% 5.15/5.45 thf(fact_5084_minus__le__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.15/5.45 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_le_iff
% 5.15/5.45 thf(fact_5085_minus__le__iff,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_le_iff
% 5.15/5.45 thf(fact_5086_le__minus__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.15/5.45 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_iff
% 5.15/5.45 thf(fact_5087_le__minus__iff,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.45 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_iff
% 5.15/5.45 thf(fact_5088_le__minus__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.15/5.45 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_iff
% 5.15/5.45 thf(fact_5089_le__minus__iff,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_iff
% 5.15/5.45 thf(fact_5090_verit__negate__coefficient_I2_J,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ord_less_int @ A @ B )
% 5.15/5.45 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % verit_negate_coefficient(2)
% 5.15/5.45 thf(fact_5091_verit__negate__coefficient_I2_J,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ord_less_real @ A @ B )
% 5.15/5.45 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % verit_negate_coefficient(2)
% 5.15/5.45 thf(fact_5092_verit__negate__coefficient_I2_J,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_rat @ A @ B )
% 5.15/5.45 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % verit_negate_coefficient(2)
% 5.15/5.45 thf(fact_5093_verit__negate__coefficient_I2_J,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.15/5.45 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % verit_negate_coefficient(2)
% 5.15/5.45 thf(fact_5094_less__minus__iff,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_iff
% 5.15/5.45 thf(fact_5095_less__minus__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.15/5.45 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_iff
% 5.15/5.45 thf(fact_5096_less__minus__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.15/5.45 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_iff
% 5.15/5.45 thf(fact_5097_less__minus__iff,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.45 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_iff
% 5.15/5.45 thf(fact_5098_minus__less__iff,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_less_iff
% 5.15/5.45 thf(fact_5099_minus__less__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.15/5.45 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_less_iff
% 5.15/5.45 thf(fact_5100_minus__less__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.15/5.45 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_less_iff
% 5.15/5.45 thf(fact_5101_minus__less__iff,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.15/5.45 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_less_iff
% 5.15/5.45 thf(fact_5102_neg__numeral__neq__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.15/5.45 != ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_neq_numeral
% 5.15/5.45 thf(fact_5103_neg__numeral__neq__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.15/5.45 != ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_neq_numeral
% 5.15/5.45 thf(fact_5104_neg__numeral__neq__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.15/5.45 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_neq_numeral
% 5.15/5.45 thf(fact_5105_neg__numeral__neq__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.15/5.45 != ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_neq_numeral
% 5.15/5.45 thf(fact_5106_neg__numeral__neq__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.15/5.45 != ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_neq_numeral
% 5.15/5.45 thf(fact_5107_numeral__neq__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( numeral_numeral_int @ M )
% 5.15/5.45 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_numeral
% 5.15/5.45 thf(fact_5108_numeral__neq__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( numeral_numeral_real @ M )
% 5.15/5.45 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_numeral
% 5.15/5.45 thf(fact_5109_numeral__neq__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( numera6690914467698888265omplex @ M )
% 5.15/5.45 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_numeral
% 5.15/5.45 thf(fact_5110_numeral__neq__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( numeral_numeral_rat @ M )
% 5.15/5.45 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_numeral
% 5.15/5.45 thf(fact_5111_numeral__neq__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ( ( numera6620942414471956472nteger @ M )
% 5.15/5.45 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_numeral
% 5.15/5.45 thf(fact_5112_square__eq__iff,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ( times_times_int @ A @ A )
% 5.15/5.45 = ( times_times_int @ B @ B ) )
% 5.15/5.45 = ( ( A = B )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_iff
% 5.15/5.45 thf(fact_5113_square__eq__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ( times_times_real @ A @ A )
% 5.15/5.45 = ( times_times_real @ B @ B ) )
% 5.15/5.45 = ( ( A = B )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_iff
% 5.15/5.45 thf(fact_5114_square__eq__iff,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( ( times_times_complex @ A @ A )
% 5.15/5.45 = ( times_times_complex @ B @ B ) )
% 5.15/5.45 = ( ( A = B )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_iff
% 5.15/5.45 thf(fact_5115_square__eq__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ( times_times_rat @ A @ A )
% 5.15/5.45 = ( times_times_rat @ B @ B ) )
% 5.15/5.45 = ( ( A = B )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_iff
% 5.15/5.45 thf(fact_5116_square__eq__iff,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.15/5.45 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.15/5.45 = ( ( A = B )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_iff
% 5.15/5.45 thf(fact_5117_minus__mult__commute,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_mult_commute
% 5.15/5.45 thf(fact_5118_minus__mult__commute,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.15/5.45 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_mult_commute
% 5.15/5.45 thf(fact_5119_minus__mult__commute,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.15/5.45 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_mult_commute
% 5.15/5.45 thf(fact_5120_minus__mult__commute,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.15/5.45 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_mult_commute
% 5.15/5.45 thf(fact_5121_minus__mult__commute,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.15/5.45 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_mult_commute
% 5.15/5.45 thf(fact_5122_one__neq__neg__one,axiom,
% 5.15/5.45 ( one_one_int
% 5.15/5.45 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_one
% 5.15/5.45 thf(fact_5123_one__neq__neg__one,axiom,
% 5.15/5.45 ( one_one_real
% 5.15/5.45 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_one
% 5.15/5.45 thf(fact_5124_one__neq__neg__one,axiom,
% 5.15/5.45 ( one_one_complex
% 5.15/5.45 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_one
% 5.15/5.45 thf(fact_5125_one__neq__neg__one,axiom,
% 5.15/5.45 ( one_one_rat
% 5.15/5.45 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_one
% 5.15/5.45 thf(fact_5126_one__neq__neg__one,axiom,
% 5.15/5.45 ( one_one_Code_integer
% 5.15/5.45 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_one
% 5.15/5.45 thf(fact_5127_group__cancel_Oneg1,axiom,
% 5.15/5.45 ! [A2: int,K: int,A: int] :
% 5.15/5.45 ( ( A2
% 5.15/5.45 = ( plus_plus_int @ K @ A ) )
% 5.15/5.45 => ( ( uminus_uminus_int @ A2 )
% 5.15/5.45 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.neg1
% 5.15/5.45 thf(fact_5128_group__cancel_Oneg1,axiom,
% 5.15/5.45 ! [A2: real,K: real,A: real] :
% 5.15/5.45 ( ( A2
% 5.15/5.45 = ( plus_plus_real @ K @ A ) )
% 5.15/5.45 => ( ( uminus_uminus_real @ A2 )
% 5.15/5.45 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.neg1
% 5.15/5.45 thf(fact_5129_group__cancel_Oneg1,axiom,
% 5.15/5.45 ! [A2: complex,K: complex,A: complex] :
% 5.15/5.45 ( ( A2
% 5.15/5.45 = ( plus_plus_complex @ K @ A ) )
% 5.15/5.45 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.15/5.45 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.neg1
% 5.15/5.45 thf(fact_5130_group__cancel_Oneg1,axiom,
% 5.15/5.45 ! [A2: rat,K: rat,A: rat] :
% 5.15/5.45 ( ( A2
% 5.15/5.45 = ( plus_plus_rat @ K @ A ) )
% 5.15/5.45 => ( ( uminus_uminus_rat @ A2 )
% 5.15/5.45 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.neg1
% 5.15/5.45 thf(fact_5131_group__cancel_Oneg1,axiom,
% 5.15/5.45 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.15/5.45 ( ( A2
% 5.15/5.45 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.15/5.45 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.15/5.45 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.neg1
% 5.15/5.45 thf(fact_5132_add_Oinverse__distrib__swap,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.15/5.45 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_distrib_swap
% 5.15/5.45 thf(fact_5133_add_Oinverse__distrib__swap,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.15/5.45 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_distrib_swap
% 5.15/5.45 thf(fact_5134_add_Oinverse__distrib__swap,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.15/5.45 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_distrib_swap
% 5.15/5.45 thf(fact_5135_add_Oinverse__distrib__swap,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.15/5.45 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_distrib_swap
% 5.15/5.45 thf(fact_5136_add_Oinverse__distrib__swap,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.15/5.45 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_distrib_swap
% 5.15/5.45 thf(fact_5137_is__num__normalize_I8_J,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.15/5.45 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % is_num_normalize(8)
% 5.15/5.45 thf(fact_5138_is__num__normalize_I8_J,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.15/5.45 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % is_num_normalize(8)
% 5.15/5.45 thf(fact_5139_is__num__normalize_I8_J,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.15/5.45 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % is_num_normalize(8)
% 5.15/5.45 thf(fact_5140_is__num__normalize_I8_J,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.15/5.45 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % is_num_normalize(8)
% 5.15/5.45 thf(fact_5141_is__num__normalize_I8_J,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.15/5.45 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % is_num_normalize(8)
% 5.15/5.45 thf(fact_5142_minus__diff__commute,axiom,
% 5.15/5.45 ! [B: int,A: int] :
% 5.15/5.45 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.15/5.45 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_commute
% 5.15/5.45 thf(fact_5143_minus__diff__commute,axiom,
% 5.15/5.45 ! [B: real,A: real] :
% 5.15/5.45 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.15/5.45 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_commute
% 5.15/5.45 thf(fact_5144_minus__diff__commute,axiom,
% 5.15/5.45 ! [B: complex,A: complex] :
% 5.15/5.45 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.15/5.45 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_commute
% 5.15/5.45 thf(fact_5145_minus__diff__commute,axiom,
% 5.15/5.45 ! [B: rat,A: rat] :
% 5.15/5.45 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.15/5.45 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_commute
% 5.15/5.45 thf(fact_5146_minus__diff__commute,axiom,
% 5.15/5.45 ! [B: code_integer,A: code_integer] :
% 5.15/5.45 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.15/5.45 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_commute
% 5.15/5.45 thf(fact_5147_minus__diff__minus,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_minus
% 5.15/5.45 thf(fact_5148_minus__diff__minus,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.15/5.45 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_minus
% 5.15/5.45 thf(fact_5149_minus__diff__minus,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_minus
% 5.15/5.45 thf(fact_5150_minus__diff__minus,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.15/5.45 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_minus
% 5.15/5.45 thf(fact_5151_minus__diff__minus,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_diff_minus
% 5.15/5.45 thf(fact_5152_div__minus__right,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % div_minus_right
% 5.15/5.45 thf(fact_5153_div__minus__right,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.45 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % div_minus_right
% 5.15/5.45 thf(fact_5154_minus__divide__right,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.45 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_right
% 5.15/5.45 thf(fact_5155_minus__divide__right,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.45 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_right
% 5.15/5.45 thf(fact_5156_minus__divide__right,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.15/5.45 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_right
% 5.15/5.45 thf(fact_5157_minus__divide__divide,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.15/5.45 = ( divide_divide_real @ A @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_divide
% 5.15/5.45 thf(fact_5158_minus__divide__divide,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.45 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_divide
% 5.15/5.45 thf(fact_5159_minus__divide__divide,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.15/5.45 = ( divide_divide_rat @ A @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_divide
% 5.15/5.45 thf(fact_5160_minus__divide__left,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.45 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_left
% 5.15/5.45 thf(fact_5161_minus__divide__left,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.45 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_left
% 5.15/5.45 thf(fact_5162_minus__divide__left,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.15/5.45 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_left
% 5.15/5.45 thf(fact_5163_mod__minus__eq,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.15/5.45 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mod_minus_eq
% 5.15/5.45 thf(fact_5164_mod__minus__eq,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.15/5.45 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mod_minus_eq
% 5.15/5.45 thf(fact_5165_mod__minus__cong,axiom,
% 5.15/5.45 ! [A: int,B: int,A4: int] :
% 5.15/5.45 ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 = ( modulo_modulo_int @ A4 @ B ) )
% 5.15/5.45 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mod_minus_cong
% 5.15/5.45 thf(fact_5166_mod__minus__cong,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer,A4: code_integer] :
% 5.15/5.45 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.15/5.45 = ( modulo364778990260209775nteger @ A4 @ B ) )
% 5.15/5.45 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.15/5.45 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mod_minus_cong
% 5.15/5.45 thf(fact_5167_mod__minus__right,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mod_minus_right
% 5.15/5.45 thf(fact_5168_mod__minus__right,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % mod_minus_right
% 5.15/5.45 thf(fact_5169_bot__enat__def,axiom,
% 5.15/5.45 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.15/5.45
% 5.15/5.45 % bot_enat_def
% 5.15/5.45 thf(fact_5170_case__prodE,axiom,
% 5.15/5.45 ! [C: code_integer > $o > $o,P2: produc6271795597528267376eger_o] :
% 5.15/5.45 ( ( produc7828578312038201481er_o_o @ C @ P2 )
% 5.15/5.45 => ~ ! [X3: code_integer,Y3: $o] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( produc6677183202524767010eger_o @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodE
% 5.15/5.45 thf(fact_5171_case__prodE,axiom,
% 5.15/5.45 ! [C: num > num > $o,P2: product_prod_num_num] :
% 5.15/5.45 ( ( produc5703948589228662326_num_o @ C @ P2 )
% 5.15/5.45 => ~ ! [X3: num,Y3: num] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_num_num @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodE
% 5.15/5.45 thf(fact_5172_case__prodE,axiom,
% 5.15/5.45 ! [C: nat > num > $o,P2: product_prod_nat_num] :
% 5.15/5.45 ( ( produc4927758841916487424_num_o @ C @ P2 )
% 5.15/5.45 => ~ ! [X3: nat,Y3: num] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_nat_num @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodE
% 5.15/5.45 thf(fact_5173_case__prodE,axiom,
% 5.15/5.45 ! [C: nat > nat > $o,P2: product_prod_nat_nat] :
% 5.15/5.45 ( ( produc6081775807080527818_nat_o @ C @ P2 )
% 5.15/5.45 => ~ ! [X3: nat,Y3: nat] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodE
% 5.15/5.45 thf(fact_5174_case__prodE,axiom,
% 5.15/5.45 ! [C: int > int > $o,P2: product_prod_int_int] :
% 5.15/5.45 ( ( produc4947309494688390418_int_o @ C @ P2 )
% 5.15/5.45 => ~ ! [X3: int,Y3: int] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodE
% 5.15/5.45 thf(fact_5175_case__prodD,axiom,
% 5.15/5.45 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.15/5.45 ( ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) )
% 5.15/5.45 => ( F @ A @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodD
% 5.15/5.45 thf(fact_5176_case__prodD,axiom,
% 5.15/5.45 ! [F: num > num > $o,A: num,B: num] :
% 5.15/5.45 ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 5.15/5.45 => ( F @ A @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodD
% 5.15/5.45 thf(fact_5177_case__prodD,axiom,
% 5.15/5.45 ! [F: nat > num > $o,A: nat,B: num] :
% 5.15/5.45 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 5.15/5.45 => ( F @ A @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodD
% 5.15/5.45 thf(fact_5178_case__prodD,axiom,
% 5.15/5.45 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.15/5.45 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.15/5.45 => ( F @ A @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodD
% 5.15/5.45 thf(fact_5179_case__prodD,axiom,
% 5.15/5.45 ! [F: int > int > $o,A: int,B: int] :
% 5.15/5.45 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.15/5.45 => ( F @ A @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodD
% 5.15/5.45 thf(fact_5180_case__prodE_H,axiom,
% 5.15/5.45 ! [C: nat > nat > product_prod_nat_nat > $o,P2: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.15/5.45 ( ( produc8739625826339149834_nat_o @ C @ P2 @ Z )
% 5.15/5.45 => ~ ! [X3: nat,Y3: nat] :
% 5.15/5.45 ( ( P2
% 5.15/5.45 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.15/5.45 => ~ ( C @ X3 @ Y3 @ Z ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodE'
% 5.15/5.45 thf(fact_5181_case__prodD_H,axiom,
% 5.15/5.45 ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.15/5.45 ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.15/5.45 => ( R @ A @ B @ C ) ) ).
% 5.15/5.45
% 5.15/5.45 % case_prodD'
% 5.15/5.45 thf(fact_5182_zero__less__eq__of__bool,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_less_eq_of_bool
% 5.15/5.45 thf(fact_5183_zero__less__eq__of__bool,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_less_eq_of_bool
% 5.15/5.45 thf(fact_5184_zero__less__eq__of__bool,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_less_eq_of_bool
% 5.15/5.45 thf(fact_5185_zero__less__eq__of__bool,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_less_eq_of_bool
% 5.15/5.45 thf(fact_5186_zero__less__eq__of__bool,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_less_eq_of_bool
% 5.15/5.45 thf(fact_5187_of__bool__less__eq__one,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_less_eq_one
% 5.15/5.45 thf(fact_5188_of__bool__less__eq__one,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_less_eq_one
% 5.15/5.45 thf(fact_5189_of__bool__less__eq__one,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_less_eq_one
% 5.15/5.45 thf(fact_5190_of__bool__less__eq__one,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_less_eq_one
% 5.15/5.45 thf(fact_5191_of__bool__less__eq__one,axiom,
% 5.15/5.45 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_less_eq_one
% 5.15/5.45 thf(fact_5192_of__bool__def,axiom,
% 5.15/5.45 ( zero_n1201886186963655149omplex
% 5.15/5.45 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_def
% 5.15/5.45 thf(fact_5193_of__bool__def,axiom,
% 5.15/5.45 ( zero_n3304061248610475627l_real
% 5.15/5.45 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_def
% 5.15/5.45 thf(fact_5194_of__bool__def,axiom,
% 5.15/5.45 ( zero_n2052037380579107095ol_rat
% 5.15/5.45 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_def
% 5.15/5.45 thf(fact_5195_of__bool__def,axiom,
% 5.15/5.45 ( zero_n2687167440665602831ol_nat
% 5.15/5.45 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_def
% 5.15/5.45 thf(fact_5196_of__bool__def,axiom,
% 5.15/5.45 ( zero_n2684676970156552555ol_int
% 5.15/5.45 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_def
% 5.15/5.45 thf(fact_5197_of__bool__def,axiom,
% 5.15/5.45 ( zero_n356916108424825756nteger
% 5.15/5.45 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_def
% 5.15/5.45 thf(fact_5198_split__of__bool,axiom,
% 5.15/5.45 ! [P: complex > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.15/5.45 = ( ( P2
% 5.15/5.45 => ( P @ one_one_complex ) )
% 5.15/5.45 & ( ~ P2
% 5.15/5.45 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool
% 5.15/5.45 thf(fact_5199_split__of__bool,axiom,
% 5.15/5.45 ! [P: real > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.15/5.45 = ( ( P2
% 5.15/5.45 => ( P @ one_one_real ) )
% 5.15/5.45 & ( ~ P2
% 5.15/5.45 => ( P @ zero_zero_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool
% 5.15/5.45 thf(fact_5200_split__of__bool,axiom,
% 5.15/5.45 ! [P: rat > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.15/5.45 = ( ( P2
% 5.15/5.45 => ( P @ one_one_rat ) )
% 5.15/5.45 & ( ~ P2
% 5.15/5.45 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool
% 5.15/5.45 thf(fact_5201_split__of__bool,axiom,
% 5.15/5.45 ! [P: nat > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.15/5.45 = ( ( P2
% 5.15/5.45 => ( P @ one_one_nat ) )
% 5.15/5.45 & ( ~ P2
% 5.15/5.45 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool
% 5.15/5.45 thf(fact_5202_split__of__bool,axiom,
% 5.15/5.45 ! [P: int > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.15/5.45 = ( ( P2
% 5.15/5.45 => ( P @ one_one_int ) )
% 5.15/5.45 & ( ~ P2
% 5.15/5.45 => ( P @ zero_zero_int ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool
% 5.15/5.45 thf(fact_5203_split__of__bool,axiom,
% 5.15/5.45 ! [P: code_integer > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.15/5.45 = ( ( P2
% 5.15/5.45 => ( P @ one_one_Code_integer ) )
% 5.15/5.45 & ( ~ P2
% 5.15/5.45 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool
% 5.15/5.45 thf(fact_5204_split__of__bool__asm,axiom,
% 5.15/5.45 ! [P: complex > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.15/5.45 = ( ~ ( ( P2
% 5.15/5.45 & ~ ( P @ one_one_complex ) )
% 5.15/5.45 | ( ~ P2
% 5.15/5.45 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool_asm
% 5.15/5.45 thf(fact_5205_split__of__bool__asm,axiom,
% 5.15/5.45 ! [P: real > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.15/5.45 = ( ~ ( ( P2
% 5.15/5.45 & ~ ( P @ one_one_real ) )
% 5.15/5.45 | ( ~ P2
% 5.15/5.45 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool_asm
% 5.15/5.45 thf(fact_5206_split__of__bool__asm,axiom,
% 5.15/5.45 ! [P: rat > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.15/5.45 = ( ~ ( ( P2
% 5.15/5.45 & ~ ( P @ one_one_rat ) )
% 5.15/5.45 | ( ~ P2
% 5.15/5.45 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool_asm
% 5.15/5.45 thf(fact_5207_split__of__bool__asm,axiom,
% 5.15/5.45 ! [P: nat > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.15/5.45 = ( ~ ( ( P2
% 5.15/5.45 & ~ ( P @ one_one_nat ) )
% 5.15/5.45 | ( ~ P2
% 5.15/5.45 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool_asm
% 5.15/5.45 thf(fact_5208_split__of__bool__asm,axiom,
% 5.15/5.45 ! [P: int > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.15/5.45 = ( ~ ( ( P2
% 5.15/5.45 & ~ ( P @ one_one_int ) )
% 5.15/5.45 | ( ~ P2
% 5.15/5.45 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool_asm
% 5.15/5.45 thf(fact_5209_split__of__bool__asm,axiom,
% 5.15/5.45 ! [P: code_integer > $o,P2: $o] :
% 5.15/5.45 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.15/5.45 = ( ~ ( ( P2
% 5.15/5.45 & ~ ( P @ one_one_Code_integer ) )
% 5.15/5.45 | ( ~ P2
% 5.15/5.45 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % split_of_bool_asm
% 5.15/5.45 thf(fact_5210_not__numeral__le__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_le_neg_numeral
% 5.15/5.45 thf(fact_5211_not__numeral__le__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_le_neg_numeral
% 5.15/5.45 thf(fact_5212_not__numeral__le__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_le_neg_numeral
% 5.15/5.45 thf(fact_5213_not__numeral__le__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_le_neg_numeral
% 5.15/5.45 thf(fact_5214_neg__numeral__le__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_numeral
% 5.15/5.45 thf(fact_5215_neg__numeral__le__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_numeral
% 5.15/5.45 thf(fact_5216_neg__numeral__le__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_numeral
% 5.15/5.45 thf(fact_5217_neg__numeral__le__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_numeral
% 5.15/5.45 thf(fact_5218_zero__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( zero_zero_int
% 5.15/5.45 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_numeral
% 5.15/5.45 thf(fact_5219_zero__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( zero_zero_real
% 5.15/5.45 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_numeral
% 5.15/5.45 thf(fact_5220_zero__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( zero_zero_complex
% 5.15/5.45 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_numeral
% 5.15/5.45 thf(fact_5221_zero__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( zero_zero_rat
% 5.15/5.45 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_numeral
% 5.15/5.45 thf(fact_5222_zero__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( zero_z3403309356797280102nteger
% 5.15/5.45 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_numeral
% 5.15/5.45 thf(fact_5223_neg__numeral__less__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_numeral
% 5.15/5.45 thf(fact_5224_neg__numeral__less__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_numeral
% 5.15/5.45 thf(fact_5225_neg__numeral__less__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_numeral
% 5.15/5.45 thf(fact_5226_neg__numeral__less__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_numeral
% 5.15/5.45 thf(fact_5227_not__numeral__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_less_neg_numeral
% 5.15/5.45 thf(fact_5228_not__numeral__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_less_neg_numeral
% 5.15/5.45 thf(fact_5229_not__numeral__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_less_neg_numeral
% 5.15/5.45 thf(fact_5230_not__numeral__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num,N2: num] :
% 5.15/5.45 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_less_neg_numeral
% 5.15/5.45 thf(fact_5231_le__minus__one__simps_I2_J,axiom,
% 5.15/5.45 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(2)
% 5.15/5.45 thf(fact_5232_le__minus__one__simps_I2_J,axiom,
% 5.15/5.45 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(2)
% 5.15/5.45 thf(fact_5233_le__minus__one__simps_I2_J,axiom,
% 5.15/5.45 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(2)
% 5.15/5.45 thf(fact_5234_le__minus__one__simps_I2_J,axiom,
% 5.15/5.45 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(2)
% 5.15/5.45 thf(fact_5235_le__minus__one__simps_I4_J,axiom,
% 5.15/5.45 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(4)
% 5.15/5.45 thf(fact_5236_le__minus__one__simps_I4_J,axiom,
% 5.15/5.45 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(4)
% 5.15/5.45 thf(fact_5237_le__minus__one__simps_I4_J,axiom,
% 5.15/5.45 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(4)
% 5.15/5.45 thf(fact_5238_le__minus__one__simps_I4_J,axiom,
% 5.15/5.45 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(4)
% 5.15/5.45 thf(fact_5239_zero__neq__neg__one,axiom,
% 5.15/5.45 ( zero_zero_int
% 5.15/5.45 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_one
% 5.15/5.45 thf(fact_5240_zero__neq__neg__one,axiom,
% 5.15/5.45 ( zero_zero_real
% 5.15/5.45 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_one
% 5.15/5.45 thf(fact_5241_zero__neq__neg__one,axiom,
% 5.15/5.45 ( zero_zero_complex
% 5.15/5.45 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_one
% 5.15/5.45 thf(fact_5242_zero__neq__neg__one,axiom,
% 5.15/5.45 ( zero_zero_rat
% 5.15/5.45 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_one
% 5.15/5.45 thf(fact_5243_zero__neq__neg__one,axiom,
% 5.15/5.45 ( zero_z3403309356797280102nteger
% 5.15/5.45 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % zero_neq_neg_one
% 5.15/5.45 thf(fact_5244_add__eq__0__iff,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ( plus_plus_int @ A @ B )
% 5.15/5.45 = zero_zero_int )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_eq_0_iff
% 5.15/5.45 thf(fact_5245_add__eq__0__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ( plus_plus_real @ A @ B )
% 5.15/5.45 = zero_zero_real )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_eq_0_iff
% 5.15/5.45 thf(fact_5246_add__eq__0__iff,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( ( plus_plus_complex @ A @ B )
% 5.15/5.45 = zero_zero_complex )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_eq_0_iff
% 5.15/5.45 thf(fact_5247_add__eq__0__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ( plus_plus_rat @ A @ B )
% 5.15/5.45 = zero_zero_rat )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_eq_0_iff
% 5.15/5.45 thf(fact_5248_add__eq__0__iff,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.15/5.45 = zero_z3403309356797280102nteger )
% 5.15/5.45 = ( B
% 5.15/5.45 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_eq_0_iff
% 5.15/5.45 thf(fact_5249_ab__group__add__class_Oab__left__minus,axiom,
% 5.15/5.45 ! [A: int] :
% 5.15/5.45 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.15/5.45 = zero_zero_int ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_left_minus
% 5.15/5.45 thf(fact_5250_ab__group__add__class_Oab__left__minus,axiom,
% 5.15/5.45 ! [A: real] :
% 5.15/5.45 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.15/5.45 = zero_zero_real ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_left_minus
% 5.15/5.45 thf(fact_5251_ab__group__add__class_Oab__left__minus,axiom,
% 5.15/5.45 ! [A: complex] :
% 5.15/5.45 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.15/5.45 = zero_zero_complex ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_left_minus
% 5.15/5.45 thf(fact_5252_ab__group__add__class_Oab__left__minus,axiom,
% 5.15/5.45 ! [A: rat] :
% 5.15/5.45 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.15/5.45 = zero_zero_rat ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_left_minus
% 5.15/5.45 thf(fact_5253_ab__group__add__class_Oab__left__minus,axiom,
% 5.15/5.45 ! [A: code_integer] :
% 5.15/5.45 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.15/5.45 = zero_z3403309356797280102nteger ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_left_minus
% 5.15/5.45 thf(fact_5254_add_Oinverse__unique,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ( plus_plus_int @ A @ B )
% 5.15/5.45 = zero_zero_int )
% 5.15/5.45 => ( ( uminus_uminus_int @ A )
% 5.15/5.45 = B ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_unique
% 5.15/5.45 thf(fact_5255_add_Oinverse__unique,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ( plus_plus_real @ A @ B )
% 5.15/5.45 = zero_zero_real )
% 5.15/5.45 => ( ( uminus_uminus_real @ A )
% 5.15/5.45 = B ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_unique
% 5.15/5.45 thf(fact_5256_add_Oinverse__unique,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( ( plus_plus_complex @ A @ B )
% 5.15/5.45 = zero_zero_complex )
% 5.15/5.45 => ( ( uminus1482373934393186551omplex @ A )
% 5.15/5.45 = B ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_unique
% 5.15/5.45 thf(fact_5257_add_Oinverse__unique,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ( plus_plus_rat @ A @ B )
% 5.15/5.45 = zero_zero_rat )
% 5.15/5.45 => ( ( uminus_uminus_rat @ A )
% 5.15/5.45 = B ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_unique
% 5.15/5.45 thf(fact_5258_add_Oinverse__unique,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.15/5.45 = zero_z3403309356797280102nteger )
% 5.15/5.45 => ( ( uminus1351360451143612070nteger @ A )
% 5.15/5.45 = B ) ) ).
% 5.15/5.45
% 5.15/5.45 % add.inverse_unique
% 5.15/5.45 thf(fact_5259_eq__neg__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( ( plus_plus_int @ A @ B )
% 5.15/5.45 = zero_zero_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_neg_iff_add_eq_0
% 5.15/5.45 thf(fact_5260_eq__neg__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus_uminus_real @ B ) )
% 5.15/5.45 = ( ( plus_plus_real @ A @ B )
% 5.15/5.45 = zero_zero_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_neg_iff_add_eq_0
% 5.15/5.45 thf(fact_5261_eq__neg__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.45 = ( ( plus_plus_complex @ A @ B )
% 5.15/5.45 = zero_zero_complex ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_neg_iff_add_eq_0
% 5.15/5.45 thf(fact_5262_eq__neg__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus_uminus_rat @ B ) )
% 5.15/5.45 = ( ( plus_plus_rat @ A @ B )
% 5.15/5.45 = zero_zero_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_neg_iff_add_eq_0
% 5.15/5.45 thf(fact_5263_eq__neg__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.45 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.15/5.45 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_neg_iff_add_eq_0
% 5.15/5.45 thf(fact_5264_neg__eq__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ( uminus_uminus_int @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( plus_plus_int @ A @ B )
% 5.15/5.45 = zero_zero_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_eq_iff_add_eq_0
% 5.15/5.45 thf(fact_5265_neg__eq__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ( uminus_uminus_real @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( plus_plus_real @ A @ B )
% 5.15/5.45 = zero_zero_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_eq_iff_add_eq_0
% 5.15/5.45 thf(fact_5266_neg__eq__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( ( uminus1482373934393186551omplex @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( plus_plus_complex @ A @ B )
% 5.15/5.45 = zero_zero_complex ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_eq_iff_add_eq_0
% 5.15/5.45 thf(fact_5267_neg__eq__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ( uminus_uminus_rat @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( plus_plus_rat @ A @ B )
% 5.15/5.45 = zero_zero_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_eq_iff_add_eq_0
% 5.15/5.45 thf(fact_5268_neg__eq__iff__add__eq__0,axiom,
% 5.15/5.45 ! [A: code_integer,B: code_integer] :
% 5.15/5.45 ( ( ( uminus1351360451143612070nteger @ A )
% 5.15/5.45 = B )
% 5.15/5.45 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.15/5.45 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_eq_iff_add_eq_0
% 5.15/5.45 thf(fact_5269_less__minus__one__simps_I4_J,axiom,
% 5.15/5.45 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(4)
% 5.15/5.45 thf(fact_5270_less__minus__one__simps_I4_J,axiom,
% 5.15/5.45 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(4)
% 5.15/5.45 thf(fact_5271_less__minus__one__simps_I4_J,axiom,
% 5.15/5.45 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(4)
% 5.15/5.45 thf(fact_5272_less__minus__one__simps_I4_J,axiom,
% 5.15/5.45 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(4)
% 5.15/5.45 thf(fact_5273_less__minus__one__simps_I2_J,axiom,
% 5.15/5.45 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(2)
% 5.15/5.45 thf(fact_5274_less__minus__one__simps_I2_J,axiom,
% 5.15/5.45 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(2)
% 5.15/5.45 thf(fact_5275_less__minus__one__simps_I2_J,axiom,
% 5.15/5.45 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(2)
% 5.15/5.45 thf(fact_5276_less__minus__one__simps_I2_J,axiom,
% 5.15/5.45 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(2)
% 5.15/5.45 thf(fact_5277_numeral__times__minus__swap,axiom,
% 5.15/5.45 ! [W: num,X: int] :
% 5.15/5.45 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 5.15/5.45 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_times_minus_swap
% 5.15/5.45 thf(fact_5278_numeral__times__minus__swap,axiom,
% 5.15/5.45 ! [W: num,X: real] :
% 5.15/5.45 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 5.15/5.45 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_times_minus_swap
% 5.15/5.45 thf(fact_5279_numeral__times__minus__swap,axiom,
% 5.15/5.45 ! [W: num,X: complex] :
% 5.15/5.45 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.15/5.45 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_times_minus_swap
% 5.15/5.45 thf(fact_5280_numeral__times__minus__swap,axiom,
% 5.15/5.45 ! [W: num,X: rat] :
% 5.15/5.45 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 5.15/5.45 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_times_minus_swap
% 5.15/5.45 thf(fact_5281_numeral__times__minus__swap,axiom,
% 5.15/5.45 ! [W: num,X: code_integer] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.15/5.45 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_times_minus_swap
% 5.15/5.45 thf(fact_5282_nonzero__minus__divide__right,axiom,
% 5.15/5.45 ! [B: real,A: real] :
% 5.15/5.45 ( ( B != zero_zero_real )
% 5.15/5.45 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.45 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_minus_divide_right
% 5.15/5.45 thf(fact_5283_nonzero__minus__divide__right,axiom,
% 5.15/5.45 ! [B: complex,A: complex] :
% 5.15/5.45 ( ( B != zero_zero_complex )
% 5.15/5.45 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.45 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_minus_divide_right
% 5.15/5.45 thf(fact_5284_nonzero__minus__divide__right,axiom,
% 5.15/5.45 ! [B: rat,A: rat] :
% 5.15/5.45 ( ( B != zero_zero_rat )
% 5.15/5.45 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.15/5.45 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_minus_divide_right
% 5.15/5.45 thf(fact_5285_nonzero__minus__divide__divide,axiom,
% 5.15/5.45 ! [B: real,A: real] :
% 5.15/5.45 ( ( B != zero_zero_real )
% 5.15/5.45 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.15/5.45 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_minus_divide_divide
% 5.15/5.45 thf(fact_5286_nonzero__minus__divide__divide,axiom,
% 5.15/5.45 ! [B: complex,A: complex] :
% 5.15/5.45 ( ( B != zero_zero_complex )
% 5.15/5.45 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.45 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_minus_divide_divide
% 5.15/5.45 thf(fact_5287_nonzero__minus__divide__divide,axiom,
% 5.15/5.45 ! [B: rat,A: rat] :
% 5.15/5.45 ( ( B != zero_zero_rat )
% 5.15/5.45 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.15/5.45 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_minus_divide_divide
% 5.15/5.45 thf(fact_5288_numeral__neq__neg__one,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( numeral_numeral_int @ N2 )
% 5.15/5.45 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_one
% 5.15/5.45 thf(fact_5289_numeral__neq__neg__one,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( numeral_numeral_real @ N2 )
% 5.15/5.45 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_one
% 5.15/5.45 thf(fact_5290_numeral__neq__neg__one,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( numera6690914467698888265omplex @ N2 )
% 5.15/5.45 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_one
% 5.15/5.45 thf(fact_5291_numeral__neq__neg__one,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( numeral_numeral_rat @ N2 )
% 5.15/5.45 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_one
% 5.15/5.45 thf(fact_5292_numeral__neq__neg__one,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( ( numera6620942414471956472nteger @ N2 )
% 5.15/5.45 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_neq_neg_one
% 5.15/5.45 thf(fact_5293_one__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( one_one_int
% 5.15/5.45 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_numeral
% 5.15/5.45 thf(fact_5294_one__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( one_one_real
% 5.15/5.45 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_numeral
% 5.15/5.45 thf(fact_5295_one__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( one_one_complex
% 5.15/5.45 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_numeral
% 5.15/5.45 thf(fact_5296_one__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( one_one_rat
% 5.15/5.45 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_numeral
% 5.15/5.45 thf(fact_5297_one__neq__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ( one_one_Code_integer
% 5.15/5.45 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % one_neq_neg_numeral
% 5.15/5.45 thf(fact_5298_square__eq__1__iff,axiom,
% 5.15/5.45 ! [X: int] :
% 5.15/5.45 ( ( ( times_times_int @ X @ X )
% 5.15/5.45 = one_one_int )
% 5.15/5.45 = ( ( X = one_one_int )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_1_iff
% 5.15/5.45 thf(fact_5299_square__eq__1__iff,axiom,
% 5.15/5.45 ! [X: real] :
% 5.15/5.45 ( ( ( times_times_real @ X @ X )
% 5.15/5.45 = one_one_real )
% 5.15/5.45 = ( ( X = one_one_real )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_1_iff
% 5.15/5.45 thf(fact_5300_square__eq__1__iff,axiom,
% 5.15/5.45 ! [X: complex] :
% 5.15/5.45 ( ( ( times_times_complex @ X @ X )
% 5.15/5.45 = one_one_complex )
% 5.15/5.45 = ( ( X = one_one_complex )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_1_iff
% 5.15/5.45 thf(fact_5301_square__eq__1__iff,axiom,
% 5.15/5.45 ! [X: rat] :
% 5.15/5.45 ( ( ( times_times_rat @ X @ X )
% 5.15/5.45 = one_one_rat )
% 5.15/5.45 = ( ( X = one_one_rat )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_1_iff
% 5.15/5.45 thf(fact_5302_square__eq__1__iff,axiom,
% 5.15/5.45 ! [X: code_integer] :
% 5.15/5.45 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.15/5.45 = one_one_Code_integer )
% 5.15/5.45 = ( ( X = one_one_Code_integer )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % square_eq_1_iff
% 5.15/5.45 thf(fact_5303_group__cancel_Osub2,axiom,
% 5.15/5.45 ! [B3: int,K: int,B: int,A: int] :
% 5.15/5.45 ( ( B3
% 5.15/5.45 = ( plus_plus_int @ K @ B ) )
% 5.15/5.45 => ( ( minus_minus_int @ A @ B3 )
% 5.15/5.45 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.sub2
% 5.15/5.45 thf(fact_5304_group__cancel_Osub2,axiom,
% 5.15/5.45 ! [B3: real,K: real,B: real,A: real] :
% 5.15/5.45 ( ( B3
% 5.15/5.45 = ( plus_plus_real @ K @ B ) )
% 5.15/5.45 => ( ( minus_minus_real @ A @ B3 )
% 5.15/5.45 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.sub2
% 5.15/5.45 thf(fact_5305_group__cancel_Osub2,axiom,
% 5.15/5.45 ! [B3: complex,K: complex,B: complex,A: complex] :
% 5.15/5.45 ( ( B3
% 5.15/5.45 = ( plus_plus_complex @ K @ B ) )
% 5.15/5.45 => ( ( minus_minus_complex @ A @ B3 )
% 5.15/5.45 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.sub2
% 5.15/5.45 thf(fact_5306_group__cancel_Osub2,axiom,
% 5.15/5.45 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.15/5.45 ( ( B3
% 5.15/5.45 = ( plus_plus_rat @ K @ B ) )
% 5.15/5.45 => ( ( minus_minus_rat @ A @ B3 )
% 5.15/5.45 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.sub2
% 5.15/5.45 thf(fact_5307_group__cancel_Osub2,axiom,
% 5.15/5.45 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.15/5.45 ( ( B3
% 5.15/5.45 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.15/5.45 => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 5.15/5.45 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % group_cancel.sub2
% 5.15/5.45 thf(fact_5308_diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_minus_int
% 5.15/5.45 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_conv_add_uminus
% 5.15/5.45 thf(fact_5309_diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_minus_real
% 5.15/5.45 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_conv_add_uminus
% 5.15/5.45 thf(fact_5310_diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_minus_complex
% 5.15/5.45 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_conv_add_uminus
% 5.15/5.45 thf(fact_5311_diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_minus_rat
% 5.15/5.45 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_conv_add_uminus
% 5.15/5.45 thf(fact_5312_diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_8373710615458151222nteger
% 5.15/5.45 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % diff_conv_add_uminus
% 5.15/5.45 thf(fact_5313_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_minus_int
% 5.15/5.45 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.15/5.45 thf(fact_5314_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_minus_real
% 5.15/5.45 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.15/5.45 thf(fact_5315_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_minus_complex
% 5.15/5.45 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.15/5.45 thf(fact_5316_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_minus_rat
% 5.15/5.45 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.15/5.45 thf(fact_5317_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.15/5.45 ( minus_8373710615458151222nteger
% 5.15/5.45 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.15/5.45 thf(fact_5318_replicate__eqI,axiom,
% 5.15/5.45 ! [Xs2: list_complex,N2: nat,X: complex] :
% 5.15/5.45 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.15/5.45 = N2 )
% 5.15/5.45 => ( ! [Y3: complex] :
% 5.15/5.45 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 5.15/5.45 => ( Y3 = X ) )
% 5.15/5.45 => ( Xs2
% 5.15/5.45 = ( replicate_complex @ N2 @ X ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_eqI
% 5.15/5.45 thf(fact_5319_replicate__eqI,axiom,
% 5.15/5.45 ! [Xs2: list_real,N2: nat,X: real] :
% 5.15/5.45 ( ( ( size_size_list_real @ Xs2 )
% 5.15/5.45 = N2 )
% 5.15/5.45 => ( ! [Y3: real] :
% 5.15/5.45 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 5.15/5.45 => ( Y3 = X ) )
% 5.15/5.45 => ( Xs2
% 5.15/5.45 = ( replicate_real @ N2 @ X ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_eqI
% 5.15/5.45 thf(fact_5320_replicate__eqI,axiom,
% 5.15/5.45 ! [Xs2: list_set_nat,N2: nat,X: set_nat] :
% 5.15/5.45 ( ( ( size_s3254054031482475050et_nat @ Xs2 )
% 5.15/5.45 = N2 )
% 5.15/5.45 => ( ! [Y3: set_nat] :
% 5.15/5.45 ( ( member_set_nat @ Y3 @ ( set_set_nat2 @ Xs2 ) )
% 5.15/5.45 => ( Y3 = X ) )
% 5.15/5.45 => ( Xs2
% 5.15/5.45 = ( replicate_set_nat @ N2 @ X ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_eqI
% 5.15/5.45 thf(fact_5321_replicate__eqI,axiom,
% 5.15/5.45 ! [Xs2: list_nat,N2: nat,X: nat] :
% 5.15/5.45 ( ( ( size_size_list_nat @ Xs2 )
% 5.15/5.45 = N2 )
% 5.15/5.45 => ( ! [Y3: nat] :
% 5.15/5.45 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 5.15/5.45 => ( Y3 = X ) )
% 5.15/5.45 => ( Xs2
% 5.15/5.45 = ( replicate_nat @ N2 @ X ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_eqI
% 5.15/5.45 thf(fact_5322_replicate__eqI,axiom,
% 5.15/5.45 ! [Xs2: list_VEBT_VEBT,N2: nat,X: vEBT_VEBT] :
% 5.15/5.45 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.15/5.45 = N2 )
% 5.15/5.45 => ( ! [Y3: vEBT_VEBT] :
% 5.15/5.45 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.45 => ( Y3 = X ) )
% 5.15/5.45 => ( Xs2
% 5.15/5.45 = ( replicate_VEBT_VEBT @ N2 @ X ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_eqI
% 5.15/5.45 thf(fact_5323_replicate__eqI,axiom,
% 5.15/5.45 ! [Xs2: list_o,N2: nat,X: $o] :
% 5.15/5.45 ( ( ( size_size_list_o @ Xs2 )
% 5.15/5.45 = N2 )
% 5.15/5.45 => ( ! [Y3: $o] :
% 5.15/5.45 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 5.15/5.45 => ( Y3 = X ) )
% 5.15/5.45 => ( Xs2
% 5.15/5.45 = ( replicate_o @ N2 @ X ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_eqI
% 5.15/5.45 thf(fact_5324_replicate__eqI,axiom,
% 5.15/5.45 ! [Xs2: list_int,N2: nat,X: int] :
% 5.15/5.45 ( ( ( size_size_list_int @ Xs2 )
% 5.15/5.45 = N2 )
% 5.15/5.45 => ( ! [Y3: int] :
% 5.15/5.45 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 5.15/5.45 => ( Y3 = X ) )
% 5.15/5.45 => ( Xs2
% 5.15/5.45 = ( replicate_int @ N2 @ X ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_eqI
% 5.15/5.45 thf(fact_5325_replicate__length__same,axiom,
% 5.15/5.45 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.15/5.45 ( ! [X3: vEBT_VEBT] :
% 5.15/5.45 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.15/5.45 => ( X3 = X ) )
% 5.15/5.45 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 5.15/5.45 = Xs2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_length_same
% 5.15/5.45 thf(fact_5326_replicate__length__same,axiom,
% 5.15/5.45 ! [Xs2: list_o,X: $o] :
% 5.15/5.45 ( ! [X3: $o] :
% 5.15/5.45 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.15/5.45 => ( X3 = X ) )
% 5.15/5.45 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 5.15/5.45 = Xs2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_length_same
% 5.15/5.45 thf(fact_5327_replicate__length__same,axiom,
% 5.15/5.45 ! [Xs2: list_int,X: int] :
% 5.15/5.45 ( ! [X3: int] :
% 5.15/5.45 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.15/5.45 => ( X3 = X ) )
% 5.15/5.45 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 5.15/5.45 = Xs2 ) ) ).
% 5.15/5.45
% 5.15/5.45 % replicate_length_same
% 5.15/5.45 thf(fact_5328_dvd__neg__div,axiom,
% 5.15/5.45 ! [B: int,A: int] :
% 5.15/5.45 ( ( dvd_dvd_int @ B @ A )
% 5.15/5.45 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_neg_div
% 5.15/5.45 thf(fact_5329_dvd__neg__div,axiom,
% 5.15/5.45 ! [B: real,A: real] :
% 5.15/5.45 ( ( dvd_dvd_real @ B @ A )
% 5.15/5.45 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.15/5.45 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_neg_div
% 5.15/5.45 thf(fact_5330_dvd__neg__div,axiom,
% 5.15/5.45 ! [B: complex,A: complex] :
% 5.15/5.45 ( ( dvd_dvd_complex @ B @ A )
% 5.15/5.45 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_neg_div
% 5.15/5.45 thf(fact_5331_dvd__neg__div,axiom,
% 5.15/5.45 ! [B: rat,A: rat] :
% 5.15/5.45 ( ( dvd_dvd_rat @ B @ A )
% 5.15/5.45 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.15/5.45 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_neg_div
% 5.15/5.45 thf(fact_5332_dvd__neg__div,axiom,
% 5.15/5.45 ! [B: code_integer,A: code_integer] :
% 5.15/5.45 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.45 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_neg_div
% 5.15/5.45 thf(fact_5333_dvd__div__neg,axiom,
% 5.15/5.45 ! [B: int,A: int] :
% 5.15/5.45 ( ( dvd_dvd_int @ B @ A )
% 5.15/5.45 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_div_neg
% 5.15/5.45 thf(fact_5334_dvd__div__neg,axiom,
% 5.15/5.45 ! [B: real,A: real] :
% 5.15/5.45 ( ( dvd_dvd_real @ B @ A )
% 5.15/5.45 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.15/5.45 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_div_neg
% 5.15/5.45 thf(fact_5335_dvd__div__neg,axiom,
% 5.15/5.45 ! [B: complex,A: complex] :
% 5.15/5.45 ( ( dvd_dvd_complex @ B @ A )
% 5.15/5.45 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_div_neg
% 5.15/5.45 thf(fact_5336_dvd__div__neg,axiom,
% 5.15/5.45 ! [B: rat,A: rat] :
% 5.15/5.45 ( ( dvd_dvd_rat @ B @ A )
% 5.15/5.45 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.15/5.45 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_div_neg
% 5.15/5.45 thf(fact_5337_dvd__div__neg,axiom,
% 5.15/5.45 ! [B: code_integer,A: code_integer] :
% 5.15/5.45 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.15/5.45 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % dvd_div_neg
% 5.15/5.45 thf(fact_5338_real__minus__mult__self__le,axiom,
% 5.15/5.45 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.15/5.45
% 5.15/5.45 % real_minus_mult_self_le
% 5.15/5.45 thf(fact_5339_pos__zmult__eq__1__iff__lemma,axiom,
% 5.15/5.45 ! [M: int,N2: int] :
% 5.15/5.45 ( ( ( times_times_int @ M @ N2 )
% 5.15/5.45 = one_one_int )
% 5.15/5.45 => ( ( M = one_one_int )
% 5.15/5.45 | ( M
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_zmult_eq_1_iff_lemma
% 5.15/5.45 thf(fact_5340_zmult__eq__1__iff,axiom,
% 5.15/5.45 ! [M: int,N2: int] :
% 5.15/5.45 ( ( ( times_times_int @ M @ N2 )
% 5.15/5.45 = one_one_int )
% 5.15/5.45 = ( ( ( M = one_one_int )
% 5.15/5.45 & ( N2 = one_one_int ) )
% 5.15/5.45 | ( ( M
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.45 & ( N2
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zmult_eq_1_iff
% 5.15/5.45 thf(fact_5341_numeral__eq__Suc,axiom,
% 5.15/5.45 ( numeral_numeral_nat
% 5.15/5.45 = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % numeral_eq_Suc
% 5.15/5.45 thf(fact_5342_zmod__zminus1__not__zero,axiom,
% 5.15/5.45 ! [K: int,L: int] :
% 5.15/5.45 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.15/5.45 != zero_zero_int )
% 5.15/5.45 => ( ( modulo_modulo_int @ K @ L )
% 5.15/5.45 != zero_zero_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % zmod_zminus1_not_zero
% 5.15/5.45 thf(fact_5343_zmod__zminus2__not__zero,axiom,
% 5.15/5.45 ! [K: int,L: int] :
% 5.15/5.45 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 5.15/5.45 != zero_zero_int )
% 5.15/5.45 => ( ( modulo_modulo_int @ K @ L )
% 5.15/5.45 != zero_zero_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % zmod_zminus2_not_zero
% 5.15/5.45 thf(fact_5344_minus__real__def,axiom,
% 5.15/5.45 ( minus_minus_real
% 5.15/5.45 = ( ^ [X2: real,Y2: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_real_def
% 5.15/5.45 thf(fact_5345_not__zero__le__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_zero_le_neg_numeral
% 5.15/5.45 thf(fact_5346_not__zero__le__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_zero_le_neg_numeral
% 5.15/5.45 thf(fact_5347_not__zero__le__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_zero_le_neg_numeral
% 5.15/5.45 thf(fact_5348_not__zero__le__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_zero_le_neg_numeral
% 5.15/5.45 thf(fact_5349_neg__numeral__le__zero,axiom,
% 5.15/5.45 ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_zero
% 5.15/5.45 thf(fact_5350_neg__numeral__le__zero,axiom,
% 5.15/5.45 ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_zero
% 5.15/5.45 thf(fact_5351_neg__numeral__le__zero,axiom,
% 5.15/5.45 ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_zero
% 5.15/5.45 thf(fact_5352_neg__numeral__le__zero,axiom,
% 5.15/5.45 ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_zero
% 5.15/5.45 thf(fact_5353_neg__numeral__less__zero,axiom,
% 5.15/5.45 ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_zero
% 5.15/5.45 thf(fact_5354_neg__numeral__less__zero,axiom,
% 5.15/5.45 ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_zero
% 5.15/5.45 thf(fact_5355_neg__numeral__less__zero,axiom,
% 5.15/5.45 ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_zero
% 5.15/5.45 thf(fact_5356_neg__numeral__less__zero,axiom,
% 5.15/5.45 ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_zero
% 5.15/5.45 thf(fact_5357_not__zero__less__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_zero_less_neg_numeral
% 5.15/5.45 thf(fact_5358_not__zero__less__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_zero_less_neg_numeral
% 5.15/5.45 thf(fact_5359_not__zero__less__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_zero_less_neg_numeral
% 5.15/5.45 thf(fact_5360_not__zero__less__neg__numeral,axiom,
% 5.15/5.45 ! [N2: num] :
% 5.15/5.45 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_zero_less_neg_numeral
% 5.15/5.45 thf(fact_5361_le__minus__one__simps_I1_J,axiom,
% 5.15/5.45 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(1)
% 5.15/5.45 thf(fact_5362_le__minus__one__simps_I1_J,axiom,
% 5.15/5.45 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(1)
% 5.15/5.45 thf(fact_5363_le__minus__one__simps_I1_J,axiom,
% 5.15/5.45 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(1)
% 5.15/5.45 thf(fact_5364_le__minus__one__simps_I1_J,axiom,
% 5.15/5.45 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(1)
% 5.15/5.45 thf(fact_5365_le__minus__one__simps_I3_J,axiom,
% 5.15/5.45 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(3)
% 5.15/5.45 thf(fact_5366_le__minus__one__simps_I3_J,axiom,
% 5.15/5.45 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(3)
% 5.15/5.45 thf(fact_5367_le__minus__one__simps_I3_J,axiom,
% 5.15/5.45 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(3)
% 5.15/5.45 thf(fact_5368_le__minus__one__simps_I3_J,axiom,
% 5.15/5.45 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_one_simps(3)
% 5.15/5.45 thf(fact_5369_less__minus__one__simps_I3_J,axiom,
% 5.15/5.45 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(3)
% 5.15/5.45 thf(fact_5370_less__minus__one__simps_I3_J,axiom,
% 5.15/5.45 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(3)
% 5.15/5.45 thf(fact_5371_less__minus__one__simps_I3_J,axiom,
% 5.15/5.45 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(3)
% 5.15/5.45 thf(fact_5372_less__minus__one__simps_I3_J,axiom,
% 5.15/5.45 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(3)
% 5.15/5.45 thf(fact_5373_less__minus__one__simps_I1_J,axiom,
% 5.15/5.45 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(1)
% 5.15/5.45 thf(fact_5374_less__minus__one__simps_I1_J,axiom,
% 5.15/5.45 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(1)
% 5.15/5.45 thf(fact_5375_less__minus__one__simps_I1_J,axiom,
% 5.15/5.45 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(1)
% 5.15/5.45 thf(fact_5376_less__minus__one__simps_I1_J,axiom,
% 5.15/5.45 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.15/5.45
% 5.15/5.45 % less_minus_one_simps(1)
% 5.15/5.45 thf(fact_5377_neg__numeral__le__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_one
% 5.15/5.45 thf(fact_5378_neg__numeral__le__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_one
% 5.15/5.45 thf(fact_5379_neg__numeral__le__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_one
% 5.15/5.45 thf(fact_5380_neg__numeral__le__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_one
% 5.15/5.45 thf(fact_5381_neg__one__le__numeral,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_le_numeral
% 5.15/5.45 thf(fact_5382_neg__one__le__numeral,axiom,
% 5.15/5.45 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_le_numeral
% 5.15/5.45 thf(fact_5383_neg__one__le__numeral,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_le_numeral
% 5.15/5.45 thf(fact_5384_neg__one__le__numeral,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_le_numeral
% 5.15/5.45 thf(fact_5385_neg__numeral__le__neg__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_neg_one
% 5.15/5.45 thf(fact_5386_neg__numeral__le__neg__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_neg_one
% 5.15/5.45 thf(fact_5387_neg__numeral__le__neg__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_neg_one
% 5.15/5.45 thf(fact_5388_neg__numeral__le__neg__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_le_neg_one
% 5.15/5.45 thf(fact_5389_not__numeral__le__neg__one,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_le_neg_one
% 5.15/5.45 thf(fact_5390_not__numeral__le__neg__one,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_le_neg_one
% 5.15/5.45 thf(fact_5391_not__numeral__le__neg__one,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_le_neg_one
% 5.15/5.45 thf(fact_5392_not__numeral__le__neg__one,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_le_neg_one
% 5.15/5.45 thf(fact_5393_not__one__le__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_one_le_neg_numeral
% 5.15/5.45 thf(fact_5394_not__one__le__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_one_le_neg_numeral
% 5.15/5.45 thf(fact_5395_not__one__le__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_one_le_neg_numeral
% 5.15/5.45 thf(fact_5396_not__one__le__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_one_le_neg_numeral
% 5.15/5.45 thf(fact_5397_neg__numeral__less__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_one
% 5.15/5.45 thf(fact_5398_neg__numeral__less__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_one
% 5.15/5.45 thf(fact_5399_neg__numeral__less__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_one
% 5.15/5.45 thf(fact_5400_neg__numeral__less__one,axiom,
% 5.15/5.45 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.15/5.45
% 5.15/5.45 % neg_numeral_less_one
% 5.15/5.45 thf(fact_5401_neg__one__less__numeral,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_less_numeral
% 5.15/5.45 thf(fact_5402_neg__one__less__numeral,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_less_numeral
% 5.15/5.45 thf(fact_5403_neg__one__less__numeral,axiom,
% 5.15/5.45 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_less_numeral
% 5.15/5.45 thf(fact_5404_neg__one__less__numeral,axiom,
% 5.15/5.45 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_less_numeral
% 5.15/5.45 thf(fact_5405_not__numeral__less__neg__one,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_less_neg_one
% 5.15/5.45 thf(fact_5406_not__numeral__less__neg__one,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_less_neg_one
% 5.15/5.45 thf(fact_5407_not__numeral__less__neg__one,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_less_neg_one
% 5.15/5.45 thf(fact_5408_not__numeral__less__neg__one,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_numeral_less_neg_one
% 5.15/5.45 thf(fact_5409_not__one__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_one_less_neg_numeral
% 5.15/5.45 thf(fact_5410_not__one__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_one_less_neg_numeral
% 5.15/5.45 thf(fact_5411_not__one__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_one_less_neg_numeral
% 5.15/5.45 thf(fact_5412_not__one__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_one_less_neg_numeral
% 5.15/5.45 thf(fact_5413_not__neg__one__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_neg_one_less_neg_numeral
% 5.15/5.45 thf(fact_5414_not__neg__one__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_neg_one_less_neg_numeral
% 5.15/5.45 thf(fact_5415_not__neg__one__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_neg_one_less_neg_numeral
% 5.15/5.45 thf(fact_5416_not__neg__one__less__neg__numeral,axiom,
% 5.15/5.45 ! [M: num] :
% 5.15/5.45 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % not_neg_one_less_neg_numeral
% 5.15/5.45 thf(fact_5417_eq__minus__divide__eq,axiom,
% 5.15/5.45 ! [A: real,B: real,C: real] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.15/5.45 = ( ( ( C != zero_zero_real )
% 5.15/5.45 => ( ( times_times_real @ A @ C )
% 5.15/5.45 = ( uminus_uminus_real @ B ) ) )
% 5.15/5.45 & ( ( C = zero_zero_real )
% 5.15/5.45 => ( A = zero_zero_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_minus_divide_eq
% 5.15/5.45 thf(fact_5418_eq__minus__divide__eq,axiom,
% 5.15/5.45 ! [A: complex,B: complex,C: complex] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.15/5.45 = ( ( ( C != zero_zero_complex )
% 5.15/5.45 => ( ( times_times_complex @ A @ C )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.15/5.45 & ( ( C = zero_zero_complex )
% 5.15/5.45 => ( A = zero_zero_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_minus_divide_eq
% 5.15/5.45 thf(fact_5419_eq__minus__divide__eq,axiom,
% 5.15/5.45 ! [A: rat,B: rat,C: rat] :
% 5.15/5.45 ( ( A
% 5.15/5.45 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.15/5.45 = ( ( ( C != zero_zero_rat )
% 5.15/5.45 => ( ( times_times_rat @ A @ C )
% 5.15/5.45 = ( uminus_uminus_rat @ B ) ) )
% 5.15/5.45 & ( ( C = zero_zero_rat )
% 5.15/5.45 => ( A = zero_zero_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_minus_divide_eq
% 5.15/5.45 thf(fact_5420_minus__divide__eq__eq,axiom,
% 5.15/5.45 ! [B: real,C: real,A: real] :
% 5.15/5.45 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.15/5.45 = A )
% 5.15/5.45 = ( ( ( C != zero_zero_real )
% 5.15/5.45 => ( ( uminus_uminus_real @ B )
% 5.15/5.45 = ( times_times_real @ A @ C ) ) )
% 5.15/5.45 & ( ( C = zero_zero_real )
% 5.15/5.45 => ( A = zero_zero_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_eq_eq
% 5.15/5.45 thf(fact_5421_minus__divide__eq__eq,axiom,
% 5.15/5.45 ! [B: complex,C: complex,A: complex] :
% 5.15/5.45 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.45 = A )
% 5.15/5.45 = ( ( ( C != zero_zero_complex )
% 5.15/5.45 => ( ( uminus1482373934393186551omplex @ B )
% 5.15/5.45 = ( times_times_complex @ A @ C ) ) )
% 5.15/5.45 & ( ( C = zero_zero_complex )
% 5.15/5.45 => ( A = zero_zero_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_eq_eq
% 5.15/5.45 thf(fact_5422_minus__divide__eq__eq,axiom,
% 5.15/5.45 ! [B: rat,C: rat,A: rat] :
% 5.15/5.45 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.45 = A )
% 5.15/5.45 = ( ( ( C != zero_zero_rat )
% 5.15/5.45 => ( ( uminus_uminus_rat @ B )
% 5.15/5.45 = ( times_times_rat @ A @ C ) ) )
% 5.15/5.45 & ( ( C = zero_zero_rat )
% 5.15/5.45 => ( A = zero_zero_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_eq_eq
% 5.15/5.45 thf(fact_5423_nonzero__neg__divide__eq__eq,axiom,
% 5.15/5.45 ! [B: real,A: real,C: real] :
% 5.15/5.45 ( ( B != zero_zero_real )
% 5.15/5.45 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.45 = C )
% 5.15/5.45 = ( ( uminus_uminus_real @ A )
% 5.15/5.45 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_neg_divide_eq_eq
% 5.15/5.45 thf(fact_5424_nonzero__neg__divide__eq__eq,axiom,
% 5.15/5.45 ! [B: complex,A: complex,C: complex] :
% 5.15/5.45 ( ( B != zero_zero_complex )
% 5.15/5.45 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.45 = C )
% 5.15/5.45 = ( ( uminus1482373934393186551omplex @ A )
% 5.15/5.45 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_neg_divide_eq_eq
% 5.15/5.45 thf(fact_5425_nonzero__neg__divide__eq__eq,axiom,
% 5.15/5.45 ! [B: rat,A: rat,C: rat] :
% 5.15/5.45 ( ( B != zero_zero_rat )
% 5.15/5.45 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.15/5.45 = C )
% 5.15/5.45 = ( ( uminus_uminus_rat @ A )
% 5.15/5.45 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_neg_divide_eq_eq
% 5.15/5.45 thf(fact_5426_nonzero__neg__divide__eq__eq2,axiom,
% 5.15/5.45 ! [B: real,C: real,A: real] :
% 5.15/5.45 ( ( B != zero_zero_real )
% 5.15/5.45 => ( ( C
% 5.15/5.45 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.15/5.45 = ( ( times_times_real @ C @ B )
% 5.15/5.45 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_neg_divide_eq_eq2
% 5.15/5.45 thf(fact_5427_nonzero__neg__divide__eq__eq2,axiom,
% 5.15/5.45 ! [B: complex,C: complex,A: complex] :
% 5.15/5.45 ( ( B != zero_zero_complex )
% 5.15/5.45 => ( ( C
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.15/5.45 = ( ( times_times_complex @ C @ B )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_neg_divide_eq_eq2
% 5.15/5.45 thf(fact_5428_nonzero__neg__divide__eq__eq2,axiom,
% 5.15/5.45 ! [B: rat,C: rat,A: rat] :
% 5.15/5.45 ( ( B != zero_zero_rat )
% 5.15/5.45 => ( ( C
% 5.15/5.45 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.15/5.45 = ( ( times_times_rat @ C @ B )
% 5.15/5.45 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % nonzero_neg_divide_eq_eq2
% 5.15/5.45 thf(fact_5429_divide__eq__minus__1__iff,axiom,
% 5.15/5.45 ! [A: real,B: real] :
% 5.15/5.45 ( ( ( divide_divide_real @ A @ B )
% 5.15/5.45 = ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.45 = ( ( B != zero_zero_real )
% 5.15/5.45 & ( A
% 5.15/5.45 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_minus_1_iff
% 5.15/5.45 thf(fact_5430_divide__eq__minus__1__iff,axiom,
% 5.15/5.45 ! [A: complex,B: complex] :
% 5.15/5.45 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.45 = ( ( B != zero_zero_complex )
% 5.15/5.45 & ( A
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_minus_1_iff
% 5.15/5.45 thf(fact_5431_divide__eq__minus__1__iff,axiom,
% 5.15/5.45 ! [A: rat,B: rat] :
% 5.15/5.45 ( ( ( divide_divide_rat @ A @ B )
% 5.15/5.45 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.45 = ( ( B != zero_zero_rat )
% 5.15/5.45 & ( A
% 5.15/5.45 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_minus_1_iff
% 5.15/5.45 thf(fact_5432_mult__1s__ring__1_I2_J,axiom,
% 5.15/5.45 ! [B: int] :
% 5.15/5.45 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.15/5.45 = ( uminus_uminus_int @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(2)
% 5.15/5.45 thf(fact_5433_mult__1s__ring__1_I2_J,axiom,
% 5.15/5.45 ! [B: real] :
% 5.15/5.45 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.15/5.45 = ( uminus_uminus_real @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(2)
% 5.15/5.45 thf(fact_5434_mult__1s__ring__1_I2_J,axiom,
% 5.15/5.45 ! [B: complex] :
% 5.15/5.45 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(2)
% 5.15/5.45 thf(fact_5435_mult__1s__ring__1_I2_J,axiom,
% 5.15/5.45 ! [B: rat] :
% 5.15/5.45 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.15/5.45 = ( uminus_uminus_rat @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(2)
% 5.15/5.45 thf(fact_5436_mult__1s__ring__1_I2_J,axiom,
% 5.15/5.45 ! [B: code_integer] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(2)
% 5.15/5.45 thf(fact_5437_mult__1s__ring__1_I1_J,axiom,
% 5.15/5.45 ! [B: int] :
% 5.15/5.45 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.15/5.45 = ( uminus_uminus_int @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(1)
% 5.15/5.45 thf(fact_5438_mult__1s__ring__1_I1_J,axiom,
% 5.15/5.45 ! [B: real] :
% 5.15/5.45 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.15/5.45 = ( uminus_uminus_real @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(1)
% 5.15/5.45 thf(fact_5439_mult__1s__ring__1_I1_J,axiom,
% 5.15/5.45 ! [B: complex] :
% 5.15/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(1)
% 5.15/5.45 thf(fact_5440_mult__1s__ring__1_I1_J,axiom,
% 5.15/5.45 ! [B: rat] :
% 5.15/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.15/5.45 = ( uminus_uminus_rat @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(1)
% 5.15/5.45 thf(fact_5441_mult__1s__ring__1_I1_J,axiom,
% 5.15/5.45 ! [B: code_integer] :
% 5.15/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.15/5.45
% 5.15/5.45 % mult_1s_ring_1(1)
% 5.15/5.45 thf(fact_5442_uminus__numeral__One,axiom,
% 5.15/5.45 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_numeral_One
% 5.15/5.45 thf(fact_5443_uminus__numeral__One,axiom,
% 5.15/5.45 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.15/5.45 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_numeral_One
% 5.15/5.45 thf(fact_5444_uminus__numeral__One,axiom,
% 5.15/5.45 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_numeral_One
% 5.15/5.45 thf(fact_5445_uminus__numeral__One,axiom,
% 5.15/5.45 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.15/5.45 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_numeral_One
% 5.15/5.45 thf(fact_5446_uminus__numeral__One,axiom,
% 5.15/5.45 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_numeral_One
% 5.15/5.45 thf(fact_5447_power__minus,axiom,
% 5.15/5.45 ! [A: int,N2: nat] :
% 5.15/5.45 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.15/5.45 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus
% 5.15/5.45 thf(fact_5448_power__minus,axiom,
% 5.15/5.45 ! [A: real,N2: nat] :
% 5.15/5.45 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.15/5.45 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus
% 5.15/5.45 thf(fact_5449_power__minus,axiom,
% 5.15/5.45 ! [A: complex,N2: nat] :
% 5.15/5.45 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.15/5.45 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus
% 5.15/5.45 thf(fact_5450_power__minus,axiom,
% 5.15/5.45 ! [A: rat,N2: nat] :
% 5.15/5.45 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.15/5.45 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus
% 5.15/5.45 thf(fact_5451_power__minus,axiom,
% 5.15/5.45 ! [A: code_integer,N2: nat] :
% 5.15/5.45 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.15/5.45 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus
% 5.15/5.45 thf(fact_5452_power__minus__Bit0,axiom,
% 5.15/5.45 ! [X: int,K: num] :
% 5.15/5.45 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.15/5.45 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit0
% 5.15/5.45 thf(fact_5453_power__minus__Bit0,axiom,
% 5.15/5.45 ! [X: real,K: num] :
% 5.15/5.45 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.15/5.45 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit0
% 5.15/5.45 thf(fact_5454_power__minus__Bit0,axiom,
% 5.15/5.45 ! [X: complex,K: num] :
% 5.15/5.45 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.15/5.45 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit0
% 5.15/5.45 thf(fact_5455_power__minus__Bit0,axiom,
% 5.15/5.45 ! [X: rat,K: num] :
% 5.15/5.45 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.15/5.45 = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit0
% 5.15/5.45 thf(fact_5456_power__minus__Bit0,axiom,
% 5.15/5.45 ! [X: code_integer,K: num] :
% 5.15/5.45 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.15/5.45 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit0
% 5.15/5.45 thf(fact_5457_power__minus__Bit1,axiom,
% 5.15/5.45 ! [X: int,K: num] :
% 5.15/5.45 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit1
% 5.15/5.45 thf(fact_5458_power__minus__Bit1,axiom,
% 5.15/5.45 ! [X: real,K: num] :
% 5.15/5.45 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.15/5.45 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit1
% 5.15/5.45 thf(fact_5459_power__minus__Bit1,axiom,
% 5.15/5.45 ! [X: complex,K: num] :
% 5.15/5.45 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit1
% 5.15/5.45 thf(fact_5460_power__minus__Bit1,axiom,
% 5.15/5.45 ! [X: rat,K: num] :
% 5.15/5.45 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.15/5.45 = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit1
% 5.15/5.45 thf(fact_5461_power__minus__Bit1,axiom,
% 5.15/5.45 ! [X: code_integer,K: num] :
% 5.15/5.45 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power_minus_Bit1
% 5.15/5.45 thf(fact_5462_real__0__less__add__iff,axiom,
% 5.15/5.45 ! [X: real,Y: real] :
% 5.15/5.45 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.45 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % real_0_less_add_iff
% 5.15/5.45 thf(fact_5463_real__add__less__0__iff,axiom,
% 5.15/5.45 ! [X: real,Y: real] :
% 5.15/5.45 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.15/5.45 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % real_add_less_0_iff
% 5.15/5.45 thf(fact_5464_real__add__le__0__iff,axiom,
% 5.15/5.45 ! [X: real,Y: real] :
% 5.15/5.45 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.15/5.45 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % real_add_le_0_iff
% 5.15/5.45 thf(fact_5465_real__0__le__add__iff,axiom,
% 5.15/5.45 ! [X: real,Y: real] :
% 5.15/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.45 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.15/5.45
% 5.15/5.45 % real_0_le_add_iff
% 5.15/5.45 thf(fact_5466_zmod__zminus1__eq__if,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 = zero_zero_int )
% 5.15/5.45 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = zero_zero_int ) )
% 5.15/5.45 & ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 != zero_zero_int )
% 5.15/5.45 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zmod_zminus1_eq_if
% 5.15/5.45 thf(fact_5467_zmod__zminus2__eq__if,axiom,
% 5.15/5.45 ! [A: int,B: int] :
% 5.15/5.45 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 = zero_zero_int )
% 5.15/5.45 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = zero_zero_int ) )
% 5.15/5.45 & ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 != zero_zero_int )
% 5.15/5.45 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zmod_zminus2_eq_if
% 5.15/5.45 thf(fact_5468_pred__numeral__def,axiom,
% 5.15/5.45 ( pred_numeral
% 5.15/5.45 = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pred_numeral_def
% 5.15/5.45 thf(fact_5469_pos__minus__divide__less__eq,axiom,
% 5.15/5.45 ! [C: real,B: real,A: real] :
% 5.15/5.45 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.15/5.45 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_minus_divide_less_eq
% 5.15/5.45 thf(fact_5470_pos__minus__divide__less__eq,axiom,
% 5.15/5.45 ! [C: rat,B: rat,A: rat] :
% 5.15/5.45 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.15/5.45 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_minus_divide_less_eq
% 5.15/5.45 thf(fact_5471_pos__less__minus__divide__eq,axiom,
% 5.15/5.45 ! [C: real,A: real,B: real] :
% 5.15/5.45 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.15/5.45 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_less_minus_divide_eq
% 5.15/5.45 thf(fact_5472_pos__less__minus__divide__eq,axiom,
% 5.15/5.45 ! [C: rat,A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.15/5.45 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_less_minus_divide_eq
% 5.15/5.45 thf(fact_5473_neg__minus__divide__less__eq,axiom,
% 5.15/5.45 ! [C: real,B: real,A: real] :
% 5.15/5.45 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.15/5.45 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_minus_divide_less_eq
% 5.15/5.45 thf(fact_5474_neg__minus__divide__less__eq,axiom,
% 5.15/5.45 ! [C: rat,B: rat,A: rat] :
% 5.15/5.45 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.15/5.45 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_minus_divide_less_eq
% 5.15/5.45 thf(fact_5475_neg__less__minus__divide__eq,axiom,
% 5.15/5.45 ! [C: real,A: real,B: real] :
% 5.15/5.45 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.15/5.45 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_less_minus_divide_eq
% 5.15/5.45 thf(fact_5476_neg__less__minus__divide__eq,axiom,
% 5.15/5.45 ! [C: rat,A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.15/5.45 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_less_minus_divide_eq
% 5.15/5.45 thf(fact_5477_minus__divide__less__eq,axiom,
% 5.15/5.45 ! [B: real,C: real,A: real] :
% 5.15/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.15/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_less_eq
% 5.15/5.45 thf(fact_5478_minus__divide__less__eq,axiom,
% 5.15/5.45 ! [B: rat,C: rat,A: rat] :
% 5.15/5.45 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.15/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_less_eq
% 5.15/5.45 thf(fact_5479_less__minus__divide__eq,axiom,
% 5.15/5.45 ! [A: real,B: real,C: real] :
% 5.15/5.45 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.15/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_divide_eq
% 5.15/5.45 thf(fact_5480_less__minus__divide__eq,axiom,
% 5.15/5.45 ! [A: rat,B: rat,C: rat] :
% 5.15/5.45 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.15/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_minus_divide_eq
% 5.15/5.45 thf(fact_5481_divide__eq__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [B: real,C: real,W: num] :
% 5.15/5.45 ( ( ( divide_divide_real @ B @ C )
% 5.15/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.45 = ( ( ( C != zero_zero_real )
% 5.15/5.45 => ( B
% 5.15/5.45 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.15/5.45 & ( ( C = zero_zero_real )
% 5.15/5.45 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.45 = zero_zero_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_eq_numeral(2)
% 5.15/5.45 thf(fact_5482_divide__eq__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [B: complex,C: complex,W: num] :
% 5.15/5.45 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.45 = ( ( ( C != zero_zero_complex )
% 5.15/5.45 => ( B
% 5.15/5.45 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.15/5.45 & ( ( C = zero_zero_complex )
% 5.15/5.45 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.45 = zero_zero_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_eq_numeral(2)
% 5.15/5.45 thf(fact_5483_divide__eq__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [B: rat,C: rat,W: num] :
% 5.15/5.45 ( ( ( divide_divide_rat @ B @ C )
% 5.15/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.15/5.45 = ( ( ( C != zero_zero_rat )
% 5.15/5.45 => ( B
% 5.15/5.45 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.15/5.45 & ( ( C = zero_zero_rat )
% 5.15/5.45 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.15/5.45 = zero_zero_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_eq_eq_numeral(2)
% 5.15/5.45 thf(fact_5484_eq__divide__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [W: num,B: real,C: real] :
% 5.15/5.45 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.45 = ( divide_divide_real @ B @ C ) )
% 5.15/5.45 = ( ( ( C != zero_zero_real )
% 5.15/5.45 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( C = zero_zero_real )
% 5.15/5.45 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.45 = zero_zero_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_divide_eq_numeral(2)
% 5.15/5.45 thf(fact_5485_eq__divide__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [W: num,B: complex,C: complex] :
% 5.15/5.45 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.45 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.15/5.45 = ( ( ( C != zero_zero_complex )
% 5.15/5.45 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( C = zero_zero_complex )
% 5.15/5.45 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.45 = zero_zero_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_divide_eq_numeral(2)
% 5.15/5.45 thf(fact_5486_eq__divide__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [W: num,B: rat,C: rat] :
% 5.15/5.45 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.15/5.45 = ( divide_divide_rat @ B @ C ) )
% 5.15/5.45 = ( ( ( C != zero_zero_rat )
% 5.15/5.45 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( C = zero_zero_rat )
% 5.15/5.45 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.15/5.45 = zero_zero_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % eq_divide_eq_numeral(2)
% 5.15/5.45 thf(fact_5487_minus__divide__add__eq__iff,axiom,
% 5.15/5.45 ! [Z: real,X: real,Y: real] :
% 5.15/5.45 ( ( Z != zero_zero_real )
% 5.15/5.45 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 5.15/5.45 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_add_eq_iff
% 5.15/5.45 thf(fact_5488_minus__divide__add__eq__iff,axiom,
% 5.15/5.45 ! [Z: complex,X: complex,Y: complex] :
% 5.15/5.45 ( ( Z != zero_zero_complex )
% 5.15/5.45 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 5.15/5.45 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_add_eq_iff
% 5.15/5.45 thf(fact_5489_minus__divide__add__eq__iff,axiom,
% 5.15/5.45 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.45 ( ( Z != zero_zero_rat )
% 5.15/5.45 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 5.15/5.45 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_add_eq_iff
% 5.15/5.45 thf(fact_5490_add__divide__eq__if__simps_I3_J,axiom,
% 5.15/5.45 ! [Z: real,A: real,B: real] :
% 5.15/5.45 ( ( ( Z = zero_zero_real )
% 5.15/5.45 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( Z != zero_zero_real )
% 5.15/5.45 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.15/5.45 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(3)
% 5.15/5.45 thf(fact_5491_add__divide__eq__if__simps_I3_J,axiom,
% 5.15/5.45 ! [Z: complex,A: complex,B: complex] :
% 5.15/5.45 ( ( ( Z = zero_zero_complex )
% 5.15/5.45 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( Z != zero_zero_complex )
% 5.15/5.45 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.15/5.45 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(3)
% 5.15/5.45 thf(fact_5492_add__divide__eq__if__simps_I3_J,axiom,
% 5.15/5.45 ! [Z: rat,A: rat,B: rat] :
% 5.15/5.45 ( ( ( Z = zero_zero_rat )
% 5.15/5.45 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.15/5.45 = B ) )
% 5.15/5.45 & ( ( Z != zero_zero_rat )
% 5.15/5.45 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.15/5.45 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(3)
% 5.15/5.45 thf(fact_5493_add__divide__eq__if__simps_I6_J,axiom,
% 5.15/5.45 ! [Z: real,A: real,B: real] :
% 5.15/5.45 ( ( ( Z = zero_zero_real )
% 5.15/5.45 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.15/5.45 = ( uminus_uminus_real @ B ) ) )
% 5.15/5.45 & ( ( Z != zero_zero_real )
% 5.15/5.45 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.15/5.45 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(6)
% 5.15/5.45 thf(fact_5494_add__divide__eq__if__simps_I6_J,axiom,
% 5.15/5.45 ! [Z: complex,A: complex,B: complex] :
% 5.15/5.45 ( ( ( Z = zero_zero_complex )
% 5.15/5.45 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.15/5.45 & ( ( Z != zero_zero_complex )
% 5.15/5.45 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.15/5.45 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(6)
% 5.15/5.45 thf(fact_5495_add__divide__eq__if__simps_I6_J,axiom,
% 5.15/5.45 ! [Z: rat,A: rat,B: rat] :
% 5.15/5.45 ( ( ( Z = zero_zero_rat )
% 5.15/5.45 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.15/5.45 = ( uminus_uminus_rat @ B ) ) )
% 5.15/5.45 & ( ( Z != zero_zero_rat )
% 5.15/5.45 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.15/5.45 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(6)
% 5.15/5.45 thf(fact_5496_add__divide__eq__if__simps_I5_J,axiom,
% 5.15/5.45 ! [Z: real,A: real,B: real] :
% 5.15/5.45 ( ( ( Z = zero_zero_real )
% 5.15/5.45 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.15/5.45 = ( uminus_uminus_real @ B ) ) )
% 5.15/5.45 & ( ( Z != zero_zero_real )
% 5.15/5.45 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.15/5.45 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(5)
% 5.15/5.45 thf(fact_5497_add__divide__eq__if__simps_I5_J,axiom,
% 5.15/5.45 ! [Z: complex,A: complex,B: complex] :
% 5.15/5.45 ( ( ( Z = zero_zero_complex )
% 5.15/5.45 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.15/5.45 & ( ( Z != zero_zero_complex )
% 5.15/5.45 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.15/5.45 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(5)
% 5.15/5.45 thf(fact_5498_add__divide__eq__if__simps_I5_J,axiom,
% 5.15/5.45 ! [Z: rat,A: rat,B: rat] :
% 5.15/5.45 ( ( ( Z = zero_zero_rat )
% 5.15/5.45 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.15/5.45 = ( uminus_uminus_rat @ B ) ) )
% 5.15/5.45 & ( ( Z != zero_zero_rat )
% 5.15/5.45 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.15/5.45 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % add_divide_eq_if_simps(5)
% 5.15/5.45 thf(fact_5499_minus__divide__diff__eq__iff,axiom,
% 5.15/5.45 ! [Z: real,X: real,Y: real] :
% 5.15/5.45 ( ( Z != zero_zero_real )
% 5.15/5.45 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 5.15/5.45 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_diff_eq_iff
% 5.15/5.45 thf(fact_5500_minus__divide__diff__eq__iff,axiom,
% 5.15/5.45 ! [Z: complex,X: complex,Y: complex] :
% 5.15/5.45 ( ( Z != zero_zero_complex )
% 5.15/5.45 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 5.15/5.45 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_diff_eq_iff
% 5.15/5.45 thf(fact_5501_minus__divide__diff__eq__iff,axiom,
% 5.15/5.45 ! [Z: rat,X: rat,Y: rat] :
% 5.15/5.45 ( ( Z != zero_zero_rat )
% 5.15/5.45 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 5.15/5.45 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_diff_eq_iff
% 5.15/5.45 thf(fact_5502_even__minus,axiom,
% 5.15/5.45 ! [A: int] :
% 5.15/5.45 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.15/5.45 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % even_minus
% 5.15/5.45 thf(fact_5503_even__minus,axiom,
% 5.15/5.45 ! [A: code_integer] :
% 5.15/5.45 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.45 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.15/5.45
% 5.15/5.45 % even_minus
% 5.15/5.45 thf(fact_5504_power2__eq__iff,axiom,
% 5.15/5.45 ! [X: int,Y: int] :
% 5.15/5.45 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.45 = ( ( X = Y )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_iff
% 5.15/5.45 thf(fact_5505_power2__eq__iff,axiom,
% 5.15/5.45 ! [X: real,Y: real] :
% 5.15/5.45 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.45 = ( ( X = Y )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_iff
% 5.15/5.45 thf(fact_5506_power2__eq__iff,axiom,
% 5.15/5.45 ! [X: complex,Y: complex] :
% 5.15/5.45 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.45 = ( ( X = Y )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_iff
% 5.15/5.45 thf(fact_5507_power2__eq__iff,axiom,
% 5.15/5.45 ! [X: rat,Y: rat] :
% 5.15/5.45 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.45 = ( ( X = Y )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_iff
% 5.15/5.45 thf(fact_5508_power2__eq__iff,axiom,
% 5.15/5.45 ! [X: code_integer,Y: code_integer] :
% 5.15/5.45 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.45 = ( ( X = Y )
% 5.15/5.45 | ( X
% 5.15/5.45 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_iff
% 5.15/5.45 thf(fact_5509_uminus__power__if,axiom,
% 5.15/5.45 ! [N2: nat,A: int] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.15/5.45 = ( power_power_int @ A @ N2 ) ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_power_if
% 5.15/5.45 thf(fact_5510_uminus__power__if,axiom,
% 5.15/5.45 ! [N2: nat,A: real] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.15/5.45 = ( power_power_real @ A @ N2 ) ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_power_if
% 5.15/5.45 thf(fact_5511_uminus__power__if,axiom,
% 5.15/5.45 ! [N2: nat,A: complex] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.15/5.45 = ( power_power_complex @ A @ N2 ) ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_power_if
% 5.15/5.45 thf(fact_5512_uminus__power__if,axiom,
% 5.15/5.45 ! [N2: nat,A: rat] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.15/5.45 = ( power_power_rat @ A @ N2 ) ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_power_if
% 5.15/5.45 thf(fact_5513_uminus__power__if,axiom,
% 5.15/5.45 ! [N2: nat,A: code_integer] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.15/5.45 = ( power_8256067586552552935nteger @ A @ N2 ) ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % uminus_power_if
% 5.15/5.45 thf(fact_5514_verit__less__mono__div__int2,axiom,
% 5.15/5.45 ! [A2: int,B3: int,N2: int] :
% 5.15/5.45 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.15/5.45 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 5.15/5.45 => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N2 ) @ ( divide_divide_int @ A2 @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % verit_less_mono_div_int2
% 5.15/5.45 thf(fact_5515_div__eq__minus1,axiom,
% 5.15/5.45 ! [B: int] :
% 5.15/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.45 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % div_eq_minus1
% 5.15/5.45 thf(fact_5516_of__bool__odd__eq__mod__2,axiom,
% 5.15/5.45 ! [A: nat] :
% 5.15/5.45 ( ( zero_n2687167440665602831ol_nat
% 5.15/5.45 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.45 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_odd_eq_mod_2
% 5.15/5.45 thf(fact_5517_of__bool__odd__eq__mod__2,axiom,
% 5.15/5.45 ! [A: int] :
% 5.15/5.45 ( ( zero_n2684676970156552555ol_int
% 5.15/5.45 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.45 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_odd_eq_mod_2
% 5.15/5.45 thf(fact_5518_of__bool__odd__eq__mod__2,axiom,
% 5.15/5.45 ! [A: code_integer] :
% 5.15/5.45 ( ( zero_n356916108424825756nteger
% 5.15/5.45 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.15/5.45 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % of_bool_odd_eq_mod_2
% 5.15/5.45 thf(fact_5519_pos__minus__divide__le__eq,axiom,
% 5.15/5.45 ! [C: real,B: real,A: real] :
% 5.15/5.45 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.15/5.45 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_minus_divide_le_eq
% 5.15/5.45 thf(fact_5520_pos__minus__divide__le__eq,axiom,
% 5.15/5.45 ! [C: rat,B: rat,A: rat] :
% 5.15/5.45 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.15/5.45 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_minus_divide_le_eq
% 5.15/5.45 thf(fact_5521_pos__le__minus__divide__eq,axiom,
% 5.15/5.45 ! [C: real,A: real,B: real] :
% 5.15/5.45 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.15/5.45 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_le_minus_divide_eq
% 5.15/5.45 thf(fact_5522_pos__le__minus__divide__eq,axiom,
% 5.15/5.45 ! [C: rat,A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.15/5.45 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % pos_le_minus_divide_eq
% 5.15/5.45 thf(fact_5523_neg__minus__divide__le__eq,axiom,
% 5.15/5.45 ! [C: real,B: real,A: real] :
% 5.15/5.45 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.15/5.45 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_minus_divide_le_eq
% 5.15/5.45 thf(fact_5524_neg__minus__divide__le__eq,axiom,
% 5.15/5.45 ! [C: rat,B: rat,A: rat] :
% 5.15/5.45 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.15/5.45 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_minus_divide_le_eq
% 5.15/5.45 thf(fact_5525_neg__le__minus__divide__eq,axiom,
% 5.15/5.45 ! [C: real,A: real,B: real] :
% 5.15/5.45 ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.15/5.45 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_le_minus_divide_eq
% 5.15/5.45 thf(fact_5526_neg__le__minus__divide__eq,axiom,
% 5.15/5.45 ! [C: rat,A: rat,B: rat] :
% 5.15/5.45 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.15/5.45 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_le_minus_divide_eq
% 5.15/5.45 thf(fact_5527_minus__divide__le__eq,axiom,
% 5.15/5.45 ! [B: real,C: real,A: real] :
% 5.15/5.45 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.15/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_le_eq
% 5.15/5.45 thf(fact_5528_minus__divide__le__eq,axiom,
% 5.15/5.45 ! [B: rat,C: rat,A: rat] :
% 5.15/5.45 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.15/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_divide_le_eq
% 5.15/5.45 thf(fact_5529_le__minus__divide__eq,axiom,
% 5.15/5.45 ! [A: real,B: real,C: real] :
% 5.15/5.45 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.15/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_divide_eq
% 5.15/5.45 thf(fact_5530_le__minus__divide__eq,axiom,
% 5.15/5.45 ! [A: rat,B: rat,C: rat] :
% 5.15/5.45 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.15/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % le_minus_divide_eq
% 5.15/5.45 thf(fact_5531_divide__less__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [B: real,C: real,W: num] :
% 5.15/5.45 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_less_eq_numeral(2)
% 5.15/5.45 thf(fact_5532_divide__less__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [B: rat,C: rat,W: num] :
% 5.15/5.45 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.15/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % divide_less_eq_numeral(2)
% 5.15/5.45 thf(fact_5533_less__divide__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [W: num,B: real,C: real] :
% 5.15/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.15/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.45 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_divide_eq_numeral(2)
% 5.15/5.45 thf(fact_5534_less__divide__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [W: num,B: rat,C: rat] :
% 5.15/5.45 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.45 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.45 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.45 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % less_divide_eq_numeral(2)
% 5.15/5.45 thf(fact_5535_power2__eq__1__iff,axiom,
% 5.15/5.45 ! [A: int] :
% 5.15/5.45 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_int )
% 5.15/5.45 = ( ( A = one_one_int )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_1_iff
% 5.15/5.45 thf(fact_5536_power2__eq__1__iff,axiom,
% 5.15/5.45 ! [A: real] :
% 5.15/5.45 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_real )
% 5.15/5.45 = ( ( A = one_one_real )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_1_iff
% 5.15/5.45 thf(fact_5537_power2__eq__1__iff,axiom,
% 5.15/5.45 ! [A: complex] :
% 5.15/5.45 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_complex )
% 5.15/5.45 = ( ( A = one_one_complex )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_1_iff
% 5.15/5.45 thf(fact_5538_power2__eq__1__iff,axiom,
% 5.15/5.45 ! [A: rat] :
% 5.15/5.45 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_rat )
% 5.15/5.45 = ( ( A = one_one_rat )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_1_iff
% 5.15/5.45 thf(fact_5539_power2__eq__1__iff,axiom,
% 5.15/5.45 ! [A: code_integer] :
% 5.15/5.45 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = one_one_Code_integer )
% 5.15/5.45 = ( ( A = one_one_Code_integer )
% 5.15/5.45 | ( A
% 5.15/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % power2_eq_1_iff
% 5.15/5.45 thf(fact_5540_minus__one__power__iff,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.15/5.45 = one_one_int ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_one_power_iff
% 5.15/5.45 thf(fact_5541_minus__one__power__iff,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.15/5.45 = one_one_real ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_one_power_iff
% 5.15/5.45 thf(fact_5542_minus__one__power__iff,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.15/5.45 = one_one_complex ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.15/5.45 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_one_power_iff
% 5.15/5.45 thf(fact_5543_minus__one__power__iff,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.15/5.45 = one_one_rat ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.15/5.45 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_one_power_iff
% 5.15/5.45 thf(fact_5544_minus__one__power__iff,axiom,
% 5.15/5.45 ! [N2: nat] :
% 5.15/5.45 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.15/5.45 = one_one_Code_integer ) )
% 5.15/5.45 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.15/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_one_power_iff
% 5.15/5.45 thf(fact_5545_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.15/5.45 ! [K: nat,N2: nat] :
% 5.15/5.45 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.45 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.15/5.45 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_power_add_eq_neg_one_power_diff
% 5.15/5.45 thf(fact_5546_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.15/5.45 ! [K: nat,N2: nat] :
% 5.15/5.45 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.45 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.15/5.45 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_power_add_eq_neg_one_power_diff
% 5.15/5.45 thf(fact_5547_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.15/5.45 ! [K: nat,N2: nat] :
% 5.15/5.45 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.45 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.15/5.45 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_power_add_eq_neg_one_power_diff
% 5.15/5.45 thf(fact_5548_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.15/5.45 ! [K: nat,N2: nat] :
% 5.15/5.45 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.45 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.15/5.45 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_power_add_eq_neg_one_power_diff
% 5.15/5.45 thf(fact_5549_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.15/5.45 ! [K: nat,N2: nat] :
% 5.15/5.45 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.45 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.15/5.45 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % neg_one_power_add_eq_neg_one_power_diff
% 5.15/5.45 thf(fact_5550_realpow__square__minus__le,axiom,
% 5.15/5.45 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % realpow_square_minus_le
% 5.15/5.45 thf(fact_5551_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.15/5.45 ! [N2: nat,K: int] :
% 5.15/5.45 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.15/5.45 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_int_less_eq_self_iff
% 5.15/5.45 thf(fact_5552_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.15/5.45 ! [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 ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_int_greater_eq_minus_exp
% 5.15/5.45 thf(fact_5553_signed__take__bit__int__greater__self__iff,axiom,
% 5.15/5.45 ! [K: int,N2: nat] :
% 5.15/5.45 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.15/5.45 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % signed_take_bit_int_greater_self_iff
% 5.15/5.45 thf(fact_5554_minus__mod__int__eq,axiom,
% 5.15/5.45 ! [L: int,K: int] :
% 5.15/5.45 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.15/5.45 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.15/5.45 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % minus_mod_int_eq
% 5.15/5.45 thf(fact_5555_zmod__minus1,axiom,
% 5.15/5.45 ! [B: int] :
% 5.15/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.15/5.45 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.15/5.45 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zmod_minus1
% 5.15/5.45 thf(fact_5556_zdiv__zminus1__eq__if,axiom,
% 5.15/5.45 ! [B: int,A: int] :
% 5.15/5.45 ( ( B != zero_zero_int )
% 5.15/5.45 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 = zero_zero_int )
% 5.15/5.45 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.15/5.45 & ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 != zero_zero_int )
% 5.15/5.45 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.45 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zdiv_zminus1_eq_if
% 5.15/5.45 thf(fact_5557_zdiv__zminus2__eq__if,axiom,
% 5.15/5.45 ! [B: int,A: int] :
% 5.15/5.45 ( ( B != zero_zero_int )
% 5.15/5.45 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 = zero_zero_int )
% 5.15/5.45 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.15/5.45 & ( ( ( modulo_modulo_int @ A @ B )
% 5.15/5.45 != zero_zero_int )
% 5.15/5.45 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.15/5.45 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zdiv_zminus2_eq_if
% 5.15/5.45 thf(fact_5558_zminus1__lemma,axiom,
% 5.15/5.45 ! [A: int,B: int,Q3: int,R2: int] :
% 5.15/5.45 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.45 => ( ( B != zero_zero_int )
% 5.15/5.45 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % zminus1_lemma
% 5.15/5.45 thf(fact_5559_bits__induct,axiom,
% 5.15/5.45 ! [P: nat > $o,A: nat] :
% 5.15/5.45 ( ! [A5: nat] :
% 5.15/5.45 ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = A5 )
% 5.15/5.45 => ( P @ A5 ) )
% 5.15/5.45 => ( ! [A5: nat,B6: $o] :
% 5.15/5.45 ( ( P @ A5 )
% 5.15/5.45 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B6 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.45 = A5 )
% 5.15/5.45 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B6 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.15/5.45 => ( P @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % bits_induct
% 5.15/5.45 thf(fact_5560_bits__induct,axiom,
% 5.15/5.45 ! [P: int > $o,A: int] :
% 5.15/5.45 ( ! [A5: int] :
% 5.15/5.45 ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.45 = A5 )
% 5.15/5.45 => ( P @ A5 ) )
% 5.15/5.45 => ( ! [A5: int,B6: $o] :
% 5.15/5.45 ( ( P @ A5 )
% 5.15/5.45 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B6 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.45 = A5 )
% 5.15/5.45 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B6 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.15/5.45 => ( P @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % bits_induct
% 5.15/5.45 thf(fact_5561_bits__induct,axiom,
% 5.15/5.45 ! [P: code_integer > $o,A: code_integer] :
% 5.15/5.45 ( ! [A5: code_integer] :
% 5.15/5.45 ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.45 = A5 )
% 5.15/5.45 => ( P @ A5 ) )
% 5.15/5.45 => ( ! [A5: code_integer,B6: $o] :
% 5.15/5.45 ( ( P @ A5 )
% 5.15/5.45 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B6 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.45 = A5 )
% 5.15/5.45 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B6 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.15/5.45 => ( P @ A ) ) ) ).
% 5.15/5.45
% 5.15/5.45 % bits_induct
% 5.15/5.45 thf(fact_5562_divide__le__eq__numeral_I2_J,axiom,
% 5.15/5.45 ! [B: real,C: real,W: num] :
% 5.15/5.45 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.15/5.45 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.45 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.46 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.15/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % divide_le_eq_numeral(2)
% 5.15/5.46 thf(fact_5563_divide__le__eq__numeral_I2_J,axiom,
% 5.15/5.46 ! [B: rat,C: rat,W: num] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.15/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.46 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.15/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.15/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % divide_le_eq_numeral(2)
% 5.15/5.46 thf(fact_5564_le__divide__eq__numeral_I2_J,axiom,
% 5.15/5.46 ! [W: num,B: real,C: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.15/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.46 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.15/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.46 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.15/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.15/5.46 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % le_divide_eq_numeral(2)
% 5.15/5.46 thf(fact_5565_le__divide__eq__numeral_I2_J,axiom,
% 5.15/5.46 ! [W: num,B: rat,C: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.15/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.46 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.15/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.15/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.46 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.15/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.15/5.46 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % le_divide_eq_numeral(2)
% 5.15/5.46 thf(fact_5566_square__le__1,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.46 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.46 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % square_le_1
% 5.15/5.46 thf(fact_5567_square__le__1,axiom,
% 5.15/5.46 ! [X: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.15/5.46 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.15/5.46 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % square_le_1
% 5.15/5.46 thf(fact_5568_square__le__1,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.15/5.46 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.15/5.46 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % square_le_1
% 5.15/5.46 thf(fact_5569_square__le__1,axiom,
% 5.15/5.46 ! [X: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.15/5.46 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.15/5.46 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % square_le_1
% 5.15/5.46 thf(fact_5570_minus__power__mult__self,axiom,
% 5.15/5.46 ! [A: int,N2: nat] :
% 5.15/5.46 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.15/5.46 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % minus_power_mult_self
% 5.15/5.46 thf(fact_5571_minus__power__mult__self,axiom,
% 5.15/5.46 ! [A: real,N2: nat] :
% 5.15/5.46 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.15/5.46 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % minus_power_mult_self
% 5.15/5.46 thf(fact_5572_minus__power__mult__self,axiom,
% 5.15/5.46 ! [A: complex,N2: nat] :
% 5.15/5.46 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) )
% 5.15/5.46 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % minus_power_mult_self
% 5.15/5.46 thf(fact_5573_minus__power__mult__self,axiom,
% 5.15/5.46 ! [A: rat,N2: nat] :
% 5.15/5.46 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.15/5.46 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % minus_power_mult_self
% 5.15/5.46 thf(fact_5574_minus__power__mult__self,axiom,
% 5.15/5.46 ! [A: code_integer,N2: nat] :
% 5.15/5.46 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.15/5.46 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % minus_power_mult_self
% 5.15/5.46 thf(fact_5575_signed__take__bit__int__eq__self,axiom,
% 5.15/5.46 ! [N2: nat,K: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.15/5.46 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.46 => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.15/5.46 = K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % signed_take_bit_int_eq_self
% 5.15/5.46 thf(fact_5576_signed__take__bit__int__eq__self__iff,axiom,
% 5.15/5.46 ! [N2: nat,K: int] :
% 5.15/5.46 ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.15/5.46 = K )
% 5.15/5.46 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.15/5.46 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % signed_take_bit_int_eq_self_iff
% 5.15/5.46 thf(fact_5577_minus__1__div__exp__eq__int,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.46 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % minus_1_div_exp_eq_int
% 5.15/5.46 thf(fact_5578_div__pos__neg__trivial,axiom,
% 5.15/5.46 ! [K: int,L: int] :
% 5.15/5.46 ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.46 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.15/5.46 => ( ( divide_divide_int @ K @ L )
% 5.15/5.46 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % div_pos_neg_trivial
% 5.15/5.46 thf(fact_5579_exp__mod__exp,axiom,
% 5.15/5.46 ! [M: nat,N2: nat] :
% 5.15/5.46 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.46 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % exp_mod_exp
% 5.15/5.46 thf(fact_5580_exp__mod__exp,axiom,
% 5.15/5.46 ! [M: nat,N2: nat] :
% 5.15/5.46 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.46 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % exp_mod_exp
% 5.15/5.46 thf(fact_5581_exp__mod__exp,axiom,
% 5.15/5.46 ! [M: nat,N2: nat] :
% 5.15/5.46 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.46 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % exp_mod_exp
% 5.15/5.46 thf(fact_5582_divmod__nat__def,axiom,
% 5.15/5.46 ( divmod_nat
% 5.15/5.46 = ( ^ [M5: nat,N3: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M5 @ N3 ) @ ( modulo_modulo_nat @ M5 @ N3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % divmod_nat_def
% 5.15/5.46 thf(fact_5583_power__minus1__odd,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.46 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_minus1_odd
% 5.15/5.46 thf(fact_5584_power__minus1__odd,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.46 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_minus1_odd
% 5.15/5.46 thf(fact_5585_power__minus1__odd,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.46 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_minus1_odd
% 5.15/5.46 thf(fact_5586_power__minus1__odd,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.46 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_minus1_odd
% 5.15/5.46 thf(fact_5587_power__minus1__odd,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.46 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_minus1_odd
% 5.15/5.46 thf(fact_5588_int__bit__induct,axiom,
% 5.15/5.46 ! [P: int > $o,K: int] :
% 5.15/5.46 ( ( P @ zero_zero_int )
% 5.15/5.46 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.46 => ( ! [K3: int] :
% 5.15/5.46 ( ( P @ K3 )
% 5.15/5.46 => ( ( K3 != zero_zero_int )
% 5.15/5.46 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.46 => ( ! [K3: int] :
% 5.15/5.46 ( ( P @ K3 )
% 5.15/5.46 => ( ( K3
% 5.15/5.46 != ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.46 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.15/5.46 => ( P @ K ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % int_bit_induct
% 5.15/5.46 thf(fact_5589_signed__take__bit__int__greater__eq,axiom,
% 5.15/5.46 ! [K: int,N2: nat] :
% 5.15/5.46 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.46 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % signed_take_bit_int_greater_eq
% 5.15/5.46 thf(fact_5590_exp__div__exp__eq,axiom,
% 5.15/5.46 ! [M: nat,N2: nat] :
% 5.15/5.46 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.46 = ( times_times_nat
% 5.15/5.46 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.46 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.15/5.46 != zero_zero_nat )
% 5.15/5.46 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.15/5.46 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % exp_div_exp_eq
% 5.15/5.46 thf(fact_5591_exp__div__exp__eq,axiom,
% 5.15/5.46 ! [M: nat,N2: nat] :
% 5.15/5.46 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.46 = ( times_times_int
% 5.15/5.46 @ ( zero_n2684676970156552555ol_int
% 5.15/5.46 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.15/5.46 != zero_zero_int )
% 5.15/5.46 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.15/5.46 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % exp_div_exp_eq
% 5.15/5.46 thf(fact_5592_exp__div__exp__eq,axiom,
% 5.15/5.46 ! [M: nat,N2: nat] :
% 5.15/5.46 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.46 = ( times_3573771949741848930nteger
% 5.15/5.46 @ ( zero_n356916108424825756nteger
% 5.15/5.46 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.15/5.46 != zero_z3403309356797280102nteger )
% 5.15/5.46 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.15/5.46 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % exp_div_exp_eq
% 5.15/5.46 thf(fact_5593_vebt__buildup_Osimps_I3_J,axiom,
% 5.15/5.46 ! [Va: nat] :
% 5.15/5.46 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.15/5.46 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.15/5.46 = ( 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 ) ) ) ) ) ) )
% 5.15/5.46 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.15/5.46 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.15/5.46 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % vebt_buildup.simps(3)
% 5.15/5.46 thf(fact_5594_one__div__minus__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % one_div_minus_numeral
% 5.15/5.46 thf(fact_5595_minus__one__div__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % minus_one_div_numeral
% 5.15/5.46 thf(fact_5596_numeral__div__minus__numeral,axiom,
% 5.15/5.46 ! [M: num,N2: num] :
% 5.15/5.46 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_div_minus_numeral
% 5.15/5.46 thf(fact_5597_minus__numeral__div__numeral,axiom,
% 5.15/5.46 ! [M: num,N2: num] :
% 5.15/5.46 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % minus_numeral_div_numeral
% 5.15/5.46 thf(fact_5598_dbl__dec__simps_I4_J,axiom,
% 5.15/5.46 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(4)
% 5.15/5.46 thf(fact_5599_dbl__dec__simps_I4_J,axiom,
% 5.15/5.46 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.46 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(4)
% 5.15/5.46 thf(fact_5600_dbl__dec__simps_I4_J,axiom,
% 5.15/5.46 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.46 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(4)
% 5.15/5.46 thf(fact_5601_dbl__dec__simps_I4_J,axiom,
% 5.15/5.46 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.46 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(4)
% 5.15/5.46 thf(fact_5602_dbl__dec__simps_I4_J,axiom,
% 5.15/5.46 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.46 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(4)
% 5.15/5.46 thf(fact_5603_Divides_Oadjust__div__eq,axiom,
% 5.15/5.46 ! [Q3: int,R2: int] :
% 5.15/5.46 ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.15/5.46 = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % Divides.adjust_div_eq
% 5.15/5.46 thf(fact_5604_of__int__code__if,axiom,
% 5.15/5.46 ( ring_1_of_int_int
% 5.15/5.46 = ( ^ [K2: int] :
% 5.15/5.46 ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 5.15/5.46 @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.15/5.46 @ ( if_int
% 5.15/5.46 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.46 = zero_zero_int )
% 5.15/5.46 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_code_if
% 5.15/5.46 thf(fact_5605_of__int__code__if,axiom,
% 5.15/5.46 ( ring_1_of_int_real
% 5.15/5.46 = ( ^ [K2: int] :
% 5.15/5.46 ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 5.15/5.46 @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 5.15/5.46 @ ( if_real
% 5.15/5.46 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.46 = zero_zero_int )
% 5.15/5.46 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_code_if
% 5.15/5.46 thf(fact_5606_of__int__code__if,axiom,
% 5.15/5.46 ( ring_17405671764205052669omplex
% 5.15/5.46 = ( ^ [K2: int] :
% 5.15/5.46 ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 5.15/5.46 @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 5.15/5.46 @ ( if_complex
% 5.15/5.46 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.46 = zero_zero_int )
% 5.15/5.46 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_code_if
% 5.15/5.46 thf(fact_5607_of__int__code__if,axiom,
% 5.15/5.46 ( ring_1_of_int_rat
% 5.15/5.46 = ( ^ [K2: int] :
% 5.15/5.46 ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 5.15/5.46 @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 5.15/5.46 @ ( if_rat
% 5.15/5.46 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.46 = zero_zero_int )
% 5.15/5.46 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_code_if
% 5.15/5.46 thf(fact_5608_of__int__code__if,axiom,
% 5.15/5.46 ( ring_18347121197199848620nteger
% 5.15/5.46 = ( ^ [K2: int] :
% 5.15/5.46 ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.15/5.46 @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 5.15/5.46 @ ( if_Code_integer
% 5.15/5.46 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.46 = zero_zero_int )
% 5.15/5.46 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_code_if
% 5.15/5.46 thf(fact_5609_split__part,axiom,
% 5.15/5.46 ! [P: $o,Q: int > int > $o] :
% 5.15/5.46 ( ( produc4947309494688390418_int_o
% 5.15/5.46 @ ^ [A3: int,B2: int] :
% 5.15/5.46 ( P
% 5.15/5.46 & ( Q @ A3 @ B2 ) ) )
% 5.15/5.46 = ( ^ [Ab: product_prod_int_int] :
% 5.15/5.46 ( P
% 5.15/5.46 & ( produc4947309494688390418_int_o @ Q @ Ab ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % split_part
% 5.15/5.46 thf(fact_5610_dbl__dec__simps_I3_J,axiom,
% 5.15/5.46 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.15/5.46 = one_one_complex ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(3)
% 5.15/5.46 thf(fact_5611_dbl__dec__simps_I3_J,axiom,
% 5.15/5.46 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.15/5.46 = one_one_real ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(3)
% 5.15/5.46 thf(fact_5612_dbl__dec__simps_I3_J,axiom,
% 5.15/5.46 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.15/5.46 = one_one_rat ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(3)
% 5.15/5.46 thf(fact_5613_dbl__dec__simps_I3_J,axiom,
% 5.15/5.46 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.15/5.46 = one_one_int ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(3)
% 5.15/5.46 thf(fact_5614_of__int__eq__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.15/5.46 = ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.46 = ( Z
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_numeral_iff
% 5.15/5.46 thf(fact_5615_of__int__eq__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ( ring_1_of_int_real @ Z )
% 5.15/5.46 = ( numeral_numeral_real @ N2 ) )
% 5.15/5.46 = ( Z
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_numeral_iff
% 5.15/5.46 thf(fact_5616_of__int__eq__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ( ring_1_of_int_rat @ Z )
% 5.15/5.46 = ( numeral_numeral_rat @ N2 ) )
% 5.15/5.46 = ( Z
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_numeral_iff
% 5.15/5.46 thf(fact_5617_of__int__eq__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ( ring_1_of_int_int @ Z )
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) )
% 5.15/5.46 = ( Z
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_numeral_iff
% 5.15/5.46 thf(fact_5618_of__int__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.15/5.46 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral
% 5.15/5.46 thf(fact_5619_of__int__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.15/5.46 = ( numeral_numeral_real @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral
% 5.15/5.46 thf(fact_5620_of__int__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.15/5.46 = ( numeral_numeral_rat @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral
% 5.15/5.46 thf(fact_5621_of__int__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.15/5.46 = ( numeral_numeral_int @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral
% 5.15/5.46 thf(fact_5622_of__int__le__iff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_iff
% 5.15/5.46 thf(fact_5623_of__int__le__iff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_iff
% 5.15/5.46 thf(fact_5624_of__int__le__iff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_iff
% 5.15/5.46 thf(fact_5625_of__int__less__iff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.46 = ( ord_less_int @ W @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_iff
% 5.15/5.46 thf(fact_5626_of__int__less__iff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.46 = ( ord_less_int @ W @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_iff
% 5.15/5.46 thf(fact_5627_of__int__less__iff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.15/5.46 = ( ord_less_int @ W @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_iff
% 5.15/5.46 thf(fact_5628_of__int__eq__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.15/5.46 = one_one_complex )
% 5.15/5.46 = ( Z = one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_1_iff
% 5.15/5.46 thf(fact_5629_of__int__eq__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ( ring_1_of_int_int @ Z )
% 5.15/5.46 = one_one_int )
% 5.15/5.46 = ( Z = one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_1_iff
% 5.15/5.46 thf(fact_5630_of__int__eq__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ( ring_1_of_int_real @ Z )
% 5.15/5.46 = one_one_real )
% 5.15/5.46 = ( Z = one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_1_iff
% 5.15/5.46 thf(fact_5631_of__int__eq__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ( ring_1_of_int_rat @ Z )
% 5.15/5.46 = one_one_rat )
% 5.15/5.46 = ( Z = one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_1_iff
% 5.15/5.46 thf(fact_5632_of__int__1,axiom,
% 5.15/5.46 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.15/5.46 = one_one_complex ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1
% 5.15/5.46 thf(fact_5633_of__int__1,axiom,
% 5.15/5.46 ( ( ring_1_of_int_int @ one_one_int )
% 5.15/5.46 = one_one_int ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1
% 5.15/5.46 thf(fact_5634_of__int__1,axiom,
% 5.15/5.46 ( ( ring_1_of_int_real @ one_one_int )
% 5.15/5.46 = one_one_real ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1
% 5.15/5.46 thf(fact_5635_of__int__1,axiom,
% 5.15/5.46 ( ( ring_1_of_int_rat @ one_one_int )
% 5.15/5.46 = one_one_rat ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1
% 5.15/5.46 thf(fact_5636_of__int__mult,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.15/5.46 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_mult
% 5.15/5.46 thf(fact_5637_of__int__mult,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.15/5.46 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_mult
% 5.15/5.46 thf(fact_5638_of__int__mult,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.15/5.46 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_mult
% 5.15/5.46 thf(fact_5639_of__int__add,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.15/5.46 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_add
% 5.15/5.46 thf(fact_5640_of__int__add,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 5.15/5.46 = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_add
% 5.15/5.46 thf(fact_5641_of__int__add,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.15/5.46 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_add
% 5.15/5.46 thf(fact_5642_of__int__add,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.15/5.46 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_add
% 5.15/5.46 thf(fact_5643_of__int__diff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 5.15/5.46 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_diff
% 5.15/5.46 thf(fact_5644_of__int__diff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 5.15/5.46 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_diff
% 5.15/5.46 thf(fact_5645_of__int__diff,axiom,
% 5.15/5.46 ! [W: int,Z: int] :
% 5.15/5.46 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 5.15/5.46 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_diff
% 5.15/5.46 thf(fact_5646_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_rat @ X )
% 5.15/5.46 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.15/5.46 = ( X
% 5.15/5.46 = ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5647_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_real @ X )
% 5.15/5.46 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.15/5.46 = ( X
% 5.15/5.46 = ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5648_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ( ring_17405671764205052669omplex @ X )
% 5.15/5.46 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.15/5.46 = ( X
% 5.15/5.46 = ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5649_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_int @ X )
% 5.15/5.46 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.15/5.46 = ( X
% 5.15/5.46 = ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5650_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.15/5.46 = ( ring_1_of_int_rat @ X ) )
% 5.15/5.46 = ( ( power_power_int @ B @ W )
% 5.15/5.46 = X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5651_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.15/5.46 = ( ring_1_of_int_real @ X ) )
% 5.15/5.46 = ( ( power_power_int @ B @ W )
% 5.15/5.46 = X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5652_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.15/5.46 = ( ring_17405671764205052669omplex @ X ) )
% 5.15/5.46 = ( ( power_power_int @ B @ W )
% 5.15/5.46 = X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5653_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.15/5.46 = ( ring_1_of_int_int @ X ) )
% 5.15/5.46 = ( ( power_power_int @ B @ W )
% 5.15/5.46 = X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5654_of__int__power,axiom,
% 5.15/5.46 ! [Z: int,N2: nat] :
% 5.15/5.46 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N2 ) )
% 5.15/5.46 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power
% 5.15/5.46 thf(fact_5655_of__int__power,axiom,
% 5.15/5.46 ! [Z: int,N2: nat] :
% 5.15/5.46 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N2 ) )
% 5.15/5.46 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power
% 5.15/5.46 thf(fact_5656_of__int__power,axiom,
% 5.15/5.46 ! [Z: int,N2: nat] :
% 5.15/5.46 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N2 ) )
% 5.15/5.46 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power
% 5.15/5.46 thf(fact_5657_of__int__power,axiom,
% 5.15/5.46 ! [Z: int,N2: nat] :
% 5.15/5.46 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N2 ) )
% 5.15/5.46 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power
% 5.15/5.46 thf(fact_5658_dbl__dec__simps_I5_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.15/5.46 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(5)
% 5.15/5.46 thf(fact_5659_dbl__dec__simps_I5_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.15/5.46 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(5)
% 5.15/5.46 thf(fact_5660_dbl__dec__simps_I5_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.15/5.46 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(5)
% 5.15/5.46 thf(fact_5661_dbl__dec__simps_I5_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.15/5.46 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(5)
% 5.15/5.46 thf(fact_5662_dbl__dec__simps_I2_J,axiom,
% 5.15/5.46 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.15/5.46 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(2)
% 5.15/5.46 thf(fact_5663_dbl__dec__simps_I2_J,axiom,
% 5.15/5.46 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.15/5.46 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(2)
% 5.15/5.46 thf(fact_5664_dbl__dec__simps_I2_J,axiom,
% 5.15/5.46 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.15/5.46 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(2)
% 5.15/5.46 thf(fact_5665_dbl__dec__simps_I2_J,axiom,
% 5.15/5.46 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.15/5.46 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(2)
% 5.15/5.46 thf(fact_5666_dbl__dec__simps_I2_J,axiom,
% 5.15/5.46 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.15/5.46 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(2)
% 5.15/5.46 thf(fact_5667_dbl__inc__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_inc_simps(1)
% 5.15/5.46 thf(fact_5668_dbl__inc__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_inc_simps(1)
% 5.15/5.46 thf(fact_5669_dbl__inc__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.15/5.46 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_inc_simps(1)
% 5.15/5.46 thf(fact_5670_dbl__inc__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_inc_simps(1)
% 5.15/5.46 thf(fact_5671_dbl__inc__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.15/5.46 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_inc_simps(1)
% 5.15/5.46 thf(fact_5672_dbl__dec__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(1)
% 5.15/5.46 thf(fact_5673_dbl__dec__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(1)
% 5.15/5.46 thf(fact_5674_dbl__dec__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.15/5.46 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(1)
% 5.15/5.46 thf(fact_5675_dbl__dec__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(1)
% 5.15/5.46 thf(fact_5676_dbl__dec__simps_I1_J,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.15/5.46 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_simps(1)
% 5.15/5.46 thf(fact_5677_of__int__0__le__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_0_le_iff
% 5.15/5.46 thf(fact_5678_of__int__0__le__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_0_le_iff
% 5.15/5.46 thf(fact_5679_of__int__0__le__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_0_le_iff
% 5.15/5.46 thf(fact_5680_of__int__le__0__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_0_iff
% 5.15/5.46 thf(fact_5681_of__int__le__0__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_0_iff
% 5.15/5.46 thf(fact_5682_of__int__le__0__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_0_iff
% 5.15/5.46 thf(fact_5683_of__int__0__less__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.46 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_0_less_iff
% 5.15/5.46 thf(fact_5684_of__int__0__less__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.46 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_0_less_iff
% 5.15/5.46 thf(fact_5685_of__int__0__less__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.15/5.46 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_0_less_iff
% 5.15/5.46 thf(fact_5686_of__int__less__0__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.15/5.46 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_0_iff
% 5.15/5.46 thf(fact_5687_of__int__less__0__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.15/5.46 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_0_iff
% 5.15/5.46 thf(fact_5688_of__int__less__0__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.15/5.46 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_0_iff
% 5.15/5.46 thf(fact_5689_of__int__le__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_numeral_iff
% 5.15/5.46 thf(fact_5690_of__int__le__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_numeral_iff
% 5.15/5.46 thf(fact_5691_of__int__le__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_numeral_iff
% 5.15/5.46 thf(fact_5692_of__int__numeral__le__iff,axiom,
% 5.15/5.46 ! [N2: num,Z: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral_le_iff
% 5.15/5.46 thf(fact_5693_of__int__numeral__le__iff,axiom,
% 5.15/5.46 ! [N2: num,Z: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral_le_iff
% 5.15/5.46 thf(fact_5694_of__int__numeral__le__iff,axiom,
% 5.15/5.46 ! [N2: num,Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral_le_iff
% 5.15/5.46 thf(fact_5695_of__int__numeral__less__iff,axiom,
% 5.15/5.46 ! [N2: num,Z: int] :
% 5.15/5.46 ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.46 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral_less_iff
% 5.15/5.46 thf(fact_5696_of__int__numeral__less__iff,axiom,
% 5.15/5.46 ! [N2: num,Z: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.46 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral_less_iff
% 5.15/5.46 thf(fact_5697_of__int__numeral__less__iff,axiom,
% 5.15/5.46 ! [N2: num,Z: int] :
% 5.15/5.46 ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.15/5.46 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_numeral_less_iff
% 5.15/5.46 thf(fact_5698_of__int__less__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_numeral_iff
% 5.15/5.46 thf(fact_5699_of__int__less__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_numeral_iff
% 5.15/5.46 thf(fact_5700_of__int__less__numeral__iff,axiom,
% 5.15/5.46 ! [Z: int,N2: num] :
% 5.15/5.46 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_numeral_iff
% 5.15/5.46 thf(fact_5701_of__int__1__le__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1_le_iff
% 5.15/5.46 thf(fact_5702_of__int__1__le__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1_le_iff
% 5.15/5.46 thf(fact_5703_of__int__1__le__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.15/5.46 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1_le_iff
% 5.15/5.46 thf(fact_5704_of__int__le__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_1_iff
% 5.15/5.46 thf(fact_5705_of__int__le__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_1_iff
% 5.15/5.46 thf(fact_5706_of__int__le__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.15/5.46 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_1_iff
% 5.15/5.46 thf(fact_5707_of__int__less__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.15/5.46 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_1_iff
% 5.15/5.46 thf(fact_5708_of__int__less__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.15/5.46 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_1_iff
% 5.15/5.46 thf(fact_5709_of__int__less__1__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.15/5.46 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_1_iff
% 5.15/5.46 thf(fact_5710_of__int__1__less__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.46 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1_less_iff
% 5.15/5.46 thf(fact_5711_of__int__1__less__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.46 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1_less_iff
% 5.15/5.46 thf(fact_5712_of__int__1__less__iff,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.15/5.46 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_1_less_iff
% 5.15/5.46 thf(fact_5713_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 )
% 5.15/5.46 = ( ring_17405671764205052669omplex @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5714_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 )
% 5.15/5.46 = ( ring_1_of_int_real @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5715_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 )
% 5.15/5.46 = ( ring_1_of_int_rat @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5716_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.15/5.46 = ( ring_1_of_int_int @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5717_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.15/5.46 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5718_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_real @ Y )
% 5.15/5.46 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5719_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_rat @ Y )
% 5.15/5.46 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5720_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_int @ Y )
% 5.15/5.46 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5721_of__int__le__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5722_of__int__le__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5723_of__int__le__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5724_of__int__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.15/5.46 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5725_of__int__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.15/5.46 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5726_of__int__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.15/5.46 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5727_of__int__less__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5728_of__int__less__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5729_of__int__less__of__int__power__cancel__iff,axiom,
% 5.15/5.46 ! [B: int,W: nat,X: int] :
% 5.15/5.46 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_of_int_power_cancel_iff
% 5.15/5.46 thf(fact_5730_of__int__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.15/5.46 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5731_of__int__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.15/5.46 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5732_of__int__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: int,B: int,W: nat] :
% 5.15/5.46 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.15/5.46 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5733_numeral__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5734_numeral__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5735_numeral__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5736_of__int__le__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5737_of__int__le__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5738_of__int__le__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5739_of__int__less__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5740_of__int__less__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5741_of__int__less__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5742_numeral__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5743_numeral__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5744_numeral__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % numeral_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5745_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.15/5.46 = ( ring_1_of_int_int @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5746_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 )
% 5.15/5.46 = ( ring_1_of_int_real @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5747_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N2 )
% 5.15/5.46 = ( ring_17405671764205052669omplex @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5748_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 )
% 5.15/5.46 = ( ring_1_of_int_rat @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5749_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,Y: int] :
% 5.15/5.46 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 )
% 5.15/5.46 = ( ring_18347121197199848620nteger @ Y ) )
% 5.15/5.46 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 )
% 5.15/5.46 = Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_eq_of_int_cancel_iff
% 5.15/5.46 thf(fact_5750_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_int @ Y )
% 5.15/5.46 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5751_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_real @ Y )
% 5.15/5.46 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5752_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.15/5.46 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5753_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_1_of_int_rat @ Y )
% 5.15/5.46 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5754_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [Y: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ( ring_18347121197199848620nteger @ Y )
% 5.15/5.46 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 5.15/5.46 = ( Y
% 5.15/5.46 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_eq_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5755_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5756_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5757_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5758_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_le_of_int_cancel_iff
% 5.15/5.46 thf(fact_5759_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5760_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5761_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5762_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 5.15/5.46 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_le_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5763_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5764_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5765_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5766_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.15/5.46 ! [X: num,N2: nat,A: int] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.15/5.46 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % neg_numeral_power_less_of_int_cancel_iff
% 5.15/5.46 thf(fact_5767_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5768_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5769_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5770_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.15/5.46 ! [A: int,X: num,N2: nat] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 5.15/5.46 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_less_neg_numeral_power_cancel_iff
% 5.15/5.46 thf(fact_5771_prod_Odisc__eq__case,axiom,
% 5.15/5.46 ! [Prod: product_prod_int_int] :
% 5.15/5.46 ( produc4947309494688390418_int_o
% 5.15/5.46 @ ^ [Uu3: int,Uv3: int] : $true
% 5.15/5.46 @ Prod ) ).
% 5.15/5.46
% 5.15/5.46 % prod.disc_eq_case
% 5.15/5.46 thf(fact_5772_mult__of__int__commute,axiom,
% 5.15/5.46 ! [X: int,Y: real] :
% 5.15/5.46 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y )
% 5.15/5.46 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % mult_of_int_commute
% 5.15/5.46 thf(fact_5773_mult__of__int__commute,axiom,
% 5.15/5.46 ! [X: int,Y: rat] :
% 5.15/5.46 ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y )
% 5.15/5.46 = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % mult_of_int_commute
% 5.15/5.46 thf(fact_5774_mult__of__int__commute,axiom,
% 5.15/5.46 ! [X: int,Y: int] :
% 5.15/5.46 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 5.15/5.46 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % mult_of_int_commute
% 5.15/5.46 thf(fact_5775_real__of__int__div4,axiom,
% 5.15/5.46 ! [N2: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % real_of_int_div4
% 5.15/5.46 thf(fact_5776_real__of__int__div,axiom,
% 5.15/5.46 ! [D: int,N2: int] :
% 5.15/5.46 ( ( dvd_dvd_int @ D @ N2 )
% 5.15/5.46 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ D ) )
% 5.15/5.46 = ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % real_of_int_div
% 5.15/5.46 thf(fact_5777_of__int__nonneg,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_nonneg
% 5.15/5.46 thf(fact_5778_of__int__nonneg,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_nonneg
% 5.15/5.46 thf(fact_5779_of__int__nonneg,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.15/5.46 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_nonneg
% 5.15/5.46 thf(fact_5780_of__int__pos,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.15/5.46 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_pos
% 5.15/5.46 thf(fact_5781_of__int__pos,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.15/5.46 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_pos
% 5.15/5.46 thf(fact_5782_of__int__pos,axiom,
% 5.15/5.46 ! [Z: int] :
% 5.15/5.46 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.15/5.46 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_pos
% 5.15/5.46 thf(fact_5783_of__int__neg__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_neg_numeral
% 5.15/5.46 thf(fact_5784_of__int__neg__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_neg_numeral
% 5.15/5.46 thf(fact_5785_of__int__neg__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.46 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_neg_numeral
% 5.15/5.46 thf(fact_5786_of__int__neg__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.46 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_neg_numeral
% 5.15/5.46 thf(fact_5787_of__int__neg__numeral,axiom,
% 5.15/5.46 ! [K: num] :
% 5.15/5.46 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.46 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_neg_numeral
% 5.15/5.46 thf(fact_5788_int__le__real__less,axiom,
% 5.15/5.46 ( ord_less_eq_int
% 5.15/5.46 = ( ^ [N3: int,M5: int] : ( ord_less_real @ ( ring_1_of_int_real @ N3 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M5 ) @ one_one_real ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % int_le_real_less
% 5.15/5.46 thf(fact_5789_int__less__real__le,axiom,
% 5.15/5.46 ( ord_less_int
% 5.15/5.46 = ( ^ [N3: int,M5: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N3 ) @ one_one_real ) @ ( ring_1_of_int_real @ M5 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % int_less_real_le
% 5.15/5.46 thf(fact_5790_real__of__int__div__aux,axiom,
% 5.15/5.46 ! [X: int,D: int] :
% 5.15/5.46 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 5.15/5.46 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % real_of_int_div_aux
% 5.15/5.46 thf(fact_5791_real__of__int__div2,axiom,
% 5.15/5.46 ! [N2: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % real_of_int_div2
% 5.15/5.46 thf(fact_5792_real__of__int__div3,axiom,
% 5.15/5.46 ! [N2: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) ) @ one_one_real ) ).
% 5.15/5.46
% 5.15/5.46 % real_of_int_div3
% 5.15/5.46 thf(fact_5793_Divides_Oadjust__div__def,axiom,
% 5.15/5.46 ( adjust_div
% 5.15/5.46 = ( produc8211389475949308722nt_int
% 5.15/5.46 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % Divides.adjust_div_def
% 5.15/5.46 thf(fact_5794_even__of__int__iff,axiom,
% 5.15/5.46 ! [K: int] :
% 5.15/5.46 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.15/5.46 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % even_of_int_iff
% 5.15/5.46 thf(fact_5795_even__of__int__iff,axiom,
% 5.15/5.46 ! [K: int] :
% 5.15/5.46 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.15/5.46 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % even_of_int_iff
% 5.15/5.46 thf(fact_5796_dbl__dec__def,axiom,
% 5.15/5.46 ( neg_nu6511756317524482435omplex
% 5.15/5.46 = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_def
% 5.15/5.46 thf(fact_5797_dbl__dec__def,axiom,
% 5.15/5.46 ( neg_nu6075765906172075777c_real
% 5.15/5.46 = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_def
% 5.15/5.46 thf(fact_5798_dbl__dec__def,axiom,
% 5.15/5.46 ( neg_nu3179335615603231917ec_rat
% 5.15/5.46 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_def
% 5.15/5.46 thf(fact_5799_dbl__dec__def,axiom,
% 5.15/5.46 ( neg_nu3811975205180677377ec_int
% 5.15/5.46 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % dbl_dec_def
% 5.15/5.46 thf(fact_5800_floor__exists,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ? [Z2: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X )
% 5.15/5.46 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % floor_exists
% 5.15/5.46 thf(fact_5801_floor__exists,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ? [Z2: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 5.15/5.46 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % floor_exists
% 5.15/5.46 thf(fact_5802_floor__exists1,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ? [X3: int] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X )
% 5.15/5.46 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.15/5.46 & ! [Y4: int] :
% 5.15/5.46 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X )
% 5.15/5.46 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.15/5.46 => ( Y4 = X3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % floor_exists1
% 5.15/5.46 thf(fact_5803_floor__exists1,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ? [X3: int] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 5.15/5.46 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.15/5.46 & ! [Y4: int] :
% 5.15/5.46 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X )
% 5.15/5.46 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.15/5.46 => ( Y4 = X3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % floor_exists1
% 5.15/5.46 thf(fact_5804_ln__one__minus__pos__lower__bound,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.46 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_one_minus_pos_lower_bound
% 5.15/5.46 thf(fact_5805_vebt__buildup_Opelims,axiom,
% 5.15/5.46 ! [X: nat,Y: vEBT_VEBT] :
% 5.15/5.46 ( ( ( vEBT_vebt_buildup @ X )
% 5.15/5.46 = Y )
% 5.15/5.46 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.15/5.46 => ( ( ( X = zero_zero_nat )
% 5.15/5.46 => ( ( Y
% 5.15/5.46 = ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.46 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.15/5.46 => ( ( ( X
% 5.15/5.46 = ( suc @ zero_zero_nat ) )
% 5.15/5.46 => ( ( Y
% 5.15/5.46 = ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.46 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.15/5.46 => ~ ! [Va3: nat] :
% 5.15/5.46 ( ( X
% 5.15/5.46 = ( suc @ ( suc @ Va3 ) ) )
% 5.15/5.46 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.15/5.46 => ( Y
% 5.15/5.46 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.15/5.46 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.15/5.46 => ( Y
% 5.15/5.46 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.15/5.46 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va3 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % vebt_buildup.pelims
% 5.15/5.46 thf(fact_5806_int__ge__less__than__def,axiom,
% 5.15/5.46 ( int_ge_less_than
% 5.15/5.46 = ( ^ [D2: int] :
% 5.15/5.46 ( collec213857154873943460nt_int
% 5.15/5.46 @ ( produc4947309494688390418_int_o
% 5.15/5.46 @ ^ [Z6: int,Z3: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ D2 @ Z6 )
% 5.15/5.46 & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % int_ge_less_than_def
% 5.15/5.46 thf(fact_5807_int__ge__less__than2__def,axiom,
% 5.15/5.46 ( int_ge_less_than2
% 5.15/5.46 = ( ^ [D2: int] :
% 5.15/5.46 ( collec213857154873943460nt_int
% 5.15/5.46 @ ( produc4947309494688390418_int_o
% 5.15/5.46 @ ^ [Z6: int,Z3: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ D2 @ Z3 )
% 5.15/5.46 & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % int_ge_less_than2_def
% 5.15/5.46 thf(fact_5808_ln__one,axiom,
% 5.15/5.46 ( ( ln_ln_real @ one_one_real )
% 5.15/5.46 = zero_zero_real ) ).
% 5.15/5.46
% 5.15/5.46 % ln_one
% 5.15/5.46 thf(fact_5809_ln__less__cancel__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.46 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.15/5.46 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_less_cancel_iff
% 5.15/5.46 thf(fact_5810_ln__inj__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.46 => ( ( ( ln_ln_real @ X )
% 5.15/5.46 = ( ln_ln_real @ Y ) )
% 5.15/5.46 = ( X = Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_inj_iff
% 5.15/5.46 thf(fact_5811_ln__le__cancel__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.46 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.15/5.46 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_le_cancel_iff
% 5.15/5.46 thf(fact_5812_ln__less__zero__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.15/5.46 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_less_zero_iff
% 5.15/5.46 thf(fact_5813_ln__gt__zero__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.15/5.46 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_gt_zero_iff
% 5.15/5.46 thf(fact_5814_ln__eq__zero__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ( ln_ln_real @ X )
% 5.15/5.46 = zero_zero_real )
% 5.15/5.46 = ( X = one_one_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_eq_zero_iff
% 5.15/5.46 thf(fact_5815_ln__le__zero__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.15/5.46 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_le_zero_iff
% 5.15/5.46 thf(fact_5816_ln__ge__zero__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.15/5.46 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_ge_zero_iff
% 5.15/5.46 thf(fact_5817_ln__less__self,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_less_self
% 5.15/5.46 thf(fact_5818_ln__bound,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_bound
% 5.15/5.46 thf(fact_5819_ln__gt__zero__imp__gt__one,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_gt_zero_imp_gt_one
% 5.15/5.46 thf(fact_5820_ln__less__zero,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.46 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_less_zero
% 5.15/5.46 thf(fact_5821_ln__gt__zero,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.46 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_gt_zero
% 5.15/5.46 thf(fact_5822_ln__ge__zero,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_ge_zero
% 5.15/5.46 thf(fact_5823_ln__ge__zero__imp__ge__one,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_ge_zero_imp_ge_one
% 5.15/5.46 thf(fact_5824_ln__add__one__self__le__self,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_add_one_self_le_self
% 5.15/5.46 thf(fact_5825_ln__mult,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.46 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 5.15/5.46 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_mult
% 5.15/5.46 thf(fact_5826_ln__eq__minus__one,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ( ln_ln_real @ X )
% 5.15/5.46 = ( minus_minus_real @ X @ one_one_real ) )
% 5.15/5.46 => ( X = one_one_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_eq_minus_one
% 5.15/5.46 thf(fact_5827_ln__div,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.46 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.46 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_div
% 5.15/5.46 thf(fact_5828_ln__2__less__1,axiom,
% 5.15/5.46 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.15/5.46
% 5.15/5.46 % ln_2_less_1
% 5.15/5.46 thf(fact_5829_ln__le__minus__one,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_le_minus_one
% 5.15/5.46 thf(fact_5830_ln__diff__le,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.46 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_diff_le
% 5.15/5.46 thf(fact_5831_ln__add__one__self__le__self2,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.46 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_add_one_self_le_self2
% 5.15/5.46 thf(fact_5832_ln__one__minus__pos__upper__bound,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.46 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_one_minus_pos_upper_bound
% 5.15/5.46 thf(fact_5833_exists__least__lemma,axiom,
% 5.15/5.46 ! [P: nat > $o] :
% 5.15/5.46 ( ~ ( P @ zero_zero_nat )
% 5.15/5.46 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.15/5.46 => ? [N: nat] :
% 5.15/5.46 ( ~ ( P @ N )
% 5.15/5.46 & ( P @ ( suc @ N ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % exists_least_lemma
% 5.15/5.46 thf(fact_5834_ex__le__of__int,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ? [Z2: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % ex_le_of_int
% 5.15/5.46 thf(fact_5835_ex__le__of__int,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ? [Z2: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % ex_le_of_int
% 5.15/5.46 thf(fact_5836_ex__of__int__less,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X ) ).
% 5.15/5.46
% 5.15/5.46 % ex_of_int_less
% 5.15/5.46 thf(fact_5837_ex__of__int__less,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X ) ).
% 5.15/5.46
% 5.15/5.46 % ex_of_int_less
% 5.15/5.46 thf(fact_5838_ex__less__of__int,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ? [Z2: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % ex_less_of_int
% 5.15/5.46 thf(fact_5839_ex__less__of__int,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ? [Z2: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % ex_less_of_int
% 5.15/5.46 thf(fact_5840_ln__one__plus__pos__lower__bound,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.46 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % ln_one_plus_pos_lower_bound
% 5.15/5.46 thf(fact_5841_artanh__def,axiom,
% 5.15/5.46 ( artanh_real
% 5.15/5.46 = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % artanh_def
% 5.15/5.46 thf(fact_5842_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.46 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.15/5.46 thf(fact_5843_round__unique,axiom,
% 5.15/5.46 ! [X: real,Y: int] :
% 5.15/5.46 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 5.15/5.46 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 => ( ( archim8280529875227126926d_real @ X )
% 5.15/5.46 = Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_unique
% 5.15/5.46 thf(fact_5844_round__unique,axiom,
% 5.15/5.46 ! [X: rat,Y: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 5.15/5.46 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 => ( ( archim7778729529865785530nd_rat @ X )
% 5.15/5.46 = Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_unique
% 5.15/5.46 thf(fact_5845_tanh__ln__real,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 5.15/5.46 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_ln_real
% 5.15/5.46 thf(fact_5846_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ln_one_plus_x_minus_x_bound
% 5.15/5.46 thf(fact_5847_of__int__round__gt,axiom,
% 5.15/5.46 ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_round_gt
% 5.15/5.46 thf(fact_5848_of__int__round__gt,axiom,
% 5.15/5.46 ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_round_gt
% 5.15/5.46 thf(fact_5849_abs__idempotent,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.15/5.46 = ( abs_abs_real @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_idempotent
% 5.15/5.46 thf(fact_5850_abs__idempotent,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.15/5.46 = ( abs_abs_int @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_idempotent
% 5.15/5.46 thf(fact_5851_abs__idempotent,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.15/5.46 = ( abs_abs_rat @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_idempotent
% 5.15/5.46 thf(fact_5852_abs__idempotent,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.15/5.46 = ( abs_abs_Code_integer @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_idempotent
% 5.15/5.46 thf(fact_5853_abs__abs,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.15/5.46 = ( abs_abs_real @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_abs
% 5.15/5.46 thf(fact_5854_abs__abs,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.15/5.46 = ( abs_abs_int @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_abs
% 5.15/5.46 thf(fact_5855_abs__abs,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.15/5.46 = ( abs_abs_rat @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_abs
% 5.15/5.46 thf(fact_5856_abs__abs,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.15/5.46 = ( abs_abs_Code_integer @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_abs
% 5.15/5.46 thf(fact_5857_abs__zero,axiom,
% 5.15/5.46 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.15/5.46 = zero_z3403309356797280102nteger ) ).
% 5.15/5.46
% 5.15/5.46 % abs_zero
% 5.15/5.46 thf(fact_5858_abs__zero,axiom,
% 5.15/5.46 ( ( abs_abs_real @ zero_zero_real )
% 5.15/5.46 = zero_zero_real ) ).
% 5.15/5.46
% 5.15/5.46 % abs_zero
% 5.15/5.46 thf(fact_5859_abs__zero,axiom,
% 5.15/5.46 ( ( abs_abs_rat @ zero_zero_rat )
% 5.15/5.46 = zero_zero_rat ) ).
% 5.15/5.46
% 5.15/5.46 % abs_zero
% 5.15/5.46 thf(fact_5860_abs__zero,axiom,
% 5.15/5.46 ( ( abs_abs_int @ zero_zero_int )
% 5.15/5.46 = zero_zero_int ) ).
% 5.15/5.46
% 5.15/5.46 % abs_zero
% 5.15/5.46 thf(fact_5861_abs__eq__0,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ( abs_abs_Code_integer @ A )
% 5.15/5.46 = zero_z3403309356797280102nteger )
% 5.15/5.46 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0
% 5.15/5.46 thf(fact_5862_abs__eq__0,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ( abs_abs_real @ A )
% 5.15/5.46 = zero_zero_real )
% 5.15/5.46 = ( A = zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0
% 5.15/5.46 thf(fact_5863_abs__eq__0,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ( abs_abs_rat @ A )
% 5.15/5.46 = zero_zero_rat )
% 5.15/5.46 = ( A = zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0
% 5.15/5.46 thf(fact_5864_abs__eq__0,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ( abs_abs_int @ A )
% 5.15/5.46 = zero_zero_int )
% 5.15/5.46 = ( A = zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0
% 5.15/5.46 thf(fact_5865_abs__0__eq,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( zero_z3403309356797280102nteger
% 5.15/5.46 = ( abs_abs_Code_integer @ A ) )
% 5.15/5.46 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0_eq
% 5.15/5.46 thf(fact_5866_abs__0__eq,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( zero_zero_real
% 5.15/5.46 = ( abs_abs_real @ A ) )
% 5.15/5.46 = ( A = zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0_eq
% 5.15/5.46 thf(fact_5867_abs__0__eq,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( zero_zero_rat
% 5.15/5.46 = ( abs_abs_rat @ A ) )
% 5.15/5.46 = ( A = zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0_eq
% 5.15/5.46 thf(fact_5868_abs__0__eq,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( zero_zero_int
% 5.15/5.46 = ( abs_abs_int @ A ) )
% 5.15/5.46 = ( A = zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0_eq
% 5.15/5.46 thf(fact_5869_abs__0,axiom,
% 5.15/5.46 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.15/5.46 = zero_z3403309356797280102nteger ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0
% 5.15/5.46 thf(fact_5870_abs__0,axiom,
% 5.15/5.46 ( ( abs_abs_complex @ zero_zero_complex )
% 5.15/5.46 = zero_zero_complex ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0
% 5.15/5.46 thf(fact_5871_abs__0,axiom,
% 5.15/5.46 ( ( abs_abs_real @ zero_zero_real )
% 5.15/5.46 = zero_zero_real ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0
% 5.15/5.46 thf(fact_5872_abs__0,axiom,
% 5.15/5.46 ( ( abs_abs_rat @ zero_zero_rat )
% 5.15/5.46 = zero_zero_rat ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0
% 5.15/5.46 thf(fact_5873_abs__0,axiom,
% 5.15/5.46 ( ( abs_abs_int @ zero_zero_int )
% 5.15/5.46 = zero_zero_int ) ).
% 5.15/5.46
% 5.15/5.46 % abs_0
% 5.15/5.46 thf(fact_5874_abs__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 5.15/5.46 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_numeral
% 5.15/5.46 thf(fact_5875_abs__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.46 = ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_numeral
% 5.15/5.46 thf(fact_5876_abs__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.46 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_numeral
% 5.15/5.46 thf(fact_5877_abs__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_numeral
% 5.15/5.46 thf(fact_5878_abs__mult__self__eq,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.15/5.46 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_self_eq
% 5.15/5.46 thf(fact_5879_abs__mult__self__eq,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.15/5.46 = ( times_times_real @ A @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_self_eq
% 5.15/5.46 thf(fact_5880_abs__mult__self__eq,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.15/5.46 = ( times_times_rat @ A @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_self_eq
% 5.15/5.46 thf(fact_5881_abs__mult__self__eq,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.15/5.46 = ( times_times_int @ A @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_self_eq
% 5.15/5.46 thf(fact_5882_abs__1,axiom,
% 5.15/5.46 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.15/5.46 = one_one_Code_integer ) ).
% 5.15/5.46
% 5.15/5.46 % abs_1
% 5.15/5.46 thf(fact_5883_abs__1,axiom,
% 5.15/5.46 ( ( abs_abs_complex @ one_one_complex )
% 5.15/5.46 = one_one_complex ) ).
% 5.15/5.46
% 5.15/5.46 % abs_1
% 5.15/5.46 thf(fact_5884_abs__1,axiom,
% 5.15/5.46 ( ( abs_abs_real @ one_one_real )
% 5.15/5.46 = one_one_real ) ).
% 5.15/5.46
% 5.15/5.46 % abs_1
% 5.15/5.46 thf(fact_5885_abs__1,axiom,
% 5.15/5.46 ( ( abs_abs_rat @ one_one_rat )
% 5.15/5.46 = one_one_rat ) ).
% 5.15/5.46
% 5.15/5.46 % abs_1
% 5.15/5.46 thf(fact_5886_abs__1,axiom,
% 5.15/5.46 ( ( abs_abs_int @ one_one_int )
% 5.15/5.46 = one_one_int ) ).
% 5.15/5.46
% 5.15/5.46 % abs_1
% 5.15/5.46 thf(fact_5887_abs__add__abs,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.15/5.46 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_add_abs
% 5.15/5.46 thf(fact_5888_abs__add__abs,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.15/5.46 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_add_abs
% 5.15/5.46 thf(fact_5889_abs__add__abs,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.15/5.46 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_add_abs
% 5.15/5.46 thf(fact_5890_abs__add__abs,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.15/5.46 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_add_abs
% 5.15/5.46 thf(fact_5891_abs__divide,axiom,
% 5.15/5.46 ! [A: complex,B: complex] :
% 5.15/5.46 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.46 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_divide
% 5.15/5.46 thf(fact_5892_abs__divide,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.46 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_divide
% 5.15/5.46 thf(fact_5893_abs__divide,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.15/5.46 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_divide
% 5.15/5.46 thf(fact_5894_abs__minus__cancel,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.15/5.46 = ( abs_abs_int @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_cancel
% 5.15/5.46 thf(fact_5895_abs__minus__cancel,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.15/5.46 = ( abs_abs_real @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_cancel
% 5.15/5.46 thf(fact_5896_abs__minus__cancel,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.15/5.46 = ( abs_abs_rat @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_cancel
% 5.15/5.46 thf(fact_5897_abs__minus__cancel,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.46 = ( abs_abs_Code_integer @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_cancel
% 5.15/5.46 thf(fact_5898_abs__minus,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.15/5.46 = ( abs_abs_int @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus
% 5.15/5.46 thf(fact_5899_abs__minus,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.15/5.46 = ( abs_abs_real @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus
% 5.15/5.46 thf(fact_5900_abs__minus,axiom,
% 5.15/5.46 ! [A: complex] :
% 5.15/5.46 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.15/5.46 = ( abs_abs_complex @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus
% 5.15/5.46 thf(fact_5901_abs__minus,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.15/5.46 = ( abs_abs_rat @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus
% 5.15/5.46 thf(fact_5902_abs__minus,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.15/5.46 = ( abs_abs_Code_integer @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus
% 5.15/5.46 thf(fact_5903_dvd__abs__iff,axiom,
% 5.15/5.46 ! [M: real,K: real] :
% 5.15/5.46 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.15/5.46 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % dvd_abs_iff
% 5.15/5.46 thf(fact_5904_dvd__abs__iff,axiom,
% 5.15/5.46 ! [M: int,K: int] :
% 5.15/5.46 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.15/5.46 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % dvd_abs_iff
% 5.15/5.46 thf(fact_5905_dvd__abs__iff,axiom,
% 5.15/5.46 ! [M: rat,K: rat] :
% 5.15/5.46 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.15/5.46 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % dvd_abs_iff
% 5.15/5.46 thf(fact_5906_dvd__abs__iff,axiom,
% 5.15/5.46 ! [M: code_integer,K: code_integer] :
% 5.15/5.46 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.15/5.46 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % dvd_abs_iff
% 5.15/5.46 thf(fact_5907_abs__dvd__iff,axiom,
% 5.15/5.46 ! [M: real,K: real] :
% 5.15/5.46 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.15/5.46 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_dvd_iff
% 5.15/5.46 thf(fact_5908_abs__dvd__iff,axiom,
% 5.15/5.46 ! [M: int,K: int] :
% 5.15/5.46 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.15/5.46 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_dvd_iff
% 5.15/5.46 thf(fact_5909_abs__dvd__iff,axiom,
% 5.15/5.46 ! [M: rat,K: rat] :
% 5.15/5.46 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.15/5.46 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_dvd_iff
% 5.15/5.46 thf(fact_5910_abs__dvd__iff,axiom,
% 5.15/5.46 ! [M: code_integer,K: code_integer] :
% 5.15/5.46 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.15/5.46 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_dvd_iff
% 5.15/5.46 thf(fact_5911_abs__bool__eq,axiom,
% 5.15/5.46 ! [P: $o] :
% 5.15/5.46 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.15/5.46 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_bool_eq
% 5.15/5.46 thf(fact_5912_abs__bool__eq,axiom,
% 5.15/5.46 ! [P: $o] :
% 5.15/5.46 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.15/5.46 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_bool_eq
% 5.15/5.46 thf(fact_5913_abs__bool__eq,axiom,
% 5.15/5.46 ! [P: $o] :
% 5.15/5.46 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.15/5.46 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_bool_eq
% 5.15/5.46 thf(fact_5914_abs__bool__eq,axiom,
% 5.15/5.46 ! [P: $o] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.15/5.46 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_bool_eq
% 5.15/5.46 thf(fact_5915_tanh__real__less__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 5.15/5.46 = ( ord_less_real @ X @ Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_real_less_iff
% 5.15/5.46 thf(fact_5916_tanh__real__le__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 5.15/5.46 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_real_le_iff
% 5.15/5.46 thf(fact_5917_abs__le__zero__iff,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.15/5.46 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_zero_iff
% 5.15/5.46 thf(fact_5918_abs__le__zero__iff,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.15/5.46 = ( A = zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_zero_iff
% 5.15/5.46 thf(fact_5919_abs__le__zero__iff,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.15/5.46 = ( A = zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_zero_iff
% 5.15/5.46 thf(fact_5920_abs__le__zero__iff,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.15/5.46 = ( A = zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_zero_iff
% 5.15/5.46 thf(fact_5921_abs__le__self__iff,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.15/5.46 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_self_iff
% 5.15/5.46 thf(fact_5922_abs__le__self__iff,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.15/5.46 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_self_iff
% 5.15/5.46 thf(fact_5923_abs__le__self__iff,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.15/5.46 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_self_iff
% 5.15/5.46 thf(fact_5924_abs__le__self__iff,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.15/5.46 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_self_iff
% 5.15/5.46 thf(fact_5925_abs__of__nonneg,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.46 => ( ( abs_abs_Code_integer @ A )
% 5.15/5.46 = A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_nonneg
% 5.15/5.46 thf(fact_5926_abs__of__nonneg,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.46 => ( ( abs_abs_real @ A )
% 5.15/5.46 = A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_nonneg
% 5.15/5.46 thf(fact_5927_abs__of__nonneg,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.46 => ( ( abs_abs_rat @ A )
% 5.15/5.46 = A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_nonneg
% 5.15/5.46 thf(fact_5928_abs__of__nonneg,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.46 => ( ( abs_abs_int @ A )
% 5.15/5.46 = A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_nonneg
% 5.15/5.46 thf(fact_5929_zero__less__abs__iff,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.15/5.46 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_abs_iff
% 5.15/5.46 thf(fact_5930_zero__less__abs__iff,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.15/5.46 = ( A != zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_abs_iff
% 5.15/5.46 thf(fact_5931_zero__less__abs__iff,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.15/5.46 = ( A != zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_abs_iff
% 5.15/5.46 thf(fact_5932_zero__less__abs__iff,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.15/5.46 = ( A != zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_abs_iff
% 5.15/5.46 thf(fact_5933_abs__neg__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_neg_numeral
% 5.15/5.46 thf(fact_5934_abs__neg__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.46 = ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_neg_numeral
% 5.15/5.46 thf(fact_5935_abs__neg__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.46 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_neg_numeral
% 5.15/5.46 thf(fact_5936_abs__neg__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.46 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_neg_numeral
% 5.15/5.46 thf(fact_5937_abs__neg__one,axiom,
% 5.15/5.46 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.46 = one_one_int ) ).
% 5.15/5.46
% 5.15/5.46 % abs_neg_one
% 5.15/5.46 thf(fact_5938_abs__neg__one,axiom,
% 5.15/5.46 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.46 = one_one_real ) ).
% 5.15/5.46
% 5.15/5.46 % abs_neg_one
% 5.15/5.46 thf(fact_5939_abs__neg__one,axiom,
% 5.15/5.46 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.46 = one_one_rat ) ).
% 5.15/5.46
% 5.15/5.46 % abs_neg_one
% 5.15/5.46 thf(fact_5940_abs__neg__one,axiom,
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.46 = one_one_Code_integer ) ).
% 5.15/5.46
% 5.15/5.46 % abs_neg_one
% 5.15/5.46 thf(fact_5941_abs__power__minus,axiom,
% 5.15/5.46 ! [A: int,N2: nat] :
% 5.15/5.46 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.15/5.46 = ( abs_abs_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_power_minus
% 5.15/5.46 thf(fact_5942_abs__power__minus,axiom,
% 5.15/5.46 ! [A: real,N2: nat] :
% 5.15/5.46 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.15/5.46 = ( abs_abs_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_power_minus
% 5.15/5.46 thf(fact_5943_abs__power__minus,axiom,
% 5.15/5.46 ! [A: rat,N2: nat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.15/5.46 = ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_power_minus
% 5.15/5.46 thf(fact_5944_abs__power__minus,axiom,
% 5.15/5.46 ! [A: code_integer,N2: nat] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.15/5.46 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_power_minus
% 5.15/5.46 thf(fact_5945_tanh__real__neg__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.15/5.46 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_real_neg_iff
% 5.15/5.46 thf(fact_5946_tanh__real__pos__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.15/5.46 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_real_pos_iff
% 5.15/5.46 thf(fact_5947_tanh__real__nonneg__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.15/5.46 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_real_nonneg_iff
% 5.15/5.46 thf(fact_5948_tanh__real__nonpos__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.15/5.46 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_real_nonpos_iff
% 5.15/5.46 thf(fact_5949_round__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_numeral
% 5.15/5.46 thf(fact_5950_round__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.46 = ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_numeral
% 5.15/5.46 thf(fact_5951_round__1,axiom,
% 5.15/5.46 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.15/5.46 = one_one_int ) ).
% 5.15/5.46
% 5.15/5.46 % round_1
% 5.15/5.46 thf(fact_5952_round__1,axiom,
% 5.15/5.46 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.15/5.46 = one_one_int ) ).
% 5.15/5.46
% 5.15/5.46 % round_1
% 5.15/5.46 thf(fact_5953_divide__le__0__abs__iff,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.15/5.46 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.46 | ( B = zero_zero_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % divide_le_0_abs_iff
% 5.15/5.46 thf(fact_5954_divide__le__0__abs__iff,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.15/5.46 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.46 | ( B = zero_zero_rat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % divide_le_0_abs_iff
% 5.15/5.46 thf(fact_5955_zero__le__divide__abs__iff,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.15/5.46 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.46 | ( B = zero_zero_real ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_le_divide_abs_iff
% 5.15/5.46 thf(fact_5956_zero__le__divide__abs__iff,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.15/5.46 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.46 | ( B = zero_zero_rat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_le_divide_abs_iff
% 5.15/5.46 thf(fact_5957_abs__of__nonpos,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.46 => ( ( abs_abs_real @ A )
% 5.15/5.46 = ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_nonpos
% 5.15/5.46 thf(fact_5958_abs__of__nonpos,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.15/5.46 => ( ( abs_abs_Code_integer @ A )
% 5.15/5.46 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_nonpos
% 5.15/5.46 thf(fact_5959_abs__of__nonpos,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.15/5.46 => ( ( abs_abs_rat @ A )
% 5.15/5.46 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_nonpos
% 5.15/5.46 thf(fact_5960_abs__of__nonpos,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.15/5.46 => ( ( abs_abs_int @ A )
% 5.15/5.46 = ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_nonpos
% 5.15/5.46 thf(fact_5961_artanh__minus__real,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.46 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 5.15/5.46 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % artanh_minus_real
% 5.15/5.46 thf(fact_5962_zero__less__power__abs__iff,axiom,
% 5.15/5.46 ! [A: code_integer,N2: nat] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 5.15/5.46 = ( ( A != zero_z3403309356797280102nteger )
% 5.15/5.46 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_power_abs_iff
% 5.15/5.46 thf(fact_5963_zero__less__power__abs__iff,axiom,
% 5.15/5.46 ! [A: real,N2: nat] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.15/5.46 = ( ( A != zero_zero_real )
% 5.15/5.46 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_power_abs_iff
% 5.15/5.46 thf(fact_5964_zero__less__power__abs__iff,axiom,
% 5.15/5.46 ! [A: rat,N2: nat] :
% 5.15/5.46 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 5.15/5.46 = ( ( A != zero_zero_rat )
% 5.15/5.46 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_power_abs_iff
% 5.15/5.46 thf(fact_5965_zero__less__power__abs__iff,axiom,
% 5.15/5.46 ! [A: int,N2: nat] :
% 5.15/5.46 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 5.15/5.46 = ( ( A != zero_zero_int )
% 5.15/5.46 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_power_abs_iff
% 5.15/5.46 thf(fact_5966_power2__abs,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.46 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power2_abs
% 5.15/5.46 thf(fact_5967_power2__abs,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.46 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power2_abs
% 5.15/5.46 thf(fact_5968_power2__abs,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.46 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power2_abs
% 5.15/5.46 thf(fact_5969_power2__abs,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.46 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power2_abs
% 5.15/5.46 thf(fact_5970_abs__power2,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_power2
% 5.15/5.46 thf(fact_5971_abs__power2,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_power2
% 5.15/5.46 thf(fact_5972_abs__power2,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_power2
% 5.15/5.46 thf(fact_5973_abs__power2,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_power2
% 5.15/5.46 thf(fact_5974_round__neg__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_neg_numeral
% 5.15/5.46 thf(fact_5975_round__neg__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.46 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_neg_numeral
% 5.15/5.46 thf(fact_5976_power__even__abs__numeral,axiom,
% 5.15/5.46 ! [W: num,A: rat] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.46 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.46 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_even_abs_numeral
% 5.15/5.46 thf(fact_5977_power__even__abs__numeral,axiom,
% 5.15/5.46 ! [W: num,A: code_integer] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.46 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.46 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_even_abs_numeral
% 5.15/5.46 thf(fact_5978_power__even__abs__numeral,axiom,
% 5.15/5.46 ! [W: num,A: real] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.46 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.46 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_even_abs_numeral
% 5.15/5.46 thf(fact_5979_power__even__abs__numeral,axiom,
% 5.15/5.46 ! [W: num,A: int] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.46 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.15/5.46 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_even_abs_numeral
% 5.15/5.46 thf(fact_5980_abs__le__D1,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_D1
% 5.15/5.46 thf(fact_5981_abs__le__D1,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.15/5.46 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_D1
% 5.15/5.46 thf(fact_5982_abs__le__D1,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_D1
% 5.15/5.46 thf(fact_5983_abs__le__D1,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_D1
% 5.15/5.46 thf(fact_5984_abs__ge__self,axiom,
% 5.15/5.46 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_self
% 5.15/5.46 thf(fact_5985_abs__ge__self,axiom,
% 5.15/5.46 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_self
% 5.15/5.46 thf(fact_5986_abs__ge__self,axiom,
% 5.15/5.46 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_self
% 5.15/5.46 thf(fact_5987_abs__ge__self,axiom,
% 5.15/5.46 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_self
% 5.15/5.46 thf(fact_5988_abs__eq__0__iff,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ( abs_abs_Code_integer @ A )
% 5.15/5.46 = zero_z3403309356797280102nteger )
% 5.15/5.46 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0_iff
% 5.15/5.46 thf(fact_5989_abs__eq__0__iff,axiom,
% 5.15/5.46 ! [A: complex] :
% 5.15/5.46 ( ( ( abs_abs_complex @ A )
% 5.15/5.46 = zero_zero_complex )
% 5.15/5.46 = ( A = zero_zero_complex ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0_iff
% 5.15/5.46 thf(fact_5990_abs__eq__0__iff,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ( abs_abs_real @ A )
% 5.15/5.46 = zero_zero_real )
% 5.15/5.46 = ( A = zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0_iff
% 5.15/5.46 thf(fact_5991_abs__eq__0__iff,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ( abs_abs_rat @ A )
% 5.15/5.46 = zero_zero_rat )
% 5.15/5.46 = ( A = zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0_iff
% 5.15/5.46 thf(fact_5992_abs__eq__0__iff,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ( abs_abs_int @ A )
% 5.15/5.46 = zero_zero_int )
% 5.15/5.46 = ( A = zero_zero_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_0_iff
% 5.15/5.46 thf(fact_5993_abs__mult,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.15/5.46 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult
% 5.15/5.46 thf(fact_5994_abs__mult,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.15/5.46 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult
% 5.15/5.46 thf(fact_5995_abs__mult,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.46 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult
% 5.15/5.46 thf(fact_5996_abs__mult,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.15/5.46 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult
% 5.15/5.46 thf(fact_5997_abs__one,axiom,
% 5.15/5.46 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.15/5.46 = one_one_Code_integer ) ).
% 5.15/5.46
% 5.15/5.46 % abs_one
% 5.15/5.46 thf(fact_5998_abs__one,axiom,
% 5.15/5.46 ( ( abs_abs_real @ one_one_real )
% 5.15/5.46 = one_one_real ) ).
% 5.15/5.46
% 5.15/5.46 % abs_one
% 5.15/5.46 thf(fact_5999_abs__one,axiom,
% 5.15/5.46 ( ( abs_abs_rat @ one_one_rat )
% 5.15/5.46 = one_one_rat ) ).
% 5.15/5.46
% 5.15/5.46 % abs_one
% 5.15/5.46 thf(fact_6000_abs__one,axiom,
% 5.15/5.46 ( ( abs_abs_int @ one_one_int )
% 5.15/5.46 = one_one_int ) ).
% 5.15/5.46
% 5.15/5.46 % abs_one
% 5.15/5.46 thf(fact_6001_abs__minus__commute,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.15/5.46 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_commute
% 5.15/5.46 thf(fact_6002_abs__minus__commute,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.15/5.46 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_commute
% 5.15/5.46 thf(fact_6003_abs__minus__commute,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.15/5.46 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_commute
% 5.15/5.46 thf(fact_6004_abs__minus__commute,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.15/5.46 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_commute
% 5.15/5.46 thf(fact_6005_abs__eq__iff,axiom,
% 5.15/5.46 ! [X: int,Y: int] :
% 5.15/5.46 ( ( ( abs_abs_int @ X )
% 5.15/5.46 = ( abs_abs_int @ Y ) )
% 5.15/5.46 = ( ( X = Y )
% 5.15/5.46 | ( X
% 5.15/5.46 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_iff
% 5.15/5.46 thf(fact_6006_abs__eq__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ( abs_abs_real @ X )
% 5.15/5.46 = ( abs_abs_real @ Y ) )
% 5.15/5.46 = ( ( X = Y )
% 5.15/5.46 | ( X
% 5.15/5.46 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_iff
% 5.15/5.46 thf(fact_6007_abs__eq__iff,axiom,
% 5.15/5.46 ! [X: rat,Y: rat] :
% 5.15/5.46 ( ( ( abs_abs_rat @ X )
% 5.15/5.46 = ( abs_abs_rat @ Y ) )
% 5.15/5.46 = ( ( X = Y )
% 5.15/5.46 | ( X
% 5.15/5.46 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_iff
% 5.15/5.46 thf(fact_6008_abs__eq__iff,axiom,
% 5.15/5.46 ! [X: code_integer,Y: code_integer] :
% 5.15/5.46 ( ( ( abs_abs_Code_integer @ X )
% 5.15/5.46 = ( abs_abs_Code_integer @ Y ) )
% 5.15/5.46 = ( ( X = Y )
% 5.15/5.46 | ( X
% 5.15/5.46 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_iff
% 5.15/5.46 thf(fact_6009_power__abs,axiom,
% 5.15/5.46 ! [A: rat,N2: nat] :
% 5.15/5.46 ( ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) )
% 5.15/5.46 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_abs
% 5.15/5.46 thf(fact_6010_power__abs,axiom,
% 5.15/5.46 ! [A: code_integer,N2: nat] :
% 5.15/5.46 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.15/5.46 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_abs
% 5.15/5.46 thf(fact_6011_power__abs,axiom,
% 5.15/5.46 ! [A: real,N2: nat] :
% 5.15/5.46 ( ( abs_abs_real @ ( power_power_real @ A @ N2 ) )
% 5.15/5.46 = ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_abs
% 5.15/5.46 thf(fact_6012_power__abs,axiom,
% 5.15/5.46 ! [A: int,N2: nat] :
% 5.15/5.46 ( ( abs_abs_int @ ( power_power_int @ A @ N2 ) )
% 5.15/5.46 = ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_abs
% 5.15/5.46 thf(fact_6013_dvd__if__abs__eq,axiom,
% 5.15/5.46 ! [L: real,K: real] :
% 5.15/5.46 ( ( ( abs_abs_real @ L )
% 5.15/5.46 = ( abs_abs_real @ K ) )
% 5.15/5.46 => ( dvd_dvd_real @ L @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % dvd_if_abs_eq
% 5.15/5.46 thf(fact_6014_dvd__if__abs__eq,axiom,
% 5.15/5.46 ! [L: int,K: int] :
% 5.15/5.46 ( ( ( abs_abs_int @ L )
% 5.15/5.46 = ( abs_abs_int @ K ) )
% 5.15/5.46 => ( dvd_dvd_int @ L @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % dvd_if_abs_eq
% 5.15/5.46 thf(fact_6015_dvd__if__abs__eq,axiom,
% 5.15/5.46 ! [L: rat,K: rat] :
% 5.15/5.46 ( ( ( abs_abs_rat @ L )
% 5.15/5.46 = ( abs_abs_rat @ K ) )
% 5.15/5.46 => ( dvd_dvd_rat @ L @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % dvd_if_abs_eq
% 5.15/5.46 thf(fact_6016_dvd__if__abs__eq,axiom,
% 5.15/5.46 ! [L: code_integer,K: code_integer] :
% 5.15/5.46 ( ( ( abs_abs_Code_integer @ L )
% 5.15/5.46 = ( abs_abs_Code_integer @ K ) )
% 5.15/5.46 => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 5.15/5.46
% 5.15/5.46 % dvd_if_abs_eq
% 5.15/5.46 thf(fact_6017_round__diff__minimal,axiom,
% 5.15/5.46 ! [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 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_diff_minimal
% 5.15/5.46 thf(fact_6018_round__diff__minimal,axiom,
% 5.15/5.46 ! [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 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_diff_minimal
% 5.15/5.46 thf(fact_6019_abs__ge__zero,axiom,
% 5.15/5.46 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_zero
% 5.15/5.46 thf(fact_6020_abs__ge__zero,axiom,
% 5.15/5.46 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_zero
% 5.15/5.46 thf(fact_6021_abs__ge__zero,axiom,
% 5.15/5.46 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_zero
% 5.15/5.46 thf(fact_6022_abs__ge__zero,axiom,
% 5.15/5.46 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_zero
% 5.15/5.46 thf(fact_6023_abs__of__pos,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.46 => ( ( abs_abs_Code_integer @ A )
% 5.15/5.46 = A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_pos
% 5.15/5.46 thf(fact_6024_abs__of__pos,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.46 => ( ( abs_abs_real @ A )
% 5.15/5.46 = A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_pos
% 5.15/5.46 thf(fact_6025_abs__of__pos,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.15/5.46 => ( ( abs_abs_rat @ A )
% 5.15/5.46 = A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_pos
% 5.15/5.46 thf(fact_6026_abs__of__pos,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ord_less_int @ zero_zero_int @ A )
% 5.15/5.46 => ( ( abs_abs_int @ A )
% 5.15/5.46 = A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_pos
% 5.15/5.46 thf(fact_6027_abs__not__less__zero,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.15/5.46
% 5.15/5.46 % abs_not_less_zero
% 5.15/5.46 thf(fact_6028_abs__not__less__zero,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.15/5.46
% 5.15/5.46 % abs_not_less_zero
% 5.15/5.46 thf(fact_6029_abs__not__less__zero,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.15/5.46
% 5.15/5.46 % abs_not_less_zero
% 5.15/5.46 thf(fact_6030_abs__not__less__zero,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.15/5.46
% 5.15/5.46 % abs_not_less_zero
% 5.15/5.46 thf(fact_6031_abs__triangle__ineq,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq
% 5.15/5.46 thf(fact_6032_abs__triangle__ineq,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq
% 5.15/5.46 thf(fact_6033_abs__triangle__ineq,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq
% 5.15/5.46 thf(fact_6034_abs__triangle__ineq,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq
% 5.15/5.46 thf(fact_6035_abs__mult__less,axiom,
% 5.15/5.46 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.15/5.46 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.15/5.46 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_less
% 5.15/5.46 thf(fact_6036_abs__mult__less,axiom,
% 5.15/5.46 ! [A: real,C: real,B: real,D: real] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.15/5.46 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.15/5.46 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_less
% 5.15/5.46 thf(fact_6037_abs__mult__less,axiom,
% 5.15/5.46 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.15/5.46 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.15/5.46 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.15/5.46 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_less
% 5.15/5.46 thf(fact_6038_abs__mult__less,axiom,
% 5.15/5.46 ! [A: int,C: int,B: int,D: int] :
% 5.15/5.46 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.15/5.46 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.15/5.46 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_less
% 5.15/5.46 thf(fact_6039_abs__triangle__ineq2,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq2
% 5.15/5.46 thf(fact_6040_abs__triangle__ineq2,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq2
% 5.15/5.46 thf(fact_6041_abs__triangle__ineq2,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq2
% 5.15/5.46 thf(fact_6042_abs__triangle__ineq2,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq2
% 5.15/5.46 thf(fact_6043_abs__triangle__ineq3,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq3
% 5.15/5.46 thf(fact_6044_abs__triangle__ineq3,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq3
% 5.15/5.46 thf(fact_6045_abs__triangle__ineq3,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq3
% 5.15/5.46 thf(fact_6046_abs__triangle__ineq3,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq3
% 5.15/5.46 thf(fact_6047_abs__triangle__ineq2__sym,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq2_sym
% 5.15/5.46 thf(fact_6048_abs__triangle__ineq2__sym,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq2_sym
% 5.15/5.46 thf(fact_6049_abs__triangle__ineq2__sym,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq2_sym
% 5.15/5.46 thf(fact_6050_abs__triangle__ineq2__sym,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq2_sym
% 5.15/5.46 thf(fact_6051_nonzero__abs__divide,axiom,
% 5.15/5.46 ! [B: real,A: real] :
% 5.15/5.46 ( ( B != zero_zero_real )
% 5.15/5.46 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.46 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % nonzero_abs_divide
% 5.15/5.46 thf(fact_6052_nonzero__abs__divide,axiom,
% 5.15/5.46 ! [B: rat,A: rat] :
% 5.15/5.46 ( ( B != zero_zero_rat )
% 5.15/5.46 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.15/5.46 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % nonzero_abs_divide
% 5.15/5.46 thf(fact_6053_abs__ge__minus__self,axiom,
% 5.15/5.46 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_minus_self
% 5.15/5.46 thf(fact_6054_abs__ge__minus__self,axiom,
% 5.15/5.46 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_minus_self
% 5.15/5.46 thf(fact_6055_abs__ge__minus__self,axiom,
% 5.15/5.46 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_minus_self
% 5.15/5.46 thf(fact_6056_abs__ge__minus__self,axiom,
% 5.15/5.46 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ge_minus_self
% 5.15/5.46 thf(fact_6057_abs__le__iff,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.15/5.46 = ( ( ord_less_eq_real @ A @ B )
% 5.15/5.46 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_iff
% 5.15/5.46 thf(fact_6058_abs__le__iff,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.15/5.46 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.15/5.46 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_iff
% 5.15/5.46 thf(fact_6059_abs__le__iff,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.15/5.46 = ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.46 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_iff
% 5.15/5.46 thf(fact_6060_abs__le__iff,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.15/5.46 = ( ( ord_less_eq_int @ A @ B )
% 5.15/5.46 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_iff
% 5.15/5.46 thf(fact_6061_abs__le__D2,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_D2
% 5.15/5.46 thf(fact_6062_abs__le__D2,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.15/5.46 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_D2
% 5.15/5.46 thf(fact_6063_abs__le__D2,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_D2
% 5.15/5.46 thf(fact_6064_abs__le__D2,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_D2
% 5.15/5.46 thf(fact_6065_abs__leI,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.46 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_leI
% 5.15/5.46 thf(fact_6066_abs__leI,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.15/5.46 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.15/5.46 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_leI
% 5.15/5.46 thf(fact_6067_abs__leI,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.15/5.46 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_leI
% 5.15/5.46 thf(fact_6068_abs__leI,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ A @ B )
% 5.15/5.46 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.15/5.46 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_leI
% 5.15/5.46 thf(fact_6069_abs__less__iff,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.15/5.46 = ( ( ord_less_int @ A @ B )
% 5.15/5.46 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_less_iff
% 5.15/5.46 thf(fact_6070_abs__less__iff,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.15/5.46 = ( ( ord_less_real @ A @ B )
% 5.15/5.46 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_less_iff
% 5.15/5.46 thf(fact_6071_abs__less__iff,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.15/5.46 = ( ( ord_less_rat @ A @ B )
% 5.15/5.46 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_less_iff
% 5.15/5.46 thf(fact_6072_abs__less__iff,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.15/5.46 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.15/5.46 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_less_iff
% 5.15/5.46 thf(fact_6073_tanh__real__lt__1,axiom,
% 5.15/5.46 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_real_lt_1
% 5.15/5.46 thf(fact_6074_dense__eq0__I,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ! [E2: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.15/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 5.15/5.46 => ( X = zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % dense_eq0_I
% 5.15/5.46 thf(fact_6075_dense__eq0__I,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ( ! [E2: rat] :
% 5.15/5.46 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 5.15/5.46 => ( X = zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % dense_eq0_I
% 5.15/5.46 thf(fact_6076_abs__mult__pos,axiom,
% 5.15/5.46 ! [X: code_integer,Y: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.15/5.46 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 5.15/5.46 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_pos
% 5.15/5.46 thf(fact_6077_abs__mult__pos,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 5.15/5.46 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_pos
% 5.15/5.46 thf(fact_6078_abs__mult__pos,axiom,
% 5.15/5.46 ! [X: rat,Y: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.15/5.46 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 5.15/5.46 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_pos
% 5.15/5.46 thf(fact_6079_abs__mult__pos,axiom,
% 5.15/5.46 ! [X: int,Y: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.46 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 5.15/5.46 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_mult_pos
% 5.15/5.46 thf(fact_6080_abs__eq__mult,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.46 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.15/5.46 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.46 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.15/5.46 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.15/5.46 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_mult
% 5.15/5.46 thf(fact_6081_abs__eq__mult,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.46 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.15/5.46 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.46 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.15/5.46 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.15/5.46 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_mult
% 5.15/5.46 thf(fact_6082_abs__eq__mult,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.46 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.15/5.46 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.46 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.15/5.46 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.15/5.46 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_mult
% 5.15/5.46 thf(fact_6083_abs__eq__mult,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.46 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.15/5.46 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.46 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.15/5.46 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.15/5.46 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_mult
% 5.15/5.46 thf(fact_6084_abs__eq__iff_H,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( ( abs_abs_real @ A )
% 5.15/5.46 = B )
% 5.15/5.46 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.46 & ( ( A = B )
% 5.15/5.46 | ( A
% 5.15/5.46 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_iff'
% 5.15/5.46 thf(fact_6085_abs__eq__iff_H,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( ( abs_abs_Code_integer @ A )
% 5.15/5.46 = B )
% 5.15/5.46 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.15/5.46 & ( ( A = B )
% 5.15/5.46 | ( A
% 5.15/5.46 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_iff'
% 5.15/5.46 thf(fact_6086_abs__eq__iff_H,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( ( abs_abs_rat @ A )
% 5.15/5.46 = B )
% 5.15/5.46 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.46 & ( ( A = B )
% 5.15/5.46 | ( A
% 5.15/5.46 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_iff'
% 5.15/5.46 thf(fact_6087_abs__eq__iff_H,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( ( abs_abs_int @ A )
% 5.15/5.46 = B )
% 5.15/5.46 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.46 & ( ( A = B )
% 5.15/5.46 | ( A
% 5.15/5.46 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_eq_iff'
% 5.15/5.46 thf(fact_6088_eq__abs__iff_H,axiom,
% 5.15/5.46 ! [A: real,B: real] :
% 5.15/5.46 ( ( A
% 5.15/5.46 = ( abs_abs_real @ B ) )
% 5.15/5.46 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.46 & ( ( B = A )
% 5.15/5.46 | ( B
% 5.15/5.46 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % eq_abs_iff'
% 5.15/5.46 thf(fact_6089_eq__abs__iff_H,axiom,
% 5.15/5.46 ! [A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( A
% 5.15/5.46 = ( abs_abs_Code_integer @ B ) )
% 5.15/5.46 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.15/5.46 & ( ( B = A )
% 5.15/5.46 | ( B
% 5.15/5.46 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % eq_abs_iff'
% 5.15/5.46 thf(fact_6090_eq__abs__iff_H,axiom,
% 5.15/5.46 ! [A: rat,B: rat] :
% 5.15/5.46 ( ( A
% 5.15/5.46 = ( abs_abs_rat @ B ) )
% 5.15/5.46 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.46 & ( ( B = A )
% 5.15/5.46 | ( B
% 5.15/5.46 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % eq_abs_iff'
% 5.15/5.46 thf(fact_6091_eq__abs__iff_H,axiom,
% 5.15/5.46 ! [A: int,B: int] :
% 5.15/5.46 ( ( A
% 5.15/5.46 = ( abs_abs_int @ B ) )
% 5.15/5.46 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.15/5.46 & ( ( B = A )
% 5.15/5.46 | ( B
% 5.15/5.46 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % eq_abs_iff'
% 5.15/5.46 thf(fact_6092_abs__minus__le__zero,axiom,
% 5.15/5.46 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_le_zero
% 5.15/5.46 thf(fact_6093_abs__minus__le__zero,axiom,
% 5.15/5.46 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_le_zero
% 5.15/5.46 thf(fact_6094_abs__minus__le__zero,axiom,
% 5.15/5.46 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_le_zero
% 5.15/5.46 thf(fact_6095_abs__minus__le__zero,axiom,
% 5.15/5.46 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.15/5.46
% 5.15/5.46 % abs_minus_le_zero
% 5.15/5.46 thf(fact_6096_abs__div__pos,axiom,
% 5.15/5.46 ! [Y: real,X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.46 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 5.15/5.46 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_div_pos
% 5.15/5.46 thf(fact_6097_abs__div__pos,axiom,
% 5.15/5.46 ! [Y: rat,X: rat] :
% 5.15/5.46 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.15/5.46 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 5.15/5.46 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_div_pos
% 5.15/5.46 thf(fact_6098_zero__le__power__abs,axiom,
% 5.15/5.46 ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_le_power_abs
% 5.15/5.46 thf(fact_6099_zero__le__power__abs,axiom,
% 5.15/5.46 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_le_power_abs
% 5.15/5.46 thf(fact_6100_zero__le__power__abs,axiom,
% 5.15/5.46 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_le_power_abs
% 5.15/5.46 thf(fact_6101_zero__le__power__abs,axiom,
% 5.15/5.46 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_le_power_abs
% 5.15/5.46 thf(fact_6102_abs__of__neg,axiom,
% 5.15/5.46 ! [A: int] :
% 5.15/5.46 ( ( ord_less_int @ A @ zero_zero_int )
% 5.15/5.46 => ( ( abs_abs_int @ A )
% 5.15/5.46 = ( uminus_uminus_int @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_neg
% 5.15/5.46 thf(fact_6103_abs__of__neg,axiom,
% 5.15/5.46 ! [A: real] :
% 5.15/5.46 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.46 => ( ( abs_abs_real @ A )
% 5.15/5.46 = ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_neg
% 5.15/5.46 thf(fact_6104_abs__of__neg,axiom,
% 5.15/5.46 ! [A: rat] :
% 5.15/5.46 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.15/5.46 => ( ( abs_abs_rat @ A )
% 5.15/5.46 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_neg
% 5.15/5.46 thf(fact_6105_abs__of__neg,axiom,
% 5.15/5.46 ! [A: code_integer] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.15/5.46 => ( ( abs_abs_Code_integer @ A )
% 5.15/5.46 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_of_neg
% 5.15/5.46 thf(fact_6106_abs__if,axiom,
% 5.15/5.46 ( abs_abs_int
% 5.15/5.46 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_if
% 5.15/5.46 thf(fact_6107_abs__if,axiom,
% 5.15/5.46 ( abs_abs_real
% 5.15/5.46 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_if
% 5.15/5.46 thf(fact_6108_abs__if,axiom,
% 5.15/5.46 ( abs_abs_rat
% 5.15/5.46 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_if
% 5.15/5.46 thf(fact_6109_abs__if,axiom,
% 5.15/5.46 ( abs_abs_Code_integer
% 5.15/5.46 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_if
% 5.15/5.46 thf(fact_6110_abs__if__raw,axiom,
% 5.15/5.46 ( abs_abs_int
% 5.15/5.46 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_if_raw
% 5.15/5.46 thf(fact_6111_abs__if__raw,axiom,
% 5.15/5.46 ( abs_abs_real
% 5.15/5.46 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_if_raw
% 5.15/5.46 thf(fact_6112_abs__if__raw,axiom,
% 5.15/5.46 ( abs_abs_rat
% 5.15/5.46 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_if_raw
% 5.15/5.46 thf(fact_6113_abs__if__raw,axiom,
% 5.15/5.46 ( abs_abs_Code_integer
% 5.15/5.46 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_if_raw
% 5.15/5.46 thf(fact_6114_abs__diff__le__iff,axiom,
% 5.15/5.46 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.15/5.46 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.15/5.46 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_le_iff
% 5.15/5.46 thf(fact_6115_abs__diff__le__iff,axiom,
% 5.15/5.46 ! [X: real,A: real,R2: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.15/5.46 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.15/5.46 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_le_iff
% 5.15/5.46 thf(fact_6116_abs__diff__le__iff,axiom,
% 5.15/5.46 ! [X: rat,A: rat,R2: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.15/5.46 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.15/5.46 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_le_iff
% 5.15/5.46 thf(fact_6117_abs__diff__le__iff,axiom,
% 5.15/5.46 ! [X: int,A: int,R2: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.15/5.46 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.15/5.46 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_le_iff
% 5.15/5.46 thf(fact_6118_abs__triangle__ineq4,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq4
% 5.15/5.46 thf(fact_6119_abs__triangle__ineq4,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq4
% 5.15/5.46 thf(fact_6120_abs__triangle__ineq4,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq4
% 5.15/5.46 thf(fact_6121_abs__triangle__ineq4,axiom,
% 5.15/5.46 ! [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 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_triangle_ineq4
% 5.15/5.46 thf(fact_6122_abs__diff__triangle__ineq,axiom,
% 5.15/5.46 ! [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 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_triangle_ineq
% 5.15/5.46 thf(fact_6123_abs__diff__triangle__ineq,axiom,
% 5.15/5.46 ! [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 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_triangle_ineq
% 5.15/5.46 thf(fact_6124_abs__diff__triangle__ineq,axiom,
% 5.15/5.46 ! [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 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_triangle_ineq
% 5.15/5.46 thf(fact_6125_abs__diff__triangle__ineq,axiom,
% 5.15/5.46 ! [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 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_triangle_ineq
% 5.15/5.46 thf(fact_6126_abs__diff__less__iff,axiom,
% 5.15/5.46 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.15/5.46 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.15/5.46 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_less_iff
% 5.15/5.46 thf(fact_6127_abs__diff__less__iff,axiom,
% 5.15/5.46 ! [X: real,A: real,R2: real] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.15/5.46 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.15/5.46 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_less_iff
% 5.15/5.46 thf(fact_6128_abs__diff__less__iff,axiom,
% 5.15/5.46 ! [X: rat,A: rat,R2: rat] :
% 5.15/5.46 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.15/5.46 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.15/5.46 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_less_iff
% 5.15/5.46 thf(fact_6129_abs__diff__less__iff,axiom,
% 5.15/5.46 ! [X: int,A: int,R2: int] :
% 5.15/5.46 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.15/5.46 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.15/5.46 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_diff_less_iff
% 5.15/5.46 thf(fact_6130_round__mono,axiom,
% 5.15/5.46 ! [X: rat,Y: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ X @ Y )
% 5.15/5.46 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_mono
% 5.15/5.46 thf(fact_6131_abs__real__def,axiom,
% 5.15/5.46 ( abs_abs_real
% 5.15/5.46 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_real_def
% 5.15/5.46 thf(fact_6132_lemma__interval__lt,axiom,
% 5.15/5.46 ! [A: real,X: real,B: real] :
% 5.15/5.46 ( ( ord_less_real @ A @ X )
% 5.15/5.46 => ( ( ord_less_real @ X @ B )
% 5.15/5.46 => ? [D3: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.46 & ! [Y4: real] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 5.15/5.46 => ( ( ord_less_real @ A @ Y4 )
% 5.15/5.46 & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % lemma_interval_lt
% 5.15/5.46 thf(fact_6133_sin__bound__lemma,axiom,
% 5.15/5.46 ! [X: real,Y: real,U: real,V: real] :
% 5.15/5.46 ( ( X = Y )
% 5.15/5.46 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.15/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sin_bound_lemma
% 5.15/5.46 thf(fact_6134_tanh__real__gt__neg1,axiom,
% 5.15/5.46 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % tanh_real_gt_neg1
% 5.15/5.46 thf(fact_6135_abs__add__one__gt__zero,axiom,
% 5.15/5.46 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_add_one_gt_zero
% 5.15/5.46 thf(fact_6136_abs__add__one__gt__zero,axiom,
% 5.15/5.46 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_add_one_gt_zero
% 5.15/5.46 thf(fact_6137_abs__add__one__gt__zero,axiom,
% 5.15/5.46 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_add_one_gt_zero
% 5.15/5.46 thf(fact_6138_abs__add__one__gt__zero,axiom,
% 5.15/5.46 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_add_one_gt_zero
% 5.15/5.46 thf(fact_6139_of__int__leD,axiom,
% 5.15/5.46 ! [N2: int,X: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 5.15/5.46 => ( ( N2 = zero_zero_int )
% 5.15/5.46 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_leD
% 5.15/5.46 thf(fact_6140_of__int__leD,axiom,
% 5.15/5.46 ! [N2: int,X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X )
% 5.15/5.46 => ( ( N2 = zero_zero_int )
% 5.15/5.46 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_leD
% 5.15/5.46 thf(fact_6141_of__int__leD,axiom,
% 5.15/5.46 ! [N2: int,X: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 5.15/5.46 => ( ( N2 = zero_zero_int )
% 5.15/5.46 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_leD
% 5.15/5.46 thf(fact_6142_of__int__leD,axiom,
% 5.15/5.46 ! [N2: int,X: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 5.15/5.46 => ( ( N2 = zero_zero_int )
% 5.15/5.46 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_leD
% 5.15/5.46 thf(fact_6143_of__int__lessD,axiom,
% 5.15/5.46 ! [N2: int,X: code_integer] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 5.15/5.46 => ( ( N2 = zero_zero_int )
% 5.15/5.46 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_lessD
% 5.15/5.46 thf(fact_6144_of__int__lessD,axiom,
% 5.15/5.46 ! [N2: int,X: real] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X )
% 5.15/5.46 => ( ( N2 = zero_zero_int )
% 5.15/5.46 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_lessD
% 5.15/5.46 thf(fact_6145_of__int__lessD,axiom,
% 5.15/5.46 ! [N2: int,X: rat] :
% 5.15/5.46 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 5.15/5.46 => ( ( N2 = zero_zero_int )
% 5.15/5.46 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_lessD
% 5.15/5.46 thf(fact_6146_of__int__lessD,axiom,
% 5.15/5.46 ! [N2: int,X: int] :
% 5.15/5.46 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 5.15/5.46 => ( ( N2 = zero_zero_int )
% 5.15/5.46 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_lessD
% 5.15/5.46 thf(fact_6147_lemma__interval,axiom,
% 5.15/5.46 ! [A: real,X: real,B: real] :
% 5.15/5.46 ( ( ord_less_real @ A @ X )
% 5.15/5.46 => ( ( ord_less_real @ X @ B )
% 5.15/5.46 => ? [D3: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.46 & ! [Y4: real] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 5.15/5.46 => ( ( ord_less_eq_real @ A @ Y4 )
% 5.15/5.46 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % lemma_interval
% 5.15/5.46 thf(fact_6148_of__int__round__abs__le,axiom,
% 5.15/5.46 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_round_abs_le
% 5.15/5.46 thf(fact_6149_of__int__round__abs__le,axiom,
% 5.15/5.46 ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_round_abs_le
% 5.15/5.46 thf(fact_6150_round__unique_H,axiom,
% 5.15/5.46 ! [X: real,N2: int] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.46 => ( ( archim8280529875227126926d_real @ X )
% 5.15/5.46 = N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_unique'
% 5.15/5.46 thf(fact_6151_round__unique_H,axiom,
% 5.15/5.46 ! [X: rat,N2: int] :
% 5.15/5.46 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 => ( ( archim7778729529865785530nd_rat @ X )
% 5.15/5.46 = N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % round_unique'
% 5.15/5.46 thf(fact_6152_abs__le__square__iff,axiom,
% 5.15/5.46 ! [X: code_integer,Y: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 5.15/5.46 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_square_iff
% 5.15/5.46 thf(fact_6153_abs__le__square__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 5.15/5.46 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_square_iff
% 5.15/5.46 thf(fact_6154_abs__le__square__iff,axiom,
% 5.15/5.46 ! [X: rat,Y: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 5.15/5.46 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_square_iff
% 5.15/5.46 thf(fact_6155_abs__le__square__iff,axiom,
% 5.15/5.46 ! [X: int,Y: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_le_square_iff
% 5.15/5.46 thf(fact_6156_abs__square__eq__1,axiom,
% 5.15/5.46 ! [X: code_integer] :
% 5.15/5.46 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.46 = one_one_Code_integer )
% 5.15/5.46 = ( ( abs_abs_Code_integer @ X )
% 5.15/5.46 = one_one_Code_integer ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_eq_1
% 5.15/5.46 thf(fact_6157_abs__square__eq__1,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.46 = one_one_rat )
% 5.15/5.46 = ( ( abs_abs_rat @ X )
% 5.15/5.46 = one_one_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_eq_1
% 5.15/5.46 thf(fact_6158_abs__square__eq__1,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.46 = one_one_real )
% 5.15/5.46 = ( ( abs_abs_real @ X )
% 5.15/5.46 = one_one_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_eq_1
% 5.15/5.46 thf(fact_6159_abs__square__eq__1,axiom,
% 5.15/5.46 ! [X: int] :
% 5.15/5.46 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.46 = one_one_int )
% 5.15/5.46 = ( ( abs_abs_int @ X )
% 5.15/5.46 = one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_eq_1
% 5.15/5.46 thf(fact_6160_power__even__abs,axiom,
% 5.15/5.46 ! [N2: nat,A: rat] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.46 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 )
% 5.15/5.46 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_even_abs
% 5.15/5.46 thf(fact_6161_power__even__abs,axiom,
% 5.15/5.46 ! [N2: nat,A: code_integer] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.46 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 )
% 5.15/5.46 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_even_abs
% 5.15/5.46 thf(fact_6162_power__even__abs,axiom,
% 5.15/5.46 ! [N2: nat,A: real] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.46 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N2 )
% 5.15/5.46 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_even_abs
% 5.15/5.46 thf(fact_6163_power__even__abs,axiom,
% 5.15/5.46 ! [N2: nat,A: int] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.46 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N2 )
% 5.15/5.46 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_even_abs
% 5.15/5.46 thf(fact_6164_power2__le__iff__abs__le,axiom,
% 5.15/5.46 ! [Y: code_integer,X: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.15/5.46 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power2_le_iff_abs_le
% 5.15/5.46 thf(fact_6165_power2__le__iff__abs__le,axiom,
% 5.15/5.46 ! [Y: real,X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.46 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power2_le_iff_abs_le
% 5.15/5.46 thf(fact_6166_power2__le__iff__abs__le,axiom,
% 5.15/5.46 ! [Y: rat,X: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.15/5.46 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power2_le_iff_abs_le
% 5.15/5.46 thf(fact_6167_power2__le__iff__abs__le,axiom,
% 5.15/5.46 ! [Y: int,X: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.46 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.46 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power2_le_iff_abs_le
% 5.15/5.46 thf(fact_6168_abs__sqrt__wlog,axiom,
% 5.15/5.46 ! [P: code_integer > code_integer > $o,X: code_integer] :
% 5.15/5.46 ( ! [X3: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.15/5.46 => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_sqrt_wlog
% 5.15/5.46 thf(fact_6169_abs__sqrt__wlog,axiom,
% 5.15/5.46 ! [P: real > real > $o,X: real] :
% 5.15/5.46 ( ! [X3: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.15/5.46 => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_sqrt_wlog
% 5.15/5.46 thf(fact_6170_abs__sqrt__wlog,axiom,
% 5.15/5.46 ! [P: rat > rat > $o,X: rat] :
% 5.15/5.46 ( ! [X3: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.15/5.46 => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_sqrt_wlog
% 5.15/5.46 thf(fact_6171_abs__sqrt__wlog,axiom,
% 5.15/5.46 ! [P: int > int > $o,X: int] :
% 5.15/5.46 ( ! [X3: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.15/5.46 => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.46 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_sqrt_wlog
% 5.15/5.46 thf(fact_6172_abs__square__le__1,axiom,
% 5.15/5.46 ! [X: code_integer] :
% 5.15/5.46 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.15/5.46 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_le_1
% 5.15/5.46 thf(fact_6173_abs__square__le__1,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.15/5.46 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_le_1
% 5.15/5.46 thf(fact_6174_abs__square__le__1,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.15/5.46 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_le_1
% 5.15/5.46 thf(fact_6175_abs__square__le__1,axiom,
% 5.15/5.46 ! [X: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.15/5.46 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_le_1
% 5.15/5.46 thf(fact_6176_abs__square__less__1,axiom,
% 5.15/5.46 ! [X: code_integer] :
% 5.15/5.46 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.15/5.46 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_less_1
% 5.15/5.46 thf(fact_6177_abs__square__less__1,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.15/5.46 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_less_1
% 5.15/5.46 thf(fact_6178_abs__square__less__1,axiom,
% 5.15/5.46 ! [X: rat] :
% 5.15/5.46 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.15/5.46 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_less_1
% 5.15/5.46 thf(fact_6179_abs__square__less__1,axiom,
% 5.15/5.46 ! [X: int] :
% 5.15/5.46 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.15/5.46 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_square_less_1
% 5.15/5.46 thf(fact_6180_power__mono__even,axiom,
% 5.15/5.46 ! [N2: nat,A: code_integer,B: code_integer] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.46 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.15/5.46 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_mono_even
% 5.15/5.46 thf(fact_6181_power__mono__even,axiom,
% 5.15/5.46 ! [N2: nat,A: real,B: real] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.46 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.15/5.46 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_mono_even
% 5.15/5.46 thf(fact_6182_power__mono__even,axiom,
% 5.15/5.46 ! [N2: nat,A: rat,B: rat] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.46 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_mono_even
% 5.15/5.46 thf(fact_6183_power__mono__even,axiom,
% 5.15/5.46 ! [N2: nat,A: int,B: int] :
% 5.15/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.46 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.15/5.46 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % power_mono_even
% 5.15/5.46 thf(fact_6184_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.46 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.15/5.46 thf(fact_6185_of__int__round__le,axiom,
% 5.15/5.46 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_round_le
% 5.15/5.46 thf(fact_6186_of__int__round__le,axiom,
% 5.15/5.46 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_round_le
% 5.15/5.46 thf(fact_6187_of__int__round__ge,axiom,
% 5.15/5.46 ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_round_ge
% 5.15/5.46 thf(fact_6188_of__int__round__ge,axiom,
% 5.15/5.46 ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_round_ge
% 5.15/5.46 thf(fact_6189_arctan__double,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.46 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.15/5.46 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % arctan_double
% 5.15/5.46 thf(fact_6190_add__scale__eq__noteq,axiom,
% 5.15/5.46 ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.15/5.46 ( ( R2 != zero_zero_complex )
% 5.15/5.46 => ( ( ( A = B )
% 5.15/5.46 & ( C != D ) )
% 5.15/5.46 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 5.15/5.46 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % add_scale_eq_noteq
% 5.15/5.46 thf(fact_6191_add__scale__eq__noteq,axiom,
% 5.15/5.46 ! [R2: real,A: real,B: real,C: real,D: real] :
% 5.15/5.46 ( ( R2 != zero_zero_real )
% 5.15/5.46 => ( ( ( A = B )
% 5.15/5.46 & ( C != D ) )
% 5.15/5.46 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 5.15/5.46 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % add_scale_eq_noteq
% 5.15/5.46 thf(fact_6192_add__scale__eq__noteq,axiom,
% 5.15/5.46 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.46 ( ( R2 != zero_zero_rat )
% 5.15/5.46 => ( ( ( A = B )
% 5.15/5.46 & ( C != D ) )
% 5.15/5.46 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 5.15/5.46 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % add_scale_eq_noteq
% 5.15/5.46 thf(fact_6193_add__scale__eq__noteq,axiom,
% 5.15/5.46 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.46 ( ( R2 != zero_zero_nat )
% 5.15/5.46 => ( ( ( A = B )
% 5.15/5.46 & ( C != D ) )
% 5.15/5.46 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 5.15/5.46 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % add_scale_eq_noteq
% 5.15/5.46 thf(fact_6194_add__scale__eq__noteq,axiom,
% 5.15/5.46 ! [R2: int,A: int,B: int,C: int,D: int] :
% 5.15/5.46 ( ( R2 != zero_zero_int )
% 5.15/5.46 => ( ( ( A = B )
% 5.15/5.46 & ( C != D ) )
% 5.15/5.46 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 5.15/5.46 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % add_scale_eq_noteq
% 5.15/5.46 thf(fact_6195_Sum__Icc__int,axiom,
% 5.15/5.46 ! [M: int,N2: int] :
% 5.15/5.46 ( ( ord_less_eq_int @ M @ N2 )
% 5.15/5.46 => ( ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [X2: int] : X2
% 5.15/5.46 @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 5.15/5.46 = ( 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 ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % Sum_Icc_int
% 5.15/5.46 thf(fact_6196_even__set__encode__iff,axiom,
% 5.15/5.46 ! [A2: set_nat] :
% 5.15/5.46 ( ( finite_finite_nat @ A2 )
% 5.15/5.46 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.15/5.46 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % even_set_encode_iff
% 5.15/5.46 thf(fact_6197_mask__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.46 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % mask_numeral
% 5.15/5.46 thf(fact_6198_mask__numeral,axiom,
% 5.15/5.46 ! [N2: num] :
% 5.15/5.46 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.46 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % mask_numeral
% 5.15/5.46 thf(fact_6199_num_Osize__gen_I3_J,axiom,
% 5.15/5.46 ! [X33: num] :
% 5.15/5.46 ( ( size_num @ ( bit1 @ X33 ) )
% 5.15/5.46 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % num.size_gen(3)
% 5.15/5.46 thf(fact_6200_mask__nat__positive__iff,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.15/5.46 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % mask_nat_positive_iff
% 5.15/5.46 thf(fact_6201_sum_Oneutral__const,axiom,
% 5.15/5.46 ! [A2: set_int] :
% 5.15/5.46 ( ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [Uu3: int] : zero_zero_int
% 5.15/5.46 @ A2 )
% 5.15/5.46 = zero_zero_int ) ).
% 5.15/5.46
% 5.15/5.46 % sum.neutral_const
% 5.15/5.46 thf(fact_6202_sum_Oneutral__const,axiom,
% 5.15/5.46 ! [A2: set_complex] :
% 5.15/5.46 ( ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [Uu3: complex] : zero_zero_complex
% 5.15/5.46 @ A2 )
% 5.15/5.46 = zero_zero_complex ) ).
% 5.15/5.46
% 5.15/5.46 % sum.neutral_const
% 5.15/5.46 thf(fact_6203_sum_Oneutral__const,axiom,
% 5.15/5.46 ! [A2: set_nat] :
% 5.15/5.46 ( ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [Uu3: nat] : zero_zero_nat
% 5.15/5.46 @ A2 )
% 5.15/5.46 = zero_zero_nat ) ).
% 5.15/5.46
% 5.15/5.46 % sum.neutral_const
% 5.15/5.46 thf(fact_6204_sum_Oneutral__const,axiom,
% 5.15/5.46 ! [A2: set_nat] :
% 5.15/5.46 ( ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [Uu3: nat] : zero_zero_real
% 5.15/5.46 @ A2 )
% 5.15/5.46 = zero_zero_real ) ).
% 5.15/5.46
% 5.15/5.46 % sum.neutral_const
% 5.15/5.46 thf(fact_6205_abs__sum__abs,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int] :
% 5.15/5.46 ( ( abs_abs_int
% 5.15/5.46 @ ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [A3: int] : ( abs_abs_int @ ( F @ A3 ) )
% 5.15/5.46 @ A2 ) )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [A3: int] : ( abs_abs_int @ ( F @ A3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_sum_abs
% 5.15/5.46 thf(fact_6206_abs__sum__abs,axiom,
% 5.15/5.46 ! [F: nat > real,A2: set_nat] :
% 5.15/5.46 ( ( abs_abs_real
% 5.15/5.46 @ ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [A3: nat] : ( abs_abs_real @ ( F @ A3 ) )
% 5.15/5.46 @ A2 ) )
% 5.15/5.46 = ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [A3: nat] : ( abs_abs_real @ ( F @ A3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % abs_sum_abs
% 5.15/5.46 thf(fact_6207_mask__0,axiom,
% 5.15/5.46 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.15/5.46 = zero_zero_nat ) ).
% 5.15/5.46
% 5.15/5.46 % mask_0
% 5.15/5.46 thf(fact_6208_mask__0,axiom,
% 5.15/5.46 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.15/5.46 = zero_zero_int ) ).
% 5.15/5.46
% 5.15/5.46 % mask_0
% 5.15/5.46 thf(fact_6209_mask__eq__0__iff,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( ( bit_se2002935070580805687sk_nat @ N2 )
% 5.15/5.46 = zero_zero_nat )
% 5.15/5.46 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.46
% 5.15/5.46 % mask_eq_0_iff
% 5.15/5.46 thf(fact_6210_mask__eq__0__iff,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( ( bit_se2000444600071755411sk_int @ N2 )
% 5.15/5.46 = zero_zero_int )
% 5.15/5.46 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.46
% 5.15/5.46 % mask_eq_0_iff
% 5.15/5.46 thf(fact_6211_zero__less__arctan__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 5.15/5.46 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_less_arctan_iff
% 5.15/5.46 thf(fact_6212_arctan__less__zero__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 5.15/5.46 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % arctan_less_zero_iff
% 5.15/5.46 thf(fact_6213_zero__le__arctan__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 5.15/5.46 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.15/5.46
% 5.15/5.46 % zero_le_arctan_iff
% 5.15/5.46 thf(fact_6214_arctan__le__zero__iff,axiom,
% 5.15/5.46 ! [X: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 5.15/5.46 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % arctan_le_zero_iff
% 5.15/5.46 thf(fact_6215_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_real,A: real,B: real > complex] :
% 5.15/5.46 ( ( finite_finite_real @ S3 )
% 5.15/5.46 => ( ( ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups5754745047067104278omplex
% 5.15/5.46 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups5754745047067104278omplex
% 5.15/5.46 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_complex ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6216_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.15/5.46 ( ( finite_finite_nat @ S3 )
% 5.15/5.46 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.46 => ( ( groups2073611262835488442omplex
% 5.15/5.46 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.46 => ( ( groups2073611262835488442omplex
% 5.15/5.46 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_complex ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6217_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_int,A: int,B: int > complex] :
% 5.15/5.46 ( ( finite_finite_int @ S3 )
% 5.15/5.46 => ( ( ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups3049146728041665814omplex
% 5.15/5.46 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups3049146728041665814omplex
% 5.15/5.46 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_complex ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6218_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_real,A: real,B: real > real] :
% 5.15/5.46 ( ( finite_finite_real @ S3 )
% 5.15/5.46 => ( ( ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups8097168146408367636l_real
% 5.15/5.46 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups8097168146408367636l_real
% 5.15/5.46 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_real ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6219_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.15/5.46 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.46 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.46 => ( ( groups5808333547571424918x_real
% 5.15/5.46 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.46 => ( ( groups5808333547571424918x_real
% 5.15/5.46 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_real ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6220_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_int,A: int,B: int > real] :
% 5.15/5.46 ( ( finite_finite_int @ S3 )
% 5.15/5.46 => ( ( ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups8778361861064173332t_real
% 5.15/5.46 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups8778361861064173332t_real
% 5.15/5.46 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_real ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6221_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_real,A: real,B: real > rat] :
% 5.15/5.46 ( ( finite_finite_real @ S3 )
% 5.15/5.46 => ( ( ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups1300246762558778688al_rat
% 5.15/5.46 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups1300246762558778688al_rat
% 5.15/5.46 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_rat ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6222_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.15/5.46 ( ( finite_finite_nat @ S3 )
% 5.15/5.46 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.46 => ( ( groups2906978787729119204at_rat
% 5.15/5.46 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.46 => ( ( groups2906978787729119204at_rat
% 5.15/5.46 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_rat ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6223_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_complex,A: complex,B: complex > rat] :
% 5.15/5.46 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.46 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.46 => ( ( groups5058264527183730370ex_rat
% 5.15/5.46 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.46 => ( ( groups5058264527183730370ex_rat
% 5.15/5.46 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_rat ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6224_sum_Odelta,axiom,
% 5.15/5.46 ! [S3: set_int,A: int,B: int > rat] :
% 5.15/5.46 ( ( finite_finite_int @ S3 )
% 5.15/5.46 => ( ( ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups3906332499630173760nt_rat
% 5.15/5.46 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups3906332499630173760nt_rat
% 5.15/5.46 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_rat ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta
% 5.15/5.46 thf(fact_6225_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_real,A: real,B: real > complex] :
% 5.15/5.46 ( ( finite_finite_real @ S3 )
% 5.15/5.46 => ( ( ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups5754745047067104278omplex
% 5.15/5.46 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups5754745047067104278omplex
% 5.15/5.46 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_complex ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6226_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.15/5.46 ( ( finite_finite_nat @ S3 )
% 5.15/5.46 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.46 => ( ( groups2073611262835488442omplex
% 5.15/5.46 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.46 => ( ( groups2073611262835488442omplex
% 5.15/5.46 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_complex ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6227_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_int,A: int,B: int > complex] :
% 5.15/5.46 ( ( finite_finite_int @ S3 )
% 5.15/5.46 => ( ( ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups3049146728041665814omplex
% 5.15/5.46 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups3049146728041665814omplex
% 5.15/5.46 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_complex ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6228_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_real,A: real,B: real > real] :
% 5.15/5.46 ( ( finite_finite_real @ S3 )
% 5.15/5.46 => ( ( ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups8097168146408367636l_real
% 5.15/5.46 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups8097168146408367636l_real
% 5.15/5.46 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_real ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6229_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.15/5.46 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.46 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.46 => ( ( groups5808333547571424918x_real
% 5.15/5.46 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.46 => ( ( groups5808333547571424918x_real
% 5.15/5.46 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_real ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6230_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_int,A: int,B: int > real] :
% 5.15/5.46 ( ( finite_finite_int @ S3 )
% 5.15/5.46 => ( ( ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups8778361861064173332t_real
% 5.15/5.46 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups8778361861064173332t_real
% 5.15/5.46 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_real ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6231_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_real,A: real,B: real > rat] :
% 5.15/5.46 ( ( finite_finite_real @ S3 )
% 5.15/5.46 => ( ( ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups1300246762558778688al_rat
% 5.15/5.46 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.46 => ( ( groups1300246762558778688al_rat
% 5.15/5.46 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_rat ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6232_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.15/5.46 ( ( finite_finite_nat @ S3 )
% 5.15/5.46 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.46 => ( ( groups2906978787729119204at_rat
% 5.15/5.46 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.46 => ( ( groups2906978787729119204at_rat
% 5.15/5.46 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_rat ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6233_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_complex,A: complex,B: complex > rat] :
% 5.15/5.46 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.46 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.46 => ( ( groups5058264527183730370ex_rat
% 5.15/5.46 @ ^ [K2: complex] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.46 => ( ( groups5058264527183730370ex_rat
% 5.15/5.46 @ ^ [K2: complex] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_rat ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6234_sum_Odelta_H,axiom,
% 5.15/5.46 ! [S3: set_int,A: int,B: int > rat] :
% 5.15/5.46 ( ( finite_finite_int @ S3 )
% 5.15/5.46 => ( ( ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups3906332499630173760nt_rat
% 5.15/5.46 @ ^ [K2: int] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = ( B @ A ) ) )
% 5.15/5.46 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.46 => ( ( groups3906332499630173760nt_rat
% 5.15/5.46 @ ^ [K2: int] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.15/5.46 @ S3 )
% 5.15/5.46 = zero_zero_rat ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.delta'
% 5.15/5.46 thf(fact_6235_sum__abs,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int] :
% 5.15/5.46 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.15/5.46 @ ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_abs
% 5.15/5.46 thf(fact_6236_sum__abs,axiom,
% 5.15/5.46 ! [F: nat > real,A2: set_nat] :
% 5.15/5.46 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.15/5.46 @ ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_abs
% 5.15/5.46 thf(fact_6237_mask__Suc__0,axiom,
% 5.15/5.46 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.15/5.46 = one_one_nat ) ).
% 5.15/5.46
% 5.15/5.46 % mask_Suc_0
% 5.15/5.46 thf(fact_6238_mask__Suc__0,axiom,
% 5.15/5.46 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.15/5.46 = one_one_int ) ).
% 5.15/5.46
% 5.15/5.46 % mask_Suc_0
% 5.15/5.46 thf(fact_6239_of__int__sum,axiom,
% 5.15/5.46 ! [F: complex > int,A2: set_complex] :
% 5.15/5.46 ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A2 ) )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [X2: complex] : ( ring_17405671764205052669omplex @ ( F @ X2 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_sum
% 5.15/5.46 thf(fact_6240_of__int__sum,axiom,
% 5.15/5.46 ! [F: nat > int,A2: set_nat] :
% 5.15/5.46 ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A2 ) )
% 5.15/5.46 = ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [X2: nat] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_sum
% 5.15/5.46 thf(fact_6241_of__int__sum,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int] :
% 5.15/5.46 ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.15/5.46 = ( groups8778361861064173332t_real
% 5.15/5.46 @ ^ [X2: int] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_sum
% 5.15/5.46 thf(fact_6242_of__int__sum,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int] :
% 5.15/5.46 ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.15/5.46 = ( groups3906332499630173760nt_rat
% 5.15/5.46 @ ^ [X2: int] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_sum
% 5.15/5.46 thf(fact_6243_of__int__sum,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int] :
% 5.15/5.46 ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [X2: int] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_sum
% 5.15/5.46 thf(fact_6244_sum__abs__ge__zero,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int] :
% 5.15/5.46 ( ord_less_eq_int @ zero_zero_int
% 5.15/5.46 @ ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_abs_ge_zero
% 5.15/5.46 thf(fact_6245_sum__abs__ge__zero,axiom,
% 5.15/5.46 ! [F: nat > real,A2: set_nat] :
% 5.15/5.46 ( ord_less_eq_real @ zero_zero_real
% 5.15/5.46 @ ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_abs_ge_zero
% 5.15/5.46 thf(fact_6246_sum_Oswap,axiom,
% 5.15/5.46 ! [G: int > int > int,B3: set_int,A2: set_int] :
% 5.15/5.46 ( ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [I3: int] : ( groups4538972089207619220nt_int @ ( G @ I3 ) @ B3 )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [J3: int] :
% 5.15/5.46 ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [I3: int] : ( G @ I3 @ J3 )
% 5.15/5.46 @ A2 )
% 5.15/5.46 @ B3 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap
% 5.15/5.46 thf(fact_6247_sum_Oswap,axiom,
% 5.15/5.46 ! [G: complex > complex > complex,B3: set_complex,A2: set_complex] :
% 5.15/5.46 ( ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [I3: complex] : ( groups7754918857620584856omplex @ ( G @ I3 ) @ B3 )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [J3: complex] :
% 5.15/5.46 ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [I3: complex] : ( G @ I3 @ J3 )
% 5.15/5.46 @ A2 )
% 5.15/5.46 @ B3 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap
% 5.15/5.46 thf(fact_6248_sum_Oswap,axiom,
% 5.15/5.46 ! [G: nat > nat > nat,B3: set_nat,A2: set_nat] :
% 5.15/5.46 ( ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( G @ I3 ) @ B3 )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [J3: nat] :
% 5.15/5.46 ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [I3: nat] : ( G @ I3 @ J3 )
% 5.15/5.46 @ A2 )
% 5.15/5.46 @ B3 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap
% 5.15/5.46 thf(fact_6249_sum_Oswap,axiom,
% 5.15/5.46 ! [G: nat > nat > real,B3: set_nat,A2: set_nat] :
% 5.15/5.46 ( ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ ( G @ I3 ) @ B3 )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [J3: nat] :
% 5.15/5.46 ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [I3: nat] : ( G @ I3 @ J3 )
% 5.15/5.46 @ A2 )
% 5.15/5.46 @ B3 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap
% 5.15/5.46 thf(fact_6250_of__int__mask__eq,axiom,
% 5.15/5.46 ! [N2: nat] :
% 5.15/5.46 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.15/5.46 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % of_int_mask_eq
% 5.15/5.46 thf(fact_6251_arctan__less__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.15/5.46 = ( ord_less_real @ X @ Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % arctan_less_iff
% 5.15/5.46 thf(fact_6252_arctan__monotone,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_real @ X @ Y )
% 5.15/5.46 => ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % arctan_monotone
% 5.15/5.46 thf(fact_6253_arctan__monotone_H,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.46 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % arctan_monotone'
% 5.15/5.46 thf(fact_6254_arctan__le__iff,axiom,
% 5.15/5.46 ! [X: real,Y: real] :
% 5.15/5.46 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.15/5.46 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.15/5.46
% 5.15/5.46 % arctan_le_iff
% 5.15/5.46 thf(fact_6255_less__eq__mask,axiom,
% 5.15/5.46 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % less_eq_mask
% 5.15/5.46 thf(fact_6256_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.15/5.46 ( ! [I2: complex] :
% 5.15/5.46 ( ( member_complex @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6257_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.15/5.46 ( ! [I2: real] :
% 5.15/5.46 ( ( member_real @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6258_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.15/5.46 ( ! [I2: nat] :
% 5.15/5.46 ( ( member_nat @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6259_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.15/5.46 ( ! [I2: int] :
% 5.15/5.46 ( ( member_int @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6260_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.15/5.46 ( ! [I2: complex] :
% 5.15/5.46 ( ( member_complex @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6261_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.15/5.46 ( ! [I2: real] :
% 5.15/5.46 ( ( member_real @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6262_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.15/5.46 ( ! [I2: int] :
% 5.15/5.46 ( ( member_int @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6263_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.15/5.46 ( ! [I2: complex] :
% 5.15/5.46 ( ( member_complex @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6264_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_real,F: real > int,G: real > int] :
% 5.15/5.46 ( ! [I2: real] :
% 5.15/5.46 ( ( member_real @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6265_sum__mono,axiom,
% 5.15/5.46 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.15/5.46 ( ! [I2: nat] :
% 5.15/5.46 ( ( member_nat @ I2 @ K5 )
% 5.15/5.46 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono
% 5.15/5.46 thf(fact_6266_sum__distrib__left,axiom,
% 5.15/5.46 ! [R2: int,F: int > int,A2: set_int] :
% 5.15/5.46 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [N3: int] : ( times_times_int @ R2 @ ( F @ N3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_distrib_left
% 5.15/5.46 thf(fact_6267_sum__distrib__left,axiom,
% 5.15/5.46 ! [R2: complex,F: complex > complex,A2: set_complex] :
% 5.15/5.46 ( ( times_times_complex @ R2 @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [N3: complex] : ( times_times_complex @ R2 @ ( F @ N3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_distrib_left
% 5.15/5.46 thf(fact_6268_sum__distrib__left,axiom,
% 5.15/5.46 ! [R2: nat,F: nat > nat,A2: set_nat] :
% 5.15/5.46 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.46 = ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [N3: nat] : ( times_times_nat @ R2 @ ( F @ N3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_distrib_left
% 5.15/5.46 thf(fact_6269_sum__distrib__left,axiom,
% 5.15/5.46 ! [R2: real,F: nat > real,A2: set_nat] :
% 5.15/5.46 ( ( times_times_real @ R2 @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.15/5.46 = ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [N3: nat] : ( times_times_real @ R2 @ ( F @ N3 ) )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_distrib_left
% 5.15/5.46 thf(fact_6270_sum__distrib__right,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int,R2: int] :
% 5.15/5.46 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R2 )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [N3: int] : ( times_times_int @ ( F @ N3 ) @ R2 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_distrib_right
% 5.15/5.46 thf(fact_6271_sum__distrib__right,axiom,
% 5.15/5.46 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.15/5.46 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [N3: complex] : ( times_times_complex @ ( F @ N3 ) @ R2 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_distrib_right
% 5.15/5.46 thf(fact_6272_sum__distrib__right,axiom,
% 5.15/5.46 ! [F: nat > nat,A2: set_nat,R2: nat] :
% 5.15/5.46 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R2 )
% 5.15/5.46 = ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [N3: nat] : ( times_times_nat @ ( F @ N3 ) @ R2 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_distrib_right
% 5.15/5.46 thf(fact_6273_sum__distrib__right,axiom,
% 5.15/5.46 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.15/5.46 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.15/5.46 = ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ R2 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_distrib_right
% 5.15/5.46 thf(fact_6274_sum__product,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int,G: int > int,B3: set_int] :
% 5.15/5.46 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [I3: int] :
% 5.15/5.46 ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [J3: int] : ( times_times_int @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.15/5.46 @ B3 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_product
% 5.15/5.46 thf(fact_6275_sum__product,axiom,
% 5.15/5.46 ! [F: complex > complex,A2: set_complex,G: complex > complex,B3: set_complex] :
% 5.15/5.46 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B3 ) )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [I3: complex] :
% 5.15/5.46 ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.15/5.46 @ B3 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_product
% 5.15/5.46 thf(fact_6276_sum__product,axiom,
% 5.15/5.46 ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
% 5.15/5.46 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
% 5.15/5.46 = ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [I3: nat] :
% 5.15/5.46 ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.15/5.46 @ B3 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_product
% 5.15/5.46 thf(fact_6277_sum__product,axiom,
% 5.15/5.46 ! [F: nat > real,A2: set_nat,G: nat > real,B3: set_nat] :
% 5.15/5.46 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B3 ) )
% 5.15/5.46 = ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [I3: nat] :
% 5.15/5.46 ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [J3: nat] : ( times_times_real @ ( F @ I3 ) @ ( G @ J3 ) )
% 5.15/5.46 @ B3 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_product
% 5.15/5.46 thf(fact_6278_sum_Odistrib,axiom,
% 5.15/5.46 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.15/5.46 ( ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.distrib
% 5.15/5.46 thf(fact_6279_sum_Odistrib,axiom,
% 5.15/5.46 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.15/5.46 ( ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.distrib
% 5.15/5.46 thf(fact_6280_sum_Odistrib,axiom,
% 5.15/5.46 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.15/5.46 ( ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.distrib
% 5.15/5.46 thf(fact_6281_sum_Odistrib,axiom,
% 5.15/5.46 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.15/5.46 ( ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.distrib
% 5.15/5.46 thf(fact_6282_sum__subtractf,axiom,
% 5.15/5.46 ! [F: int > int,G: int > int,A2: set_int] :
% 5.15/5.46 ( ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [X2: int] : ( minus_minus_int @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_subtractf
% 5.15/5.46 thf(fact_6283_sum__subtractf,axiom,
% 5.15/5.46 ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 5.15/5.46 ( ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [X2: complex] : ( minus_minus_complex @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_subtractf
% 5.15/5.46 thf(fact_6284_sum__subtractf,axiom,
% 5.15/5.46 ! [F: nat > real,G: nat > real,A2: set_nat] :
% 5.15/5.46 ( ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [X2: nat] : ( minus_minus_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_subtractf
% 5.15/5.46 thf(fact_6285_sum__divide__distrib,axiom,
% 5.15/5.46 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.15/5.46 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [N3: complex] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ R2 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_divide_distrib
% 5.15/5.46 thf(fact_6286_sum__divide__distrib,axiom,
% 5.15/5.46 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.15/5.46 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.15/5.46 = ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ R2 )
% 5.15/5.46 @ A2 ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_divide_distrib
% 5.15/5.46 thf(fact_6287_sum__negf,axiom,
% 5.15/5.46 ! [F: int > int,A2: set_int] :
% 5.15/5.46 ( ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [X2: int] : ( uminus_uminus_int @ ( F @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( uminus_uminus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_negf
% 5.15/5.46 thf(fact_6288_sum__negf,axiom,
% 5.15/5.46 ! [F: complex > complex,A2: set_complex] :
% 5.15/5.46 ( ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [X2: complex] : ( uminus1482373934393186551omplex @ ( F @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( uminus1482373934393186551omplex @ ( groups7754918857620584856omplex @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_negf
% 5.15/5.46 thf(fact_6289_sum__negf,axiom,
% 5.15/5.46 ! [F: nat > real,A2: set_nat] :
% 5.15/5.46 ( ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [X2: nat] : ( uminus_uminus_real @ ( F @ X2 ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( uminus_uminus_real @ ( groups6591440286371151544t_real @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_negf
% 5.15/5.46 thf(fact_6290_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_real,B3: set_int,G: real > int > int,R: real > int > $o] :
% 5.15/5.46 ( ( finite_finite_real @ A2 )
% 5.15/5.46 => ( ( finite_finite_int @ B3 )
% 5.15/5.46 => ( ( groups1932886352136224148al_int
% 5.15/5.46 @ ^ [X2: real] :
% 5.15/5.46 ( groups4538972089207619220nt_int @ ( G @ X2 )
% 5.15/5.46 @ ( collect_int
% 5.15/5.46 @ ^ [Y2: int] :
% 5.15/5.46 ( ( member_int @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [Y2: int] :
% 5.15/5.46 ( groups1932886352136224148al_int
% 5.15/5.46 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_real
% 5.15/5.46 @ ^ [X2: real] :
% 5.15/5.46 ( ( member_real @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6291_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_nat,B3: set_int,G: nat > int > int,R: nat > int > $o] :
% 5.15/5.46 ( ( finite_finite_nat @ A2 )
% 5.15/5.46 => ( ( finite_finite_int @ B3 )
% 5.15/5.46 => ( ( groups3539618377306564664at_int
% 5.15/5.46 @ ^ [X2: nat] :
% 5.15/5.46 ( groups4538972089207619220nt_int @ ( G @ X2 )
% 5.15/5.46 @ ( collect_int
% 5.15/5.46 @ ^ [Y2: int] :
% 5.15/5.46 ( ( member_int @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [Y2: int] :
% 5.15/5.46 ( groups3539618377306564664at_int
% 5.15/5.46 @ ^ [X2: nat] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_nat
% 5.15/5.46 @ ^ [X2: nat] :
% 5.15/5.46 ( ( member_nat @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6292_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_complex,B3: set_int,G: complex > int > int,R: complex > int > $o] :
% 5.15/5.46 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.46 => ( ( finite_finite_int @ B3 )
% 5.15/5.46 => ( ( groups5690904116761175830ex_int
% 5.15/5.46 @ ^ [X2: complex] :
% 5.15/5.46 ( groups4538972089207619220nt_int @ ( G @ X2 )
% 5.15/5.46 @ ( collect_int
% 5.15/5.46 @ ^ [Y2: int] :
% 5.15/5.46 ( ( member_int @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [Y2: int] :
% 5.15/5.46 ( groups5690904116761175830ex_int
% 5.15/5.46 @ ^ [X2: complex] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_complex
% 5.15/5.46 @ ^ [X2: complex] :
% 5.15/5.46 ( ( member_complex @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6293_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_real,B3: set_complex,G: real > complex > complex,R: real > complex > $o] :
% 5.15/5.46 ( ( finite_finite_real @ A2 )
% 5.15/5.46 => ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.46 => ( ( groups5754745047067104278omplex
% 5.15/5.46 @ ^ [X2: real] :
% 5.15/5.46 ( groups7754918857620584856omplex @ ( G @ X2 )
% 5.15/5.46 @ ( collect_complex
% 5.15/5.46 @ ^ [Y2: complex] :
% 5.15/5.46 ( ( member_complex @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [Y2: complex] :
% 5.15/5.46 ( groups5754745047067104278omplex
% 5.15/5.46 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_real
% 5.15/5.46 @ ^ [X2: real] :
% 5.15/5.46 ( ( member_real @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6294_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_nat,B3: set_complex,G: nat > complex > complex,R: nat > complex > $o] :
% 5.15/5.46 ( ( finite_finite_nat @ A2 )
% 5.15/5.46 => ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.46 => ( ( groups2073611262835488442omplex
% 5.15/5.46 @ ^ [X2: nat] :
% 5.15/5.46 ( groups7754918857620584856omplex @ ( G @ X2 )
% 5.15/5.46 @ ( collect_complex
% 5.15/5.46 @ ^ [Y2: complex] :
% 5.15/5.46 ( ( member_complex @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [Y2: complex] :
% 5.15/5.46 ( groups2073611262835488442omplex
% 5.15/5.46 @ ^ [X2: nat] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_nat
% 5.15/5.46 @ ^ [X2: nat] :
% 5.15/5.46 ( ( member_nat @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6295_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_int,B3: set_complex,G: int > complex > complex,R: int > complex > $o] :
% 5.15/5.46 ( ( finite_finite_int @ A2 )
% 5.15/5.46 => ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.46 => ( ( groups3049146728041665814omplex
% 5.15/5.46 @ ^ [X2: int] :
% 5.15/5.46 ( groups7754918857620584856omplex @ ( G @ X2 )
% 5.15/5.46 @ ( collect_complex
% 5.15/5.46 @ ^ [Y2: complex] :
% 5.15/5.46 ( ( member_complex @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups7754918857620584856omplex
% 5.15/5.46 @ ^ [Y2: complex] :
% 5.15/5.46 ( groups3049146728041665814omplex
% 5.15/5.46 @ ^ [X2: int] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_int
% 5.15/5.46 @ ^ [X2: int] :
% 5.15/5.46 ( ( member_int @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6296_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_real,B3: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 5.15/5.46 ( ( finite_finite_real @ A2 )
% 5.15/5.46 => ( ( finite_finite_nat @ B3 )
% 5.15/5.46 => ( ( groups1935376822645274424al_nat
% 5.15/5.46 @ ^ [X2: real] :
% 5.15/5.46 ( groups3542108847815614940at_nat @ ( G @ X2 )
% 5.15/5.46 @ ( collect_nat
% 5.15/5.46 @ ^ [Y2: nat] :
% 5.15/5.46 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [Y2: nat] :
% 5.15/5.46 ( groups1935376822645274424al_nat
% 5.15/5.46 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_real
% 5.15/5.46 @ ^ [X2: real] :
% 5.15/5.46 ( ( member_real @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6297_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_complex,B3: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 5.15/5.46 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.46 => ( ( finite_finite_nat @ B3 )
% 5.15/5.46 => ( ( groups5693394587270226106ex_nat
% 5.15/5.46 @ ^ [X2: complex] :
% 5.15/5.46 ( groups3542108847815614940at_nat @ ( G @ X2 )
% 5.15/5.46 @ ( collect_nat
% 5.15/5.46 @ ^ [Y2: nat] :
% 5.15/5.46 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [Y2: nat] :
% 5.15/5.46 ( groups5693394587270226106ex_nat
% 5.15/5.46 @ ^ [X2: complex] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_complex
% 5.15/5.46 @ ^ [X2: complex] :
% 5.15/5.46 ( ( member_complex @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6298_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_int,B3: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 5.15/5.46 ( ( finite_finite_int @ A2 )
% 5.15/5.46 => ( ( finite_finite_nat @ B3 )
% 5.15/5.46 => ( ( groups4541462559716669496nt_nat
% 5.15/5.46 @ ^ [X2: int] :
% 5.15/5.46 ( groups3542108847815614940at_nat @ ( G @ X2 )
% 5.15/5.46 @ ( collect_nat
% 5.15/5.46 @ ^ [Y2: nat] :
% 5.15/5.46 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [Y2: nat] :
% 5.15/5.46 ( groups4541462559716669496nt_nat
% 5.15/5.46 @ ^ [X2: int] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_int
% 5.15/5.46 @ ^ [X2: int] :
% 5.15/5.46 ( ( member_int @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6299_sum_Oswap__restrict,axiom,
% 5.15/5.46 ! [A2: set_real,B3: set_nat,G: real > nat > real,R: real > nat > $o] :
% 5.15/5.46 ( ( finite_finite_real @ A2 )
% 5.15/5.46 => ( ( finite_finite_nat @ B3 )
% 5.15/5.46 => ( ( groups8097168146408367636l_real
% 5.15/5.46 @ ^ [X2: real] :
% 5.15/5.46 ( groups6591440286371151544t_real @ ( G @ X2 )
% 5.15/5.46 @ ( collect_nat
% 5.15/5.46 @ ^ [Y2: nat] :
% 5.15/5.46 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ A2 )
% 5.15/5.46 = ( groups6591440286371151544t_real
% 5.15/5.46 @ ^ [Y2: nat] :
% 5.15/5.46 ( groups8097168146408367636l_real
% 5.15/5.46 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.15/5.46 @ ( collect_real
% 5.15/5.46 @ ^ [X2: real] :
% 5.15/5.46 ( ( member_real @ X2 @ A2 )
% 5.15/5.46 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.46 @ B3 ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum.swap_restrict
% 5.15/5.46 thf(fact_6300_mod__sum__eq,axiom,
% 5.15/5.46 ! [F: int > int,A: int,A2: set_int] :
% 5.15/5.46 ( ( modulo_modulo_int
% 5.15/5.46 @ ( groups4538972089207619220nt_int
% 5.15/5.46 @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.15/5.46 @ A2 )
% 5.15/5.46 @ A )
% 5.15/5.46 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % mod_sum_eq
% 5.15/5.46 thf(fact_6301_mod__sum__eq,axiom,
% 5.15/5.46 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.15/5.46 ( ( modulo_modulo_nat
% 5.15/5.46 @ ( groups3542108847815614940at_nat
% 5.15/5.46 @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 5.15/5.46 @ A2 )
% 5.15/5.46 @ A )
% 5.15/5.46 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.15/5.46
% 5.15/5.46 % mod_sum_eq
% 5.15/5.46 thf(fact_6302_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_complex,F: complex > real] :
% 5.15/5.46 ( ! [X3: complex] :
% 5.15/5.46 ( ( member_complex @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.15/5.46 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6303_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_real,F: real > real] :
% 5.15/5.46 ( ! [X3: real] :
% 5.15/5.46 ( ( member_real @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.15/5.46 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6304_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_int,F: int > real] :
% 5.15/5.46 ( ! [X3: int] :
% 5.15/5.46 ( ( member_int @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.15/5.46 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6305_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_complex,F: complex > rat] :
% 5.15/5.46 ( ! [X3: complex] :
% 5.15/5.46 ( ( member_complex @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6306_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_real,F: real > rat] :
% 5.15/5.46 ( ! [X3: real] :
% 5.15/5.46 ( ( member_real @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6307_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_nat,F: nat > rat] :
% 5.15/5.46 ( ! [X3: nat] :
% 5.15/5.46 ( ( member_nat @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6308_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_int,F: int > rat] :
% 5.15/5.46 ( ! [X3: int] :
% 5.15/5.46 ( ( member_int @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.15/5.46 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6309_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_complex,F: complex > nat] :
% 5.15/5.46 ( ! [X3: complex] :
% 5.15/5.46 ( ( member_complex @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.15/5.46 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6310_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_real,F: real > nat] :
% 5.15/5.46 ( ! [X3: real] :
% 5.15/5.46 ( ( member_real @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.15/5.46 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6311_sum__nonpos,axiom,
% 5.15/5.46 ! [A2: set_int,F: int > nat] :
% 5.15/5.46 ( ! [X3: int] :
% 5.15/5.46 ( ( member_int @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.15/5.46 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonpos
% 5.15/5.46 thf(fact_6312_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_complex,F: complex > real] :
% 5.15/5.46 ( ! [X3: complex] :
% 5.15/5.46 ( ( member_complex @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6313_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_real,F: real > real] :
% 5.15/5.46 ( ! [X3: real] :
% 5.15/5.46 ( ( member_real @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6314_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_int,F: int > real] :
% 5.15/5.46 ( ! [X3: int] :
% 5.15/5.46 ( ( member_int @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6315_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_complex,F: complex > rat] :
% 5.15/5.46 ( ! [X3: complex] :
% 5.15/5.46 ( ( member_complex @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6316_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_real,F: real > rat] :
% 5.15/5.46 ( ! [X3: real] :
% 5.15/5.46 ( ( member_real @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6317_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_nat,F: nat > rat] :
% 5.15/5.46 ( ! [X3: nat] :
% 5.15/5.46 ( ( member_nat @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6318_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_int,F: int > rat] :
% 5.15/5.46 ( ! [X3: int] :
% 5.15/5.46 ( ( member_int @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6319_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_complex,F: complex > nat] :
% 5.15/5.46 ( ! [X3: complex] :
% 5.15/5.46 ( ( member_complex @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6320_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_real,F: real > nat] :
% 5.15/5.46 ( ! [X3: real] :
% 5.15/5.46 ( ( member_real @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6321_sum__nonneg,axiom,
% 5.15/5.46 ! [A2: set_int,F: int > nat] :
% 5.15/5.46 ( ! [X3: int] :
% 5.15/5.46 ( ( member_int @ X3 @ A2 )
% 5.15/5.46 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.46 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_nonneg
% 5.15/5.46 thf(fact_6322_sum__mono__inv,axiom,
% 5.15/5.46 ! [F: real > rat,I5: set_real,G: real > rat,I: real] :
% 5.15/5.46 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 5.15/5.46 = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 5.15/5.46 => ( ! [I2: real] :
% 5.15/5.46 ( ( member_real @ I2 @ I5 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ( member_real @ I @ I5 )
% 5.15/5.46 => ( ( finite_finite_real @ I5 )
% 5.15/5.46 => ( ( F @ I )
% 5.15/5.46 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono_inv
% 5.15/5.46 thf(fact_6323_sum__mono__inv,axiom,
% 5.15/5.46 ! [F: nat > rat,I5: set_nat,G: nat > rat,I: nat] :
% 5.15/5.46 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 5.15/5.46 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 5.15/5.46 => ( ! [I2: nat] :
% 5.15/5.46 ( ( member_nat @ I2 @ I5 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ( member_nat @ I @ I5 )
% 5.15/5.46 => ( ( finite_finite_nat @ I5 )
% 5.15/5.46 => ( ( F @ I )
% 5.15/5.46 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.46
% 5.15/5.46 % sum_mono_inv
% 5.15/5.46 thf(fact_6324_sum__mono__inv,axiom,
% 5.15/5.46 ! [F: complex > rat,I5: set_complex,G: complex > rat,I: complex] :
% 5.15/5.46 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 5.15/5.46 = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 5.15/5.46 => ( ! [I2: complex] :
% 5.15/5.46 ( ( member_complex @ I2 @ I5 )
% 5.15/5.46 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.46 => ( ( member_complex @ I @ I5 )
% 5.15/5.46 => ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.46 => ( ( F @ I )
% 5.15/5.46 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono_inv
% 5.15/5.47 thf(fact_6325_sum__mono__inv,axiom,
% 5.15/5.47 ! [F: int > rat,I5: set_int,G: int > rat,I: int] :
% 5.15/5.47 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 5.15/5.47 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.47 => ( ( member_int @ I @ I5 )
% 5.15/5.47 => ( ( finite_finite_int @ I5 )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono_inv
% 5.15/5.47 thf(fact_6326_sum__mono__inv,axiom,
% 5.15/5.47 ! [F: real > nat,I5: set_real,G: real > nat,I: real] :
% 5.15/5.47 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 5.15/5.47 = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.47 => ( ( member_real @ I @ I5 )
% 5.15/5.47 => ( ( finite_finite_real @ I5 )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono_inv
% 5.15/5.47 thf(fact_6327_sum__mono__inv,axiom,
% 5.15/5.47 ! [F: complex > nat,I5: set_complex,G: complex > nat,I: complex] :
% 5.15/5.47 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 5.15/5.47 = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.47 => ( ( member_complex @ I @ I5 )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono_inv
% 5.15/5.47 thf(fact_6328_sum__mono__inv,axiom,
% 5.15/5.47 ! [F: int > nat,I5: set_int,G: int > nat,I: int] :
% 5.15/5.47 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 5.15/5.47 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.47 => ( ( member_int @ I @ I5 )
% 5.15/5.47 => ( ( finite_finite_int @ I5 )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono_inv
% 5.15/5.47 thf(fact_6329_sum__mono__inv,axiom,
% 5.15/5.47 ! [F: real > int,I5: set_real,G: real > int,I: real] :
% 5.15/5.47 ( ( ( groups1932886352136224148al_int @ F @ I5 )
% 5.15/5.47 = ( groups1932886352136224148al_int @ G @ I5 ) )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.47 => ( ( member_real @ I @ I5 )
% 5.15/5.47 => ( ( finite_finite_real @ I5 )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono_inv
% 5.15/5.47 thf(fact_6330_sum__mono__inv,axiom,
% 5.15/5.47 ! [F: nat > int,I5: set_nat,G: nat > int,I: nat] :
% 5.15/5.47 ( ( ( groups3539618377306564664at_int @ F @ I5 )
% 5.15/5.47 = ( groups3539618377306564664at_int @ G @ I5 ) )
% 5.15/5.47 => ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.47 => ( ( member_nat @ I @ I5 )
% 5.15/5.47 => ( ( finite_finite_nat @ I5 )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono_inv
% 5.15/5.47 thf(fact_6331_sum__mono__inv,axiom,
% 5.15/5.47 ! [F: complex > int,I5: set_complex,G: complex > int,I: complex] :
% 5.15/5.47 ( ( ( groups5690904116761175830ex_int @ F @ I5 )
% 5.15/5.47 = ( groups5690904116761175830ex_int @ G @ I5 ) )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.15/5.47 => ( ( member_complex @ I @ I5 )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = ( G @ I ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono_inv
% 5.15/5.47 thf(fact_6332_abs__zmult__eq__1,axiom,
% 5.15/5.47 ! [M: int,N2: int] :
% 5.15/5.47 ( ( ( abs_abs_int @ ( times_times_int @ M @ N2 ) )
% 5.15/5.47 = one_one_int )
% 5.15/5.47 => ( ( abs_abs_int @ M )
% 5.15/5.47 = one_one_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % abs_zmult_eq_1
% 5.15/5.47 thf(fact_6333_abs__div,axiom,
% 5.15/5.47 ! [Y: int,X: int] :
% 5.15/5.47 ( ( dvd_dvd_int @ Y @ X )
% 5.15/5.47 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 5.15/5.47 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % abs_div
% 5.15/5.47 thf(fact_6334_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_real,G: real > complex,P: real > $o] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ( groups5754745047067104278omplex @ G
% 5.15/5.47 @ ( collect_real
% 5.15/5.47 @ ^ [X2: real] :
% 5.15/5.47 ( ( member_real @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups5754745047067104278omplex
% 5.15/5.47 @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6335_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( groups2073611262835488442omplex @ G
% 5.15/5.47 @ ( collect_nat
% 5.15/5.47 @ ^ [X2: nat] :
% 5.15/5.47 ( ( member_nat @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6336_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_int,G: int > complex,P: int > $o] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups3049146728041665814omplex @ G
% 5.15/5.47 @ ( collect_int
% 5.15/5.47 @ ^ [X2: int] :
% 5.15/5.47 ( ( member_int @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups3049146728041665814omplex
% 5.15/5.47 @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6337_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_real,G: real > real,P: real > $o] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ( groups8097168146408367636l_real @ G
% 5.15/5.47 @ ( collect_real
% 5.15/5.47 @ ^ [X2: real] :
% 5.15/5.47 ( ( member_real @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups8097168146408367636l_real
% 5.15/5.47 @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6338_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5808333547571424918x_real @ G
% 5.15/5.47 @ ( collect_complex
% 5.15/5.47 @ ^ [X2: complex] :
% 5.15/5.47 ( ( member_complex @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups5808333547571424918x_real
% 5.15/5.47 @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6339_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_int,G: int > real,P: int > $o] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups8778361861064173332t_real @ G
% 5.15/5.47 @ ( collect_int
% 5.15/5.47 @ ^ [X2: int] :
% 5.15/5.47 ( ( member_int @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups8778361861064173332t_real
% 5.15/5.47 @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6340_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_real,G: real > rat,P: real > $o] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ( groups1300246762558778688al_rat @ G
% 5.15/5.47 @ ( collect_real
% 5.15/5.47 @ ^ [X2: real] :
% 5.15/5.47 ( ( member_real @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups1300246762558778688al_rat
% 5.15/5.47 @ ^ [X2: real] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6341_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_nat,G: nat > rat,P: nat > $o] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ G
% 5.15/5.47 @ ( collect_nat
% 5.15/5.47 @ ^ [X2: nat] :
% 5.15/5.47 ( ( member_nat @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [X2: nat] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6342_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_complex,G: complex > rat,P: complex > $o] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5058264527183730370ex_rat @ G
% 5.15/5.47 @ ( collect_complex
% 5.15/5.47 @ ^ [X2: complex] :
% 5.15/5.47 ( ( member_complex @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups5058264527183730370ex_rat
% 5.15/5.47 @ ^ [X2: complex] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6343_sum_Ointer__filter,axiom,
% 5.15/5.47 ! [A2: set_int,G: int > rat,P: int > $o] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups3906332499630173760nt_rat @ G
% 5.15/5.47 @ ( collect_int
% 5.15/5.47 @ ^ [X2: int] :
% 5.15/5.47 ( ( member_int @ X2 @ A2 )
% 5.15/5.47 & ( P @ X2 ) ) ) )
% 5.15/5.47 = ( groups3906332499630173760nt_rat
% 5.15/5.47 @ ^ [X2: int] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 5.15/5.47 @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.inter_filter
% 5.15/5.47 thf(fact_6344_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_int,G: int > complex] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups3049146728041665814omplex @ G
% 5.15/5.47 @ ( minus_minus_set_int @ A2
% 5.15/5.47 @ ( collect_int
% 5.15/5.47 @ ^ [X2: int] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_complex ) ) ) )
% 5.15/5.47 = ( groups3049146728041665814omplex @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6345_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_complex,G: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5808333547571424918x_real @ G
% 5.15/5.47 @ ( minus_811609699411566653omplex @ A2
% 5.15/5.47 @ ( collect_complex
% 5.15/5.47 @ ^ [X2: complex] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_real ) ) ) )
% 5.15/5.47 = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6346_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_int,G: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups8778361861064173332t_real @ G
% 5.15/5.47 @ ( minus_minus_set_int @ A2
% 5.15/5.47 @ ( collect_int
% 5.15/5.47 @ ^ [X2: int] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_real ) ) ) )
% 5.15/5.47 = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6347_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_complex,G: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5058264527183730370ex_rat @ G
% 5.15/5.47 @ ( minus_811609699411566653omplex @ A2
% 5.15/5.47 @ ( collect_complex
% 5.15/5.47 @ ^ [X2: complex] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_rat ) ) ) )
% 5.15/5.47 = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6348_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_int,G: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups3906332499630173760nt_rat @ G
% 5.15/5.47 @ ( minus_minus_set_int @ A2
% 5.15/5.47 @ ( collect_int
% 5.15/5.47 @ ^ [X2: int] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_rat ) ) ) )
% 5.15/5.47 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6349_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_complex,G: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5693394587270226106ex_nat @ G
% 5.15/5.47 @ ( minus_811609699411566653omplex @ A2
% 5.15/5.47 @ ( collect_complex
% 5.15/5.47 @ ^ [X2: complex] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_nat ) ) ) )
% 5.15/5.47 = ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6350_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_int,G: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups4541462559716669496nt_nat @ G
% 5.15/5.47 @ ( minus_minus_set_int @ A2
% 5.15/5.47 @ ( collect_int
% 5.15/5.47 @ ^ [X2: int] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_nat ) ) ) )
% 5.15/5.47 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6351_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_complex,G: complex > int] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5690904116761175830ex_int @ G
% 5.15/5.47 @ ( minus_811609699411566653omplex @ A2
% 5.15/5.47 @ ( collect_complex
% 5.15/5.47 @ ^ [X2: complex] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_int ) ) ) )
% 5.15/5.47 = ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6352_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_nat,G: nat > complex] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( groups2073611262835488442omplex @ G
% 5.15/5.47 @ ( minus_minus_set_nat @ A2
% 5.15/5.47 @ ( collect_nat
% 5.15/5.47 @ ^ [X2: nat] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_complex ) ) ) )
% 5.15/5.47 = ( groups2073611262835488442omplex @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6353_sum_Osetdiff__irrelevant,axiom,
% 5.15/5.47 ! [A2: set_nat,G: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ G
% 5.15/5.47 @ ( minus_minus_set_nat @ A2
% 5.15/5.47 @ ( collect_nat
% 5.15/5.47 @ ^ [X2: nat] :
% 5.15/5.47 ( ( G @ X2 )
% 5.15/5.47 = zero_zero_rat ) ) ) )
% 5.15/5.47 = ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.setdiff_irrelevant
% 5.15/5.47 thf(fact_6354_mask__nonnegative__int,axiom,
% 5.15/5.47 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_nonnegative_int
% 5.15/5.47 thf(fact_6355_not__mask__negative__int,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % not_mask_negative_int
% 5.15/5.47 thf(fact_6356_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ T )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ S )
% 5.15/5.47 => ? [Xa: complex] :
% 5.15/5.47 ( ( member_complex @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6357_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ( finite_finite_int @ T )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ S )
% 5.15/5.47 => ? [Xa: int] :
% 5.15/5.47 ( ( member_int @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6358_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ S )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ T )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ S )
% 5.15/5.47 => ? [Xa: complex] :
% 5.15/5.47 ( ( member_complex @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6359_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ S )
% 5.15/5.47 => ( ( finite_finite_int @ T )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ S )
% 5.15/5.47 => ? [Xa: int] :
% 5.15/5.47 ( ( member_int @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6360_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ S )
% 5.15/5.47 => ( ( finite_finite_nat @ T )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ S )
% 5.15/5.47 => ? [Xa: nat] :
% 5.15/5.47 ( ( member_nat @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6361_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_nat,T: set_complex,G: complex > rat,I: complex > nat,F: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ S )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ T )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ S )
% 5.15/5.47 => ? [Xa: complex] :
% 5.15/5.47 ( ( member_complex @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6362_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_nat,T: set_int,G: int > rat,I: int > nat,F: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ S )
% 5.15/5.47 => ( ( finite_finite_int @ T )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ S )
% 5.15/5.47 => ? [Xa: int] :
% 5.15/5.47 ( ( member_int @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6363_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_complex,T: set_nat,G: nat > rat,I: nat > complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ( finite_finite_nat @ T )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ S )
% 5.15/5.47 => ? [Xa: nat] :
% 5.15/5.47 ( ( member_nat @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6364_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_complex,T: set_complex,G: complex > rat,I: complex > complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ T )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ S )
% 5.15/5.47 => ? [Xa: complex] :
% 5.15/5.47 ( ( member_complex @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6365_sum__le__included,axiom,
% 5.15/5.47 ! [S: set_complex,T: set_int,G: int > rat,I: int > complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ( finite_finite_int @ T )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ T )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ S )
% 5.15/5.47 => ? [Xa: int] :
% 5.15/5.47 ( ( member_int @ Xa @ T )
% 5.15/5.47 & ( ( I @ Xa )
% 5.15/5.47 = X3 )
% 5.15/5.47 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_le_included
% 5.15/5.47 thf(fact_6366_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_real,F: real > real] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 = ( ! [X2: real] :
% 5.15/5.47 ( ( member_real @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6367_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 = ( ! [X2: complex] :
% 5.15/5.47 ( ( member_complex @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6368_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 = ( ! [X2: int] :
% 5.15/5.47 ( ( member_int @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_real ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6369_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_real,F: real > rat] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 = ( ! [X2: real] :
% 5.15/5.47 ( ( member_real @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6370_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_nat,F: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 = ( ! [X2: nat] :
% 5.15/5.47 ( ( member_nat @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6371_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 = ( ! [X2: complex] :
% 5.15/5.47 ( ( member_complex @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6372_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 = ( ! [X2: int] :
% 5.15/5.47 ( ( member_int @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_rat ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6373_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_real,F: real > nat] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 = ( ! [X2: real] :
% 5.15/5.47 ( ( member_real @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6374_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 = ( ! [X2: complex] :
% 5.15/5.47 ( ( member_complex @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6375_sum__nonneg__eq__0__iff,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 = ( ! [X2: int] :
% 5.15/5.47 ( ( member_int @ X2 @ A2 )
% 5.15/5.47 => ( ( F @ X2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_eq_0_iff
% 5.15/5.47 thf(fact_6376_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: complex] :
% 5.15/5.47 ( ( member_complex @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6377_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > real,G: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: int] :
% 5.15/5.47 ( ( member_int @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6378_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: nat] :
% 5.15/5.47 ( ( member_nat @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6379_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: complex] :
% 5.15/5.47 ( ( member_complex @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6380_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: int] :
% 5.15/5.47 ( ( member_int @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6381_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: complex] :
% 5.15/5.47 ( ( member_complex @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6382_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: int] :
% 5.15/5.47 ( ( member_int @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6383_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: nat] :
% 5.15/5.47 ( ( member_nat @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6384_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: complex] :
% 5.15/5.47 ( ( member_complex @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6385_sum__strict__mono__ex1,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > int,G: int > int] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ? [X5: int] :
% 5.15/5.47 ( ( member_int @ X5 @ A2 )
% 5.15/5.47 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.15/5.47 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono_ex1
% 5.15/5.47 thf(fact_6386_sum_Orelated,axiom,
% 5.15/5.47 ! [R: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.15/5.47 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.15/5.47 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_complex @ X16 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite_finite_nat @ S3 )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups2073611262835488442omplex @ H2 @ S3 ) @ ( groups2073611262835488442omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6387_sum_Orelated,axiom,
% 5.15/5.47 ! [R: complex > complex > $o,S3: set_int,H2: int > complex,G: int > complex] :
% 5.15/5.47 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.15/5.47 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_complex @ X16 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite_finite_int @ S3 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups3049146728041665814omplex @ H2 @ S3 ) @ ( groups3049146728041665814omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6388_sum_Orelated,axiom,
% 5.15/5.47 ! [R: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.15/5.47 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.15/5.47 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_real @ X16 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups5808333547571424918x_real @ H2 @ S3 ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6389_sum_Orelated,axiom,
% 5.15/5.47 ! [R: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.15/5.47 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.15/5.47 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_real @ X16 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite_finite_int @ S3 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups8778361861064173332t_real @ H2 @ S3 ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6390_sum_Orelated,axiom,
% 5.15/5.47 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.15/5.47 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.15/5.47 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite_finite_nat @ S3 )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups2906978787729119204at_rat @ H2 @ S3 ) @ ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6391_sum_Orelated,axiom,
% 5.15/5.47 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.15/5.47 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.15/5.47 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6392_sum_Orelated,axiom,
% 5.15/5.47 ! [R: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.15/5.47 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.15/5.47 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite_finite_int @ S3 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups3906332499630173760nt_rat @ H2 @ S3 ) @ ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6393_sum_Orelated,axiom,
% 5.15/5.47 ! [R: nat > nat > $o,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.15/5.47 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.15/5.47 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_nat @ X16 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S3 ) @ ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6394_sum_Orelated,axiom,
% 5.15/5.47 ! [R: nat > nat > $o,S3: set_int,H2: int > nat,G: int > nat] :
% 5.15/5.47 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.15/5.47 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_nat @ X16 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite_finite_int @ S3 )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups4541462559716669496nt_nat @ H2 @ S3 ) @ ( groups4541462559716669496nt_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6395_sum_Orelated,axiom,
% 5.15/5.47 ! [R: int > int > $o,S3: set_nat,H2: nat > int,G: nat > int] :
% 5.15/5.47 ( ( R @ zero_zero_int @ zero_zero_int )
% 5.15/5.47 => ( ! [X16: int,Y15: int,X23: int,Y23: int] :
% 5.15/5.47 ( ( ( R @ X16 @ X23 )
% 5.15/5.47 & ( R @ Y15 @ Y23 ) )
% 5.15/5.47 => ( R @ ( plus_plus_int @ X16 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.15/5.47 => ( ( finite_finite_nat @ S3 )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ S3 )
% 5.15/5.47 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( R @ ( groups3539618377306564664at_int @ H2 @ S3 ) @ ( groups3539618377306564664at_int @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.related
% 5.15/5.47 thf(fact_6396_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_complex )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6397_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > real,G: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_int )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6398_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_real,F: real > real,G: real > real] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_real )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6399_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_complex )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6400_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_nat )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6401_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_int )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6402_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_real )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6403_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_complex )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6404_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_int )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6405_sum__strict__mono,axiom,
% 5.15/5.47 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.15/5.47 ( ( finite_finite_real @ A2 )
% 5.15/5.47 => ( ( A2 != bot_bot_set_real )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.47 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono
% 5.15/5.47 thf(fact_6406_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,G: complex > real] :
% 5.15/5.47 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.15/5.47 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5808333547571424918x_real @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6407_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,G: int > real] :
% 5.15/5.47 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.15/5.47 => ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.15/5.47 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups8778361861064173332t_real @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6408_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,G: complex > rat] :
% 5.15/5.47 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.15/5.47 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5058264527183730370ex_rat @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6409_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,G: int > rat] :
% 5.15/5.47 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.15/5.47 => ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.15/5.47 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6410_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,G: complex > nat] :
% 5.15/5.47 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.15/5.47 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5693394587270226106ex_nat @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6411_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,G: int > nat] :
% 5.15/5.47 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.15/5.47 => ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.15/5.47 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6412_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,G: complex > int] :
% 5.15/5.47 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.15/5.47 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5690904116761175830ex_int @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6413_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,G: int > complex] :
% 5.15/5.47 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.15/5.47 => ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( groups3049146728041665814omplex @ G @ A2 )
% 5.15/5.47 = ( plus_plus_complex @ ( groups3049146728041665814omplex @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups3049146728041665814omplex @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6414_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_nat,A2: set_nat,G: nat > rat] :
% 5.15/5.47 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.15/5.47 => ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.15/5.47 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6415_sum_Osubset__diff,axiom,
% 5.15/5.47 ! [B3: set_nat,A2: set_nat,G: nat > int] :
% 5.15/5.47 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.15/5.47 => ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 5.15/5.47 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.subset_diff
% 5.15/5.47 thf(fact_6416_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_complex,B3: set_complex,F: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6417_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_int,B3: set_int,F: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.15/5.47 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6418_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_complex,B3: set_complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6419_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_int,B3: set_int,F: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.15/5.47 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6420_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_complex,B3: set_complex,F: complex > int] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6421_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_nat,B3: set_nat,F: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6422_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_nat,B3: set_nat,F: nat > int] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.15/5.47 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6423_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_int,B3: set_int,F: int > int] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.15/5.47 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6424_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_complex,B3: set_complex,F: complex > complex] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6425_sum__diff,axiom,
% 5.15/5.47 ! [A2: set_nat,B3: set_nat,F: nat > real] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.15/5.47 => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff
% 5.15/5.47 thf(fact_6426_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_real,F: real > real,I: real] :
% 5.15/5.47 ( ( finite_finite_real @ S )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 => ( ( member_real @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_real ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6427_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_complex,F: complex > real,I: complex] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 => ( ( member_complex @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_real ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6428_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_int,F: int > real,I: int] :
% 5.15/5.47 ( ( finite_finite_int @ S )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 => ( ( member_int @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_real ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6429_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_real,F: real > rat,I: real] :
% 5.15/5.47 ( ( finite_finite_real @ S )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 => ( ( member_real @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_rat ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6430_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_nat,F: nat > rat,I: nat] :
% 5.15/5.47 ( ( finite_finite_nat @ S )
% 5.15/5.47 => ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 => ( ( member_nat @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_rat ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6431_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_complex,F: complex > rat,I: complex] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 => ( ( member_complex @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_rat ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6432_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_int,F: int > rat,I: int] :
% 5.15/5.47 ( ( finite_finite_int @ S )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 => ( ( member_int @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_rat ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6433_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_real,F: real > nat,I: real] :
% 5.15/5.47 ( ( finite_finite_real @ S )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 => ( ( member_real @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6434_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_complex,F: complex > nat,I: complex] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 => ( ( member_complex @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6435_sum__nonneg__0,axiom,
% 5.15/5.47 ! [S: set_int,F: int > nat,I: int] :
% 5.15/5.47 ( ( finite_finite_int @ S )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 => ( ( member_int @ I @ S )
% 5.15/5.47 => ( ( F @ I )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_0
% 5.15/5.47 thf(fact_6436_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_real,F: real > real,B3: real,I: real] :
% 5.15/5.47 ( ( finite_finite_real @ S )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_real @ I @ S )
% 5.15/5.47 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6437_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_complex,F: complex > real,B3: real,I: complex] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_complex @ I @ S )
% 5.15/5.47 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6438_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_int,F: int > real,B3: real,I: int] :
% 5.15/5.47 ( ( finite_finite_int @ S )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_int @ I @ S )
% 5.15/5.47 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6439_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_real,F: real > rat,B3: rat,I: real] :
% 5.15/5.47 ( ( finite_finite_real @ S )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_real @ I @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6440_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_nat,F: nat > rat,B3: rat,I: nat] :
% 5.15/5.47 ( ( finite_finite_nat @ S )
% 5.15/5.47 => ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_nat @ I @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6441_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_complex,F: complex > rat,B3: rat,I: complex] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_complex @ I @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6442_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_int,F: int > rat,B3: rat,I: int] :
% 5.15/5.47 ( ( finite_finite_int @ S )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_int @ I @ S )
% 5.15/5.47 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6443_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_real,F: real > nat,B3: nat,I: real] :
% 5.15/5.47 ( ( finite_finite_real @ S )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_real @ I @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6444_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_complex,F: complex > nat,B3: nat,I: complex] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ S )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_complex @ I @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6445_sum__nonneg__leq__bound,axiom,
% 5.15/5.47 ! [S: set_int,F: int > nat,B3: nat,I: int] :
% 5.15/5.47 ( ( finite_finite_int @ S )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 5.15/5.47 = B3 )
% 5.15/5.47 => ( ( member_int @ I @ S )
% 5.15/5.47 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nonneg_leq_bound
% 5.15/5.47 thf(fact_6446_abs__mod__less,axiom,
% 5.15/5.47 ! [L: int,K: int] :
% 5.15/5.47 ( ( L != zero_zero_int )
% 5.15/5.47 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % abs_mod_less
% 5.15/5.47 thf(fact_6447_less__mask,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.47 => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % less_mask
% 5.15/5.47 thf(fact_6448_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_real,I: real,F: real > real] :
% 5.15/5.47 ( ( finite_finite_real @ I5 )
% 5.15/5.47 => ( ( member_real @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6449_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_complex,I: complex,F: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.47 => ( ( member_complex @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6450_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_int,I: int,F: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ I5 )
% 5.15/5.47 => ( ( member_int @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6451_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_real,I: real,F: real > rat] :
% 5.15/5.47 ( ( finite_finite_real @ I5 )
% 5.15/5.47 => ( ( member_real @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6452_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_nat,I: nat,F: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ I5 )
% 5.15/5.47 => ( ( member_nat @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6453_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_complex,I: complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.47 => ( ( member_complex @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6454_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_int,I: int,F: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ I5 )
% 5.15/5.47 => ( ( member_int @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6455_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_real,I: real,F: real > nat] :
% 5.15/5.47 ( ( finite_finite_real @ I5 )
% 5.15/5.47 => ( ( member_real @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6456_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_complex,I: complex,F: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.47 => ( ( member_complex @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6457_sum__pos2,axiom,
% 5.15/5.47 ! [I5: set_int,I: int,F: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ I5 )
% 5.15/5.47 => ( ( member_int @ I @ I5 )
% 5.15/5.47 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos2
% 5.15/5.47 thf(fact_6458_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_real,A2: set_real,F: real > real] :
% 5.15/5.47 ( ( finite_finite_real @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: real] :
% 5.15/5.47 ( ( member_real @ B6 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6459_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,F: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: complex] :
% 5.15/5.47 ( ( member_complex @ B6 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6460_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,F: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: int] :
% 5.15/5.47 ( ( member_int @ B6 @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6461_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_real,A2: set_real,F: real > rat] :
% 5.15/5.47 ( ( finite_finite_real @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: real] :
% 5.15/5.47 ( ( member_real @ B6 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6462_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: complex] :
% 5.15/5.47 ( ( member_complex @ B6 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6463_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,F: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: int] :
% 5.15/5.47 ( ( member_int @ B6 @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6464_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_real,A2: set_real,F: real > nat] :
% 5.15/5.47 ( ( finite_finite_real @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: real] :
% 5.15/5.47 ( ( member_real @ B6 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6465_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: complex] :
% 5.15/5.47 ( ( member_complex @ B6 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6466_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,F: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: int] :
% 5.15/5.47 ( ( member_int @ B6 @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6467_sum__mono2,axiom,
% 5.15/5.47 ! [B3: set_real,A2: set_real,F: real > int] :
% 5.15/5.47 ( ( finite_finite_real @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.15/5.47 => ( ! [B6: real] :
% 5.15/5.47 ( ( member_real @ B6 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.15/5.47 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B6 ) ) )
% 5.15/5.47 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_mono2
% 5.15/5.47 thf(fact_6468_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_complex,F: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_complex )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6469_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_int,F: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_int )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6470_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_real,F: real > real] :
% 5.15/5.47 ( ( finite_finite_real @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_real )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6471_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_complex )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6472_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_nat,F: nat > rat] :
% 5.15/5.47 ( ( finite_finite_nat @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_nat )
% 5.15/5.47 => ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6473_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_int,F: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_int )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6474_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_real,F: real > rat] :
% 5.15/5.47 ( ( finite_finite_real @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_real )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6475_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_complex,F: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_complex )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6476_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_int,F: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_int )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6477_sum__pos,axiom,
% 5.15/5.47 ! [I5: set_real,F: real > nat] :
% 5.15/5.47 ( ( finite_finite_real @ I5 )
% 5.15/5.47 => ( ( I5 != bot_bot_set_real )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 5.15/5.47 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_pos
% 5.15/5.47 thf(fact_6478_zdvd__mult__cancel1,axiom,
% 5.15/5.47 ! [M: int,N2: int] :
% 5.15/5.47 ( ( M != zero_zero_int )
% 5.15/5.47 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N2 ) @ M )
% 5.15/5.47 = ( ( abs_abs_int @ N2 )
% 5.15/5.47 = one_one_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % zdvd_mult_cancel1
% 5.15/5.47 thf(fact_6479_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_real,A2: set_real,B: real,F: real > real] :
% 5.15/5.47 ( ( finite_finite_real @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.15/5.47 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6480_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.15/5.47 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6481_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,B: int,F: int > real] :
% 5.15/5.47 ( ( finite_finite_int @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.15/5.47 => ( ( member_int @ B @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6482_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_real,A2: set_real,B: real,F: real > rat] :
% 5.15/5.47 ( ( finite_finite_real @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.15/5.47 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6483_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.15/5.47 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6484_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,B: int,F: int > rat] :
% 5.15/5.47 ( ( finite_finite_int @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.15/5.47 => ( ( member_int @ B @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6485_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_real,A2: set_real,B: real,F: real > nat] :
% 5.15/5.47 ( ( finite_finite_real @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.15/5.47 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6486_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.15/5.47 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6487_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,B: int,F: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.15/5.47 => ( ( member_int @ B @ ( minus_minus_set_int @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6488_sum__strict__mono2,axiom,
% 5.15/5.47 ! [B3: set_real,A2: set_real,B: real,F: real > int] :
% 5.15/5.47 ( ( finite_finite_real @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.15/5.47 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.15/5.47 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.15/5.47 => ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ B3 )
% 5.15/5.47 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_strict_mono2
% 5.15/5.47 thf(fact_6489_even__add__abs__iff,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 5.15/5.47 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_add_abs_iff
% 5.15/5.47 thf(fact_6490_even__abs__add__iff,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 5.15/5.47 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_abs_add_iff
% 5.15/5.47 thf(fact_6491_num_Osize__gen_I1_J,axiom,
% 5.15/5.47 ( ( size_num @ one )
% 5.15/5.47 = zero_zero_nat ) ).
% 5.15/5.47
% 5.15/5.47 % num.size_gen(1)
% 5.15/5.47 thf(fact_6492_Suc__mask__eq__exp,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.15/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.47
% 5.15/5.47 % Suc_mask_eq_exp
% 5.15/5.47 thf(fact_6493_mask__nat__less__exp,axiom,
% 5.15/5.47 ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_nat_less_exp
% 5.15/5.47 thf(fact_6494_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.15/5.47 ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups6621422865394947399nteger @ X @ I5 )
% 5.15/5.47 = one_one_Code_integer )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_le3102999989581377725nteger
% 5.15/5.47 @ ( abs_abs_Code_integer
% 5.15/5.47 @ ( minus_8373710615458151222nteger
% 5.15/5.47 @ ( groups6621422865394947399nteger
% 5.15/5.47 @ ^ [I3: complex] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6495_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.15/5.47 ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups7713935264441627589nteger @ X @ I5 )
% 5.15/5.47 = one_one_Code_integer )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_le3102999989581377725nteger
% 5.15/5.47 @ ( abs_abs_Code_integer
% 5.15/5.47 @ ( minus_8373710615458151222nteger
% 5.15/5.47 @ ( groups7713935264441627589nteger
% 5.15/5.47 @ ^ [I3: real] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6496_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.15/5.47 ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ I5 )
% 5.15/5.47 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 5.15/5.47 = one_one_Code_integer )
% 5.15/5.47 => ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ I5 )
% 5.15/5.47 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_le3102999989581377725nteger
% 5.15/5.47 @ ( abs_abs_Code_integer
% 5.15/5.47 @ ( minus_8373710615458151222nteger
% 5.15/5.47 @ ( groups7501900531339628137nteger
% 5.15/5.47 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6497_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.15/5.47 ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 5.15/5.47 = one_one_Code_integer )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_le3102999989581377725nteger
% 5.15/5.47 @ ( abs_abs_Code_integer
% 5.15/5.47 @ ( minus_8373710615458151222nteger
% 5.15/5.47 @ ( groups7873554091576472773nteger
% 5.15/5.47 @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6498_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 5.15/5.47 ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups5808333547571424918x_real @ X @ I5 )
% 5.15/5.47 = one_one_real )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_less_eq_real
% 5.15/5.47 @ ( abs_abs_real
% 5.15/5.47 @ ( minus_minus_real
% 5.15/5.47 @ ( groups5808333547571424918x_real
% 5.15/5.47 @ ^ [I3: complex] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6499_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 5.15/5.47 ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups8097168146408367636l_real @ X @ I5 )
% 5.15/5.47 = one_one_real )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_less_eq_real
% 5.15/5.47 @ ( abs_abs_real
% 5.15/5.47 @ ( minus_minus_real
% 5.15/5.47 @ ( groups8097168146408367636l_real
% 5.15/5.47 @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6500_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 5.15/5.47 ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups8778361861064173332t_real @ X @ I5 )
% 5.15/5.47 = one_one_real )
% 5.15/5.47 => ( ! [I2: int] :
% 5.15/5.47 ( ( member_int @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_less_eq_real
% 5.15/5.47 @ ( abs_abs_real
% 5.15/5.47 @ ( minus_minus_real
% 5.15/5.47 @ ( groups8778361861064173332t_real
% 5.15/5.47 @ ^ [I3: int] : ( times_times_real @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6501_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.15/5.47 ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups5058264527183730370ex_rat @ X @ I5 )
% 5.15/5.47 = one_one_rat )
% 5.15/5.47 => ( ! [I2: complex] :
% 5.15/5.47 ( ( member_complex @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_less_eq_rat
% 5.15/5.47 @ ( abs_abs_rat
% 5.15/5.47 @ ( minus_minus_rat
% 5.15/5.47 @ ( groups5058264527183730370ex_rat
% 5.15/5.47 @ ^ [I3: complex] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6502_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.15/5.47 ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups1300246762558778688al_rat @ X @ I5 )
% 5.15/5.47 = one_one_rat )
% 5.15/5.47 => ( ! [I2: real] :
% 5.15/5.47 ( ( member_real @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_less_eq_rat
% 5.15/5.47 @ ( abs_abs_rat
% 5.15/5.47 @ ( minus_minus_rat
% 5.15/5.47 @ ( groups1300246762558778688al_rat
% 5.15/5.47 @ ^ [I3: real] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6503_convex__sum__bound__le,axiom,
% 5.15/5.47 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.15/5.47 ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 5.15/5.47 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 5.15/5.47 = one_one_rat )
% 5.15/5.47 => ( ! [I2: nat] :
% 5.15/5.47 ( ( member_nat @ I2 @ I5 )
% 5.15/5.47 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.15/5.47 => ( ord_less_eq_rat
% 5.15/5.47 @ ( abs_abs_rat
% 5.15/5.47 @ ( minus_minus_rat
% 5.15/5.47 @ ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 @ B ) )
% 5.15/5.47 @ Delta ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % convex_sum_bound_le
% 5.15/5.47 thf(fact_6504_nat__intermed__int__val,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > int,K: int] :
% 5.15/5.47 ( ! [I2: nat] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ M @ I2 )
% 5.15/5.47 & ( ord_less_nat @ I2 @ N2 ) )
% 5.15/5.47 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.15/5.47 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.15/5.47 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.15/5.47 => ? [I2: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ I2 )
% 5.15/5.47 & ( ord_less_eq_nat @ I2 @ N2 )
% 5.15/5.47 & ( ( F @ I2 )
% 5.15/5.47 = K ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % nat_intermed_int_val
% 5.15/5.47 thf(fact_6505_decr__lemma,axiom,
% 5.15/5.47 ! [D: int,X: int,Z: int] :
% 5.15/5.47 ( ( ord_less_int @ zero_zero_int @ D )
% 5.15/5.47 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.15/5.47
% 5.15/5.47 % decr_lemma
% 5.15/5.47 thf(fact_6506_incr__lemma,axiom,
% 5.15/5.47 ! [D: int,Z: int,X: int] :
% 5.15/5.47 ( ( ord_less_int @ zero_zero_int @ D )
% 5.15/5.47 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % incr_lemma
% 5.15/5.47 thf(fact_6507_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N2 ) )
% 5.15/5.47 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.47
% 5.15/5.47 % semiring_bit_operations_class.even_mask_iff
% 5.15/5.47 thf(fact_6508_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.15/5.47 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.47
% 5.15/5.47 % semiring_bit_operations_class.even_mask_iff
% 5.15/5.47 thf(fact_6509_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.15/5.47 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.47
% 5.15/5.47 % semiring_bit_operations_class.even_mask_iff
% 5.15/5.47 thf(fact_6510_add__0__iff,axiom,
% 5.15/5.47 ! [B: complex,A: complex] :
% 5.15/5.47 ( ( B
% 5.15/5.47 = ( plus_plus_complex @ B @ A ) )
% 5.15/5.47 = ( A = zero_zero_complex ) ) ).
% 5.15/5.47
% 5.15/5.47 % add_0_iff
% 5.15/5.47 thf(fact_6511_add__0__iff,axiom,
% 5.15/5.47 ! [B: real,A: real] :
% 5.15/5.47 ( ( B
% 5.15/5.47 = ( plus_plus_real @ B @ A ) )
% 5.15/5.47 = ( A = zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % add_0_iff
% 5.15/5.47 thf(fact_6512_add__0__iff,axiom,
% 5.15/5.47 ! [B: rat,A: rat] :
% 5.15/5.47 ( ( B
% 5.15/5.47 = ( plus_plus_rat @ B @ A ) )
% 5.15/5.47 = ( A = zero_zero_rat ) ) ).
% 5.15/5.47
% 5.15/5.47 % add_0_iff
% 5.15/5.47 thf(fact_6513_add__0__iff,axiom,
% 5.15/5.47 ! [B: nat,A: nat] :
% 5.15/5.47 ( ( B
% 5.15/5.47 = ( plus_plus_nat @ B @ A ) )
% 5.15/5.47 = ( A = zero_zero_nat ) ) ).
% 5.15/5.47
% 5.15/5.47 % add_0_iff
% 5.15/5.47 thf(fact_6514_add__0__iff,axiom,
% 5.15/5.47 ! [B: int,A: int] :
% 5.15/5.47 ( ( B
% 5.15/5.47 = ( plus_plus_int @ B @ A ) )
% 5.15/5.47 = ( A = zero_zero_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % add_0_iff
% 5.15/5.47 thf(fact_6515_crossproduct__eq,axiom,
% 5.15/5.47 ! [W: complex,Y: complex,X: complex,Z: complex] :
% 5.15/5.47 ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y ) @ ( times_times_complex @ X @ Z ) )
% 5.15/5.47 = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X @ Y ) ) )
% 5.15/5.47 = ( ( W = X )
% 5.15/5.47 | ( Y = Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_eq
% 5.15/5.47 thf(fact_6516_crossproduct__eq,axiom,
% 5.15/5.47 ! [W: real,Y: real,X: real,Z: real] :
% 5.15/5.47 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X @ Z ) )
% 5.15/5.47 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y ) ) )
% 5.15/5.47 = ( ( W = X )
% 5.15/5.47 | ( Y = Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_eq
% 5.15/5.47 thf(fact_6517_crossproduct__eq,axiom,
% 5.15/5.47 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 5.15/5.47 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 5.15/5.47 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 5.15/5.47 = ( ( W = X )
% 5.15/5.47 | ( Y = Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_eq
% 5.15/5.47 thf(fact_6518_crossproduct__eq,axiom,
% 5.15/5.47 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 5.15/5.47 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 5.15/5.47 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 5.15/5.47 = ( ( W = X )
% 5.15/5.47 | ( Y = Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_eq
% 5.15/5.47 thf(fact_6519_crossproduct__eq,axiom,
% 5.15/5.47 ! [W: int,Y: int,X: int,Z: int] :
% 5.15/5.47 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 5.15/5.47 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 5.15/5.47 = ( ( W = X )
% 5.15/5.47 | ( Y = Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_eq
% 5.15/5.47 thf(fact_6520_crossproduct__noteq,axiom,
% 5.15/5.47 ! [A: complex,B: complex,C: complex,D: complex] :
% 5.15/5.47 ( ( ( A != B )
% 5.15/5.47 & ( C != D ) )
% 5.15/5.47 = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) )
% 5.15/5.47 != ( plus_plus_complex @ ( times_times_complex @ A @ D ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_noteq
% 5.15/5.47 thf(fact_6521_crossproduct__noteq,axiom,
% 5.15/5.47 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.47 ( ( ( A != B )
% 5.15/5.47 & ( C != D ) )
% 5.15/5.47 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.15/5.47 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_noteq
% 5.15/5.47 thf(fact_6522_crossproduct__noteq,axiom,
% 5.15/5.47 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.15/5.47 ( ( ( A != B )
% 5.15/5.47 & ( C != D ) )
% 5.15/5.47 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.15/5.47 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_noteq
% 5.15/5.47 thf(fact_6523_crossproduct__noteq,axiom,
% 5.15/5.47 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.15/5.47 ( ( ( A != B )
% 5.15/5.47 & ( C != D ) )
% 5.15/5.47 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.15/5.47 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_noteq
% 5.15/5.47 thf(fact_6524_crossproduct__noteq,axiom,
% 5.15/5.47 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.47 ( ( ( A != B )
% 5.15/5.47 & ( C != D ) )
% 5.15/5.47 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.15/5.47 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % crossproduct_noteq
% 5.15/5.47 thf(fact_6525_mask__nat__def,axiom,
% 5.15/5.47 ( bit_se2002935070580805687sk_nat
% 5.15/5.47 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_nat_def
% 5.15/5.47 thf(fact_6526_mask__half__int,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.47 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_half_int
% 5.15/5.47 thf(fact_6527_mask__int__def,axiom,
% 5.15/5.47 ( bit_se2000444600071755411sk_int
% 5.15/5.47 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_int_def
% 5.15/5.47 thf(fact_6528_nat__ivt__aux,axiom,
% 5.15/5.47 ! [N2: nat,F: nat > int,K: int] :
% 5.15/5.47 ( ! [I2: nat] :
% 5.15/5.47 ( ( ord_less_nat @ I2 @ N2 )
% 5.15/5.47 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.15/5.47 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.15/5.47 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.15/5.47 => ? [I2: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.15/5.47 & ( ( F @ I2 )
% 5.15/5.47 = K ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % nat_ivt_aux
% 5.15/5.47 thf(fact_6529_mask__eq__exp__minus__1,axiom,
% 5.15/5.47 ( bit_se2002935070580805687sk_nat
% 5.15/5.47 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_eq_exp_minus_1
% 5.15/5.47 thf(fact_6530_mask__eq__exp__minus__1,axiom,
% 5.15/5.47 ( bit_se2000444600071755411sk_int
% 5.15/5.47 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_eq_exp_minus_1
% 5.15/5.47 thf(fact_6531_nat0__intermed__int__val,axiom,
% 5.15/5.47 ! [N2: nat,F: nat > int,K: int] :
% 5.15/5.47 ( ! [I2: nat] :
% 5.15/5.47 ( ( ord_less_nat @ I2 @ N2 )
% 5.15/5.47 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.15/5.47 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.15/5.47 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.15/5.47 => ? [I2: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.15/5.47 & ( ( F @ I2 )
% 5.15/5.47 = K ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % nat0_intermed_int_val
% 5.15/5.47 thf(fact_6532_arctan__add,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.47 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.15/5.47 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.15/5.47 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % arctan_add
% 5.15/5.47 thf(fact_6533_num_Osize__gen_I2_J,axiom,
% 5.15/5.47 ! [X22: num] :
% 5.15/5.47 ( ( size_num @ ( bit0 @ X22 ) )
% 5.15/5.47 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % num.size_gen(2)
% 5.15/5.47 thf(fact_6534_take__bit__rec,axiom,
% 5.15/5.47 ( bit_se1745604003318907178nteger
% 5.15/5.47 = ( ^ [N3: nat,A3: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_rec
% 5.15/5.47 thf(fact_6535_take__bit__rec,axiom,
% 5.15/5.47 ( bit_se2923211474154528505it_int
% 5.15/5.47 = ( ^ [N3: nat,A3: 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 @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_rec
% 5.15/5.47 thf(fact_6536_take__bit__rec,axiom,
% 5.15/5.47 ( bit_se2925701944663578781it_nat
% 5.15/5.47 = ( ^ [N3: nat,A3: 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 @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_rec
% 5.15/5.47 thf(fact_6537_tanh__real__altdef,axiom,
% 5.15/5.47 ( tanh_real
% 5.15/5.47 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % tanh_real_altdef
% 5.15/5.47 thf(fact_6538_and__int__unfold,axiom,
% 5.15/5.47 ( bit_se725231765392027082nd_int
% 5.15/5.47 = ( ^ [K2: int,L2: int] :
% 5.15/5.47 ( if_int
% 5.15/5.47 @ ( ( K2 = zero_zero_int )
% 5.15/5.47 | ( L2 = zero_zero_int ) )
% 5.15/5.47 @ zero_zero_int
% 5.15/5.47 @ ( if_int
% 5.15/5.47 @ ( K2
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 @ L2
% 5.15/5.47 @ ( if_int
% 5.15/5.47 @ ( L2
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 @ K2
% 5.15/5.47 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_int_unfold
% 5.15/5.47 thf(fact_6539_power__numeral,axiom,
% 5.15/5.47 ! [K: num,L: num] :
% 5.15/5.47 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.15/5.47 = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % power_numeral
% 5.15/5.47 thf(fact_6540_power__numeral,axiom,
% 5.15/5.47 ! [K: num,L: num] :
% 5.15/5.47 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.15/5.47 = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % power_numeral
% 5.15/5.47 thf(fact_6541_power__numeral,axiom,
% 5.15/5.47 ! [K: num,L: num] :
% 5.15/5.47 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.15/5.47 = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % power_numeral
% 5.15/5.47 thf(fact_6542_power__numeral,axiom,
% 5.15/5.47 ! [K: num,L: num] :
% 5.15/5.47 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.15/5.47 = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % power_numeral
% 5.15/5.47 thf(fact_6543_power__numeral,axiom,
% 5.15/5.47 ! [K: num,L: num] :
% 5.15/5.47 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.15/5.47 = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % power_numeral
% 5.15/5.47 thf(fact_6544_or__int__unfold,axiom,
% 5.15/5.47 ( bit_se1409905431419307370or_int
% 5.15/5.47 = ( ^ [K2: int,L2: int] :
% 5.15/5.47 ( if_int
% 5.15/5.47 @ ( ( K2
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 | ( L2
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.15/5.47 @ ( uminus_uminus_int @ one_one_int )
% 5.15/5.47 @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_int_unfold
% 5.15/5.47 thf(fact_6545_arctan__half,axiom,
% 5.15/5.47 ( arctan
% 5.15/5.47 = ( ^ [X2: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X2 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % arctan_half
% 5.15/5.47 thf(fact_6546_and_Oright__idem,axiom,
% 5.15/5.47 ! [A: int,B: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.15/5.47 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.right_idem
% 5.15/5.47 thf(fact_6547_and_Oright__idem,axiom,
% 5.15/5.47 ! [A: nat,B: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.15/5.47 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.right_idem
% 5.15/5.47 thf(fact_6548_and_Oleft__idem,axiom,
% 5.15/5.47 ! [A: int,B: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.15/5.47 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.left_idem
% 5.15/5.47 thf(fact_6549_and_Oleft__idem,axiom,
% 5.15/5.47 ! [A: nat,B: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.15/5.47 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.left_idem
% 5.15/5.47 thf(fact_6550_and_Oidem,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % and.idem
% 5.15/5.47 thf(fact_6551_and_Oidem,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % and.idem
% 5.15/5.47 thf(fact_6552_or_Oright__idem,axiom,
% 5.15/5.47 ! [A: int,B: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ B )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.right_idem
% 5.15/5.47 thf(fact_6553_or_Oright__idem,axiom,
% 5.15/5.47 ! [A: nat,B: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ B )
% 5.15/5.47 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.right_idem
% 5.15/5.47 thf(fact_6554_or_Oleft__idem,axiom,
% 5.15/5.47 ! [A: int,B: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.left_idem
% 5.15/5.47 thf(fact_6555_or_Oleft__idem,axiom,
% 5.15/5.47 ! [A: nat,B: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.15/5.47 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.left_idem
% 5.15/5.47 thf(fact_6556_or_Oidem,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ A @ A )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % or.idem
% 5.15/5.47 thf(fact_6557_or_Oidem,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ A @ A )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % or.idem
% 5.15/5.47 thf(fact_6558_real__sqrt__eq__iff,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ( sqrt @ X )
% 5.15/5.47 = ( sqrt @ Y ) )
% 5.15/5.47 = ( X = Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_eq_iff
% 5.15/5.47 thf(fact_6559_take__bit__of__0,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_0
% 5.15/5.47 thf(fact_6560_take__bit__of__0,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 5.15/5.47 = zero_zero_nat ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_0
% 5.15/5.47 thf(fact_6561_bit_Oconj__zero__right,axiom,
% 5.15/5.47 ! [X: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % bit.conj_zero_right
% 5.15/5.47 thf(fact_6562_bit_Oconj__zero__left,axiom,
% 5.15/5.47 ! [X: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % bit.conj_zero_left
% 5.15/5.47 thf(fact_6563_zero__and__eq,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % zero_and_eq
% 5.15/5.47 thf(fact_6564_zero__and__eq,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.15/5.47 = zero_zero_nat ) ).
% 5.15/5.47
% 5.15/5.47 % zero_and_eq
% 5.15/5.47 thf(fact_6565_and__zero__eq,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_zero_eq
% 5.15/5.47 thf(fact_6566_and__zero__eq,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.15/5.47 = zero_zero_nat ) ).
% 5.15/5.47
% 5.15/5.47 % and_zero_eq
% 5.15/5.47 thf(fact_6567_or_Oright__neutral,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ A @ zero_zero_int )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % or.right_neutral
% 5.15/5.47 thf(fact_6568_or_Oright__neutral,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ A @ zero_zero_nat )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % or.right_neutral
% 5.15/5.47 thf(fact_6569_or_Oleft__neutral,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ zero_zero_int @ A )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % or.left_neutral
% 5.15/5.47 thf(fact_6570_or_Oleft__neutral,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ zero_zero_nat @ A )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % or.left_neutral
% 5.15/5.47 thf(fact_6571_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ( sqrt @ X )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 = ( X = zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_eq_zero_cancel_iff
% 5.15/5.47 thf(fact_6572_real__sqrt__zero,axiom,
% 5.15/5.47 ( ( sqrt @ zero_zero_real )
% 5.15/5.47 = zero_zero_real ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_zero
% 5.15/5.47 thf(fact_6573_real__sqrt__less__iff,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 5.15/5.47 = ( ord_less_real @ X @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_less_iff
% 5.15/5.47 thf(fact_6574_real__sqrt__le__iff,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 5.15/5.47 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_le_iff
% 5.15/5.47 thf(fact_6575_real__sqrt__eq__1__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ( sqrt @ X )
% 5.15/5.47 = one_one_real )
% 5.15/5.47 = ( X = one_one_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_eq_1_iff
% 5.15/5.47 thf(fact_6576_real__sqrt__one,axiom,
% 5.15/5.47 ( ( sqrt @ one_one_real )
% 5.15/5.47 = one_one_real ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_one
% 5.15/5.47 thf(fact_6577_exp__less__cancel__iff,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.15/5.47 = ( ord_less_real @ X @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_less_cancel_iff
% 5.15/5.47 thf(fact_6578_exp__less__mono,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_real @ X @ Y )
% 5.15/5.47 => ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_less_mono
% 5.15/5.47 thf(fact_6579_take__bit__and,axiom,
% 5.15/5.47 ! [N2: nat,A: int,B: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.15/5.47 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_and
% 5.15/5.47 thf(fact_6580_take__bit__and,axiom,
% 5.15/5.47 ! [N2: nat,A: nat,B: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.15/5.47 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_and
% 5.15/5.47 thf(fact_6581_exp__le__cancel__iff,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.15/5.47 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_le_cancel_iff
% 5.15/5.47 thf(fact_6582_take__bit__or,axiom,
% 5.15/5.47 ! [N2: nat,A: int,B: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_or
% 5.15/5.47 thf(fact_6583_take__bit__or,axiom,
% 5.15/5.47 ! [N2: nat,A: nat,B: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.15/5.47 = ( bit_se1412395901928357646or_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_or
% 5.15/5.47 thf(fact_6584_concat__bit__of__zero__2,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( bit_concat_bit @ N2 @ K @ zero_zero_int )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.15/5.47
% 5.15/5.47 % concat_bit_of_zero_2
% 5.15/5.47 thf(fact_6585_exp__zero,axiom,
% 5.15/5.47 ( ( exp_complex @ zero_zero_complex )
% 5.15/5.47 = one_one_complex ) ).
% 5.15/5.47
% 5.15/5.47 % exp_zero
% 5.15/5.47 thf(fact_6586_exp__zero,axiom,
% 5.15/5.47 ( ( exp_real @ zero_zero_real )
% 5.15/5.47 = one_one_real ) ).
% 5.15/5.47
% 5.15/5.47 % exp_zero
% 5.15/5.47 thf(fact_6587_take__bit__0,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_0
% 5.15/5.47 thf(fact_6588_take__bit__0,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.15/5.47 = zero_zero_nat ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_0
% 5.15/5.47 thf(fact_6589_take__bit__Suc__1,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 5.15/5.47 = one_one_int ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_1
% 5.15/5.47 thf(fact_6590_take__bit__Suc__1,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.15/5.47 = one_one_nat ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_1
% 5.15/5.47 thf(fact_6591_and_Oleft__neutral,axiom,
% 5.15/5.47 ! [A: code_integer] :
% 5.15/5.47 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % and.left_neutral
% 5.15/5.47 thf(fact_6592_and_Oleft__neutral,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % and.left_neutral
% 5.15/5.47 thf(fact_6593_and_Oright__neutral,axiom,
% 5.15/5.47 ! [A: code_integer] :
% 5.15/5.47 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % and.right_neutral
% 5.15/5.47 thf(fact_6594_and_Oright__neutral,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 = A ) ).
% 5.15/5.47
% 5.15/5.47 % and.right_neutral
% 5.15/5.47 thf(fact_6595_bit_Oconj__one__right,axiom,
% 5.15/5.47 ! [X: code_integer] :
% 5.15/5.47 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 = X ) ).
% 5.15/5.47
% 5.15/5.47 % bit.conj_one_right
% 5.15/5.47 thf(fact_6596_bit_Oconj__one__right,axiom,
% 5.15/5.47 ! [X: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 = X ) ).
% 5.15/5.47
% 5.15/5.47 % bit.conj_one_right
% 5.15/5.47 thf(fact_6597_take__bit__numeral__1,axiom,
% 5.15/5.47 ! [L: num] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 5.15/5.47 = one_one_int ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_numeral_1
% 5.15/5.47 thf(fact_6598_take__bit__numeral__1,axiom,
% 5.15/5.47 ! [L: num] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 5.15/5.47 = one_one_nat ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_numeral_1
% 5.15/5.47 thf(fact_6599_bit_Odisj__one__right,axiom,
% 5.15/5.47 ! [X: code_integer] :
% 5.15/5.47 ( ( bit_se1080825931792720795nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.disj_one_right
% 5.15/5.47 thf(fact_6600_bit_Odisj__one__right,axiom,
% 5.15/5.47 ! [X: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.disj_one_right
% 5.15/5.47 thf(fact_6601_bit_Odisj__one__left,axiom,
% 5.15/5.47 ! [X: code_integer] :
% 5.15/5.47 ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.15/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.disj_one_left
% 5.15/5.47 thf(fact_6602_bit_Odisj__one__left,axiom,
% 5.15/5.47 ! [X: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.disj_one_left
% 5.15/5.47 thf(fact_6603_real__sqrt__lt__0__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.15/5.47 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_lt_0_iff
% 5.15/5.47 thf(fact_6604_real__sqrt__gt__0__iff,axiom,
% 5.15/5.47 ! [Y: real] :
% 5.15/5.47 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.15/5.47 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_gt_0_iff
% 5.15/5.47 thf(fact_6605_real__sqrt__le__0__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.15/5.47 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_le_0_iff
% 5.15/5.47 thf(fact_6606_real__sqrt__ge__0__iff,axiom,
% 5.15/5.47 ! [Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.15/5.47 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_ge_0_iff
% 5.15/5.47 thf(fact_6607_real__sqrt__lt__1__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 5.15/5.47 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_lt_1_iff
% 5.15/5.47 thf(fact_6608_real__sqrt__gt__1__iff,axiom,
% 5.15/5.47 ! [Y: real] :
% 5.15/5.47 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.15/5.47 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_gt_1_iff
% 5.15/5.47 thf(fact_6609_real__sqrt__ge__1__iff,axiom,
% 5.15/5.47 ! [Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.15/5.47 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_ge_1_iff
% 5.15/5.47 thf(fact_6610_real__sqrt__le__1__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 5.15/5.47 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_le_1_iff
% 5.15/5.47 thf(fact_6611_exp__eq__one__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ( exp_real @ X )
% 5.15/5.47 = one_one_real )
% 5.15/5.47 = ( X = zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_eq_one_iff
% 5.15/5.47 thf(fact_6612_and__nonnegative__int__iff,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.15/5.47 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.47 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_nonnegative_int_iff
% 5.15/5.47 thf(fact_6613_and__negative__int__iff,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.15/5.47 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.47 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_negative_int_iff
% 5.15/5.47 thf(fact_6614_real__sqrt__abs2,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 5.15/5.47 = ( abs_abs_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_abs2
% 5.15/5.47 thf(fact_6615_real__sqrt__mult__self,axiom,
% 5.15/5.47 ! [A: real] :
% 5.15/5.47 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.15/5.47 = ( abs_abs_real @ A ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_mult_self
% 5.15/5.47 thf(fact_6616_or__nonnegative__int__iff,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.15/5.47 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.47 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_nonnegative_int_iff
% 5.15/5.47 thf(fact_6617_or__negative__int__iff,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.15/5.47 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.47 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_negative_int_iff
% 5.15/5.47 thf(fact_6618_take__bit__of__1__eq__0__iff,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.15/5.47 = zero_zero_int )
% 5.15/5.47 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_1_eq_0_iff
% 5.15/5.47 thf(fact_6619_take__bit__of__1__eq__0__iff,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_1_eq_0_iff
% 5.15/5.47 thf(fact_6620_and__numerals_I2_J,axiom,
% 5.15/5.47 ! [Y: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.15/5.47 = one_one_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(2)
% 5.15/5.47 thf(fact_6621_and__numerals_I2_J,axiom,
% 5.15/5.47 ! [Y: num] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.47 = one_one_nat ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(2)
% 5.15/5.47 thf(fact_6622_and__numerals_I8_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.15/5.47 = one_one_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(8)
% 5.15/5.47 thf(fact_6623_and__numerals_I8_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.15/5.47 = one_one_nat ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(8)
% 5.15/5.47 thf(fact_6624_or__numerals_I2_J,axiom,
% 5.15/5.47 ! [Y: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(2)
% 5.15/5.47 thf(fact_6625_or__numerals_I2_J,axiom,
% 5.15/5.47 ! [Y: num] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(2)
% 5.15/5.47 thf(fact_6626_or__numerals_I8_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.15/5.47 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(8)
% 5.15/5.47 thf(fact_6627_or__numerals_I8_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.15/5.47 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(8)
% 5.15/5.47 thf(fact_6628_real__sqrt__four,axiom,
% 5.15/5.47 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.47 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_four
% 5.15/5.47 thf(fact_6629_exp__less__one__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 5.15/5.47 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_less_one_iff
% 5.15/5.47 thf(fact_6630_one__less__exp__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 5.15/5.47 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % one_less_exp_iff
% 5.15/5.47 thf(fact_6631_exp__le__one__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 5.15/5.47 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_le_one_iff
% 5.15/5.47 thf(fact_6632_one__le__exp__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 5.15/5.47 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % one_le_exp_iff
% 5.15/5.47 thf(fact_6633_take__bit__minus__one__eq__mask,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se1745604003318907178nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_minus_one_eq_mask
% 5.15/5.47 thf(fact_6634_take__bit__minus__one__eq__mask,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_minus_one_eq_mask
% 5.15/5.47 thf(fact_6635_exp__ln__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.15/5.47 = X )
% 5.15/5.47 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_ln_iff
% 5.15/5.47 thf(fact_6636_exp__ln,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.15/5.47 = X ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_ln
% 5.15/5.47 thf(fact_6637_take__bit__of__Suc__0,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.15/5.47 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_Suc_0
% 5.15/5.47 thf(fact_6638_and__numerals_I1_J,axiom,
% 5.15/5.47 ! [Y: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(1)
% 5.15/5.47 thf(fact_6639_and__numerals_I1_J,axiom,
% 5.15/5.47 ! [Y: num] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.47 = zero_zero_nat ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(1)
% 5.15/5.47 thf(fact_6640_and__numerals_I5_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(5)
% 5.15/5.47 thf(fact_6641_and__numerals_I5_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.15/5.47 = zero_zero_nat ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(5)
% 5.15/5.47 thf(fact_6642_and__numerals_I3_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(3)
% 5.15/5.47 thf(fact_6643_and__numerals_I3_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(3)
% 5.15/5.47 thf(fact_6644_or__numerals_I3_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(3)
% 5.15/5.47 thf(fact_6645_or__numerals_I3_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(3)
% 5.15/5.47 thf(fact_6646_sum_Ocl__ivl__Suc,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,G: nat > complex] :
% 5.15/5.47 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = zero_zero_complex ) )
% 5.15/5.47 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.cl_ivl_Suc
% 5.15/5.47 thf(fact_6647_sum_Ocl__ivl__Suc,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,G: nat > rat] :
% 5.15/5.47 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = zero_zero_rat ) )
% 5.15/5.47 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.cl_ivl_Suc
% 5.15/5.47 thf(fact_6648_sum_Ocl__ivl__Suc,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,G: nat > int] :
% 5.15/5.47 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = zero_zero_int ) )
% 5.15/5.47 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.cl_ivl_Suc
% 5.15/5.47 thf(fact_6649_sum_Ocl__ivl__Suc,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,G: nat > nat] :
% 5.15/5.47 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = zero_zero_nat ) )
% 5.15/5.47 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.cl_ivl_Suc
% 5.15/5.47 thf(fact_6650_sum_Ocl__ivl__Suc,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,G: nat > real] :
% 5.15/5.47 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = zero_zero_real ) )
% 5.15/5.47 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.47 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.cl_ivl_Suc
% 5.15/5.47 thf(fact_6651_or__numerals_I1_J,axiom,
% 5.15/5.47 ! [Y: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(1)
% 5.15/5.47 thf(fact_6652_or__numerals_I1_J,axiom,
% 5.15/5.47 ! [Y: num] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(1)
% 5.15/5.47 thf(fact_6653_or__numerals_I5_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.15/5.47 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(5)
% 5.15/5.47 thf(fact_6654_or__numerals_I5_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.15/5.47 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(5)
% 5.15/5.47 thf(fact_6655_take__bit__of__1,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 5.15/5.47 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_1
% 5.15/5.47 thf(fact_6656_take__bit__of__1,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.15/5.47 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_1
% 5.15/5.47 thf(fact_6657_take__bit__of__1,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.15/5.47 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_1
% 5.15/5.47 thf(fact_6658_and__minus__numerals_I2_J,axiom,
% 5.15/5.47 ! [N2: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.47 = one_one_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_minus_numerals(2)
% 5.15/5.47 thf(fact_6659_and__minus__numerals_I6_J,axiom,
% 5.15/5.47 ! [N2: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.15/5.47 = one_one_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_minus_numerals(6)
% 5.15/5.47 thf(fact_6660_or__minus__numerals_I2_J,axiom,
% 5.15/5.47 ! [N2: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.47 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_minus_numerals(2)
% 5.15/5.47 thf(fact_6661_or__minus__numerals_I6_J,axiom,
% 5.15/5.47 ! [N2: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.15/5.47 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_minus_numerals(6)
% 5.15/5.47 thf(fact_6662_sum__zero__power,axiom,
% 5.15/5.47 ! [A2: set_nat,C: nat > complex] :
% 5.15/5.47 ( ( ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( C @ zero_zero_nat ) ) )
% 5.15/5.47 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = zero_zero_complex ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_zero_power
% 5.15/5.47 thf(fact_6663_sum__zero__power,axiom,
% 5.15/5.47 ! [A2: set_nat,C: nat > rat] :
% 5.15/5.47 ( ( ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( C @ zero_zero_nat ) ) )
% 5.15/5.47 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = zero_zero_rat ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_zero_power
% 5.15/5.47 thf(fact_6664_sum__zero__power,axiom,
% 5.15/5.47 ! [A2: set_nat,C: nat > real] :
% 5.15/5.47 ( ( ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( C @ zero_zero_nat ) ) )
% 5.15/5.47 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = zero_zero_real ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_zero_power
% 5.15/5.47 thf(fact_6665_and__numerals_I4_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(4)
% 5.15/5.47 thf(fact_6666_and__numerals_I4_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(4)
% 5.15/5.47 thf(fact_6667_and__numerals_I6_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(6)
% 5.15/5.47 thf(fact_6668_and__numerals_I6_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(6)
% 5.15/5.47 thf(fact_6669_even__take__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,A: code_integer] :
% 5.15/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 5.15/5.47 = ( ( N2 = zero_zero_nat )
% 5.15/5.47 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_take_bit_eq
% 5.15/5.47 thf(fact_6670_even__take__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,A: int] :
% 5.15/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.15/5.47 = ( ( N2 = zero_zero_nat )
% 5.15/5.47 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_take_bit_eq
% 5.15/5.47 thf(fact_6671_even__take__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,A: nat] :
% 5.15/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 5.15/5.47 = ( ( N2 = zero_zero_nat )
% 5.15/5.47 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_take_bit_eq
% 5.15/5.47 thf(fact_6672_real__sqrt__abs,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.47 = ( abs_abs_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_abs
% 5.15/5.47 thf(fact_6673_and__minus__numerals_I5_J,axiom,
% 5.15/5.47 ! [N2: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_minus_numerals(5)
% 5.15/5.47 thf(fact_6674_and__minus__numerals_I1_J,axiom,
% 5.15/5.47 ! [N2: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.47 = zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % and_minus_numerals(1)
% 5.15/5.47 thf(fact_6675_sum__zero__power_H,axiom,
% 5.15/5.47 ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 5.15/5.47 ( ( ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.15/5.47 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [I3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) ) @ ( D @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = zero_zero_complex ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_zero_power'
% 5.15/5.47 thf(fact_6676_sum__zero__power_H,axiom,
% 5.15/5.47 ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 5.15/5.47 ( ( ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.15/5.47 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = zero_zero_rat ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_zero_power'
% 5.15/5.47 thf(fact_6677_sum__zero__power_H,axiom,
% 5.15/5.47 ! [A2: set_nat,C: nat > real,D: nat > real] :
% 5.15/5.47 ( ( ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.15/5.47 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.15/5.47 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.15/5.47 => ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) ) @ ( D @ I3 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = zero_zero_real ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_zero_power'
% 5.15/5.47 thf(fact_6678_take__bit__Suc__0,axiom,
% 5.15/5.47 ! [A: code_integer] :
% 5.15/5.47 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.15/5.47 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_0
% 5.15/5.47 thf(fact_6679_take__bit__Suc__0,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.15/5.47 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_0
% 5.15/5.47 thf(fact_6680_take__bit__Suc__0,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.15/5.47 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_0
% 5.15/5.47 thf(fact_6681_real__sqrt__pow2__iff,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.47 = X )
% 5.15/5.47 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_pow2_iff
% 5.15/5.47 thf(fact_6682_real__sqrt__pow2,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.47 = X ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_pow2
% 5.15/5.47 thf(fact_6683_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.15/5.47 ! [X: real,Y: real,Xa2: real,Ya: real] :
% 5.15/5.47 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.47 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_sum_squares_mult_squared_eq
% 5.15/5.47 thf(fact_6684_and__numerals_I7_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(7)
% 5.15/5.47 thf(fact_6685_and__numerals_I7_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_numerals(7)
% 5.15/5.47 thf(fact_6686_or__numerals_I4_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(4)
% 5.15/5.47 thf(fact_6687_or__numerals_I4_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(4)
% 5.15/5.47 thf(fact_6688_or__numerals_I6_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(6)
% 5.15/5.47 thf(fact_6689_or__numerals_I6_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.47 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(6)
% 5.15/5.47 thf(fact_6690_or__numerals_I7_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(7)
% 5.15/5.47 thf(fact_6691_or__numerals_I7_J,axiom,
% 5.15/5.47 ! [X: num,Y: num] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.47 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_numerals(7)
% 5.15/5.47 thf(fact_6692_take__bit__of__exp,axiom,
% 5.15/5.47 ! [M: nat,N2: nat] :
% 5.15/5.47 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.47 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_exp
% 5.15/5.47 thf(fact_6693_take__bit__of__exp,axiom,
% 5.15/5.47 ! [M: nat,N2: nat] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.47 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_exp
% 5.15/5.47 thf(fact_6694_take__bit__of__exp,axiom,
% 5.15/5.47 ! [M: nat,N2: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.47 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_exp
% 5.15/5.47 thf(fact_6695_take__bit__of__2,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.47 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_2
% 5.15/5.47 thf(fact_6696_take__bit__of__2,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.47 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_2
% 5.15/5.47 thf(fact_6697_take__bit__of__2,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.47 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_2
% 5.15/5.47 thf(fact_6698_take__bit__eq__mask,axiom,
% 5.15/5.47 ( bit_se2923211474154528505it_int
% 5.15/5.47 = ( ^ [N3: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N3 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_mask
% 5.15/5.47 thf(fact_6699_take__bit__eq__mask,axiom,
% 5.15/5.47 ( bit_se2925701944663578781it_nat
% 5.15/5.47 = ( ^ [N3: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N3 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_mask
% 5.15/5.47 thf(fact_6700_take__bit__of__int,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 5.15/5.47 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_of_int
% 5.15/5.47 thf(fact_6701_of__int__and__eq,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.15/5.47 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % of_int_and_eq
% 5.15/5.47 thf(fact_6702_of__int__or__eq,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( ring_1_of_int_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % of_int_or_eq
% 5.15/5.47 thf(fact_6703_plus__and__or,axiom,
% 5.15/5.47 ! [X: int,Y: int] :
% 5.15/5.47 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 5.15/5.47 = ( plus_plus_int @ X @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % plus_and_or
% 5.15/5.47 thf(fact_6704_bit_Odisj__conj__distrib2,axiom,
% 5.15/5.47 ! [Y: int,Z: int,X: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y @ Z ) @ X )
% 5.15/5.47 = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y @ X ) @ ( bit_se1409905431419307370or_int @ Z @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.disj_conj_distrib2
% 5.15/5.47 thf(fact_6705_bit_Oconj__disj__distrib2,axiom,
% 5.15/5.47 ! [Y: int,Z: int,X: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y @ Z ) @ X )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y @ X ) @ ( bit_se725231765392027082nd_int @ Z @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.conj_disj_distrib2
% 5.15/5.47 thf(fact_6706_bit_Odisj__conj__distrib,axiom,
% 5.15/5.47 ! [X: int,Y: int,Z: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ X @ ( bit_se725231765392027082nd_int @ Y @ Z ) )
% 5.15/5.47 = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.disj_conj_distrib
% 5.15/5.47 thf(fact_6707_bit_Oconj__disj__distrib,axiom,
% 5.15/5.47 ! [X: int,Y: int,Z: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ X @ ( bit_se1409905431419307370or_int @ Y @ Z ) )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se725231765392027082nd_int @ X @ Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.conj_disj_distrib
% 5.15/5.47 thf(fact_6708_and_Oleft__commute,axiom,
% 5.15/5.47 ! [B: int,A: int,C: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.15/5.47 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.left_commute
% 5.15/5.47 thf(fact_6709_and_Oleft__commute,axiom,
% 5.15/5.47 ! [B: nat,A: nat,C: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.15/5.47 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.left_commute
% 5.15/5.47 thf(fact_6710_or_Oleft__commute,axiom,
% 5.15/5.47 ! [B: int,A: int,C: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ B @ ( bit_se1409905431419307370or_int @ A @ C ) )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.left_commute
% 5.15/5.47 thf(fact_6711_or_Oleft__commute,axiom,
% 5.15/5.47 ! [B: nat,A: nat,C: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ B @ ( bit_se1412395901928357646or_nat @ A @ C ) )
% 5.15/5.47 = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.left_commute
% 5.15/5.47 thf(fact_6712_and_Ocommute,axiom,
% 5.15/5.47 ( bit_se725231765392027082nd_int
% 5.15/5.47 = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.commute
% 5.15/5.47 thf(fact_6713_and_Ocommute,axiom,
% 5.15/5.47 ( bit_se727722235901077358nd_nat
% 5.15/5.47 = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.commute
% 5.15/5.47 thf(fact_6714_or_Ocommute,axiom,
% 5.15/5.47 ( bit_se1409905431419307370or_int
% 5.15/5.47 = ( ^ [A3: int,B2: int] : ( bit_se1409905431419307370or_int @ B2 @ A3 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.commute
% 5.15/5.47 thf(fact_6715_or_Ocommute,axiom,
% 5.15/5.47 ( bit_se1412395901928357646or_nat
% 5.15/5.47 = ( ^ [A3: nat,B2: nat] : ( bit_se1412395901928357646or_nat @ B2 @ A3 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.commute
% 5.15/5.47 thf(fact_6716_and_Oassoc,axiom,
% 5.15/5.47 ! [A: int,B: int,C: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.15/5.47 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.assoc
% 5.15/5.47 thf(fact_6717_and_Oassoc,axiom,
% 5.15/5.47 ! [A: nat,B: nat,C: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.15/5.47 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and.assoc
% 5.15/5.47 thf(fact_6718_or_Oassoc,axiom,
% 5.15/5.47 ! [A: int,B: int,C: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ C )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.assoc
% 5.15/5.47 thf(fact_6719_or_Oassoc,axiom,
% 5.15/5.47 ! [A: nat,B: nat,C: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ C )
% 5.15/5.47 = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or.assoc
% 5.15/5.47 thf(fact_6720_take__bit__add,axiom,
% 5.15/5.47 ! [N2: nat,A: int,B: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_add
% 5.15/5.47 thf(fact_6721_take__bit__add,axiom,
% 5.15/5.47 ! [N2: nat,A: nat,B: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 5.15/5.47 = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_add
% 5.15/5.47 thf(fact_6722_bit_Odisj__zero__right,axiom,
% 5.15/5.47 ! [X: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ X @ zero_zero_int )
% 5.15/5.47 = X ) ).
% 5.15/5.47
% 5.15/5.47 % bit.disj_zero_right
% 5.15/5.47 thf(fact_6723_or__eq__0__iff,axiom,
% 5.15/5.47 ! [A: int,B: int] :
% 5.15/5.47 ( ( ( bit_se1409905431419307370or_int @ A @ B )
% 5.15/5.47 = zero_zero_int )
% 5.15/5.47 = ( ( A = zero_zero_int )
% 5.15/5.47 & ( B = zero_zero_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_eq_0_iff
% 5.15/5.47 thf(fact_6724_or__eq__0__iff,axiom,
% 5.15/5.47 ! [A: nat,B: nat] :
% 5.15/5.47 ( ( ( bit_se1412395901928357646or_nat @ A @ B )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 = ( ( A = zero_zero_nat )
% 5.15/5.47 & ( B = zero_zero_nat ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_eq_0_iff
% 5.15/5.47 thf(fact_6725_take__bit__tightened,axiom,
% 5.15/5.47 ! [N2: nat,A: int,B: int,M: nat] :
% 5.15/5.47 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.15/5.47 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_tightened
% 5.15/5.47 thf(fact_6726_take__bit__tightened,axiom,
% 5.15/5.47 ! [N2: nat,A: nat,B: nat,M: nat] :
% 5.15/5.47 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.15/5.47 = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 5.15/5.47 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.15/5.47 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_tightened
% 5.15/5.47 thf(fact_6727_take__bit__nat__less__eq__self,axiom,
% 5.15/5.47 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_nat_less_eq_self
% 5.15/5.47 thf(fact_6728_take__bit__tightened__less__eq__nat,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,Q3: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q3 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_tightened_less_eq_nat
% 5.15/5.47 thf(fact_6729_real__sqrt__less__mono,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_real @ X @ Y )
% 5.15/5.47 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_less_mono
% 5.15/5.47 thf(fact_6730_exp__less__cancel,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.15/5.47 => ( ord_less_real @ X @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_less_cancel
% 5.15/5.47 thf(fact_6731_real__sqrt__le__mono,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.47 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_le_mono
% 5.15/5.47 thf(fact_6732_real__sqrt__divide,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( sqrt @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.47 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_divide
% 5.15/5.47 thf(fact_6733_real__sqrt__mult,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 5.15/5.47 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_mult
% 5.15/5.47 thf(fact_6734_real__sqrt__power,axiom,
% 5.15/5.47 ! [X: real,K: nat] :
% 5.15/5.47 ( ( sqrt @ ( power_power_real @ X @ K ) )
% 5.15/5.47 = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_power
% 5.15/5.47 thf(fact_6735_real__sqrt__minus,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 5.15/5.47 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_minus
% 5.15/5.47 thf(fact_6736_take__bit__minus,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_minus
% 5.15/5.47 thf(fact_6737_exp__times__arg__commute,axiom,
% 5.15/5.47 ! [A2: complex] :
% 5.15/5.47 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.15/5.47 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_times_arg_commute
% 5.15/5.47 thf(fact_6738_exp__times__arg__commute,axiom,
% 5.15/5.47 ! [A2: real] :
% 5.15/5.47 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.15/5.47 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_times_arg_commute
% 5.15/5.47 thf(fact_6739_take__bit__mult,axiom,
% 5.15/5.47 ! [N2: nat,K: int,L: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_mult
% 5.15/5.47 thf(fact_6740_take__bit__diff,axiom,
% 5.15/5.47 ! [N2: nat,K: int,L: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_diff
% 5.15/5.47 thf(fact_6741_bit_Ocomplement__unique,axiom,
% 5.15/5.47 ! [A: code_integer,X: code_integer,Y: code_integer] :
% 5.15/5.47 ( ( ( bit_se3949692690581998587nteger @ A @ X )
% 5.15/5.47 = zero_z3403309356797280102nteger )
% 5.15/5.47 => ( ( ( bit_se1080825931792720795nteger @ A @ X )
% 5.15/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 => ( ( ( bit_se3949692690581998587nteger @ A @ Y )
% 5.15/5.47 = zero_z3403309356797280102nteger )
% 5.15/5.47 => ( ( ( bit_se1080825931792720795nteger @ A @ Y )
% 5.15/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 => ( X = Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.complement_unique
% 5.15/5.47 thf(fact_6742_bit_Ocomplement__unique,axiom,
% 5.15/5.47 ! [A: int,X: int,Y: int] :
% 5.15/5.47 ( ( ( bit_se725231765392027082nd_int @ A @ X )
% 5.15/5.47 = zero_zero_int )
% 5.15/5.47 => ( ( ( bit_se1409905431419307370or_int @ A @ X )
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 => ( ( ( bit_se725231765392027082nd_int @ A @ Y )
% 5.15/5.47 = zero_zero_int )
% 5.15/5.47 => ( ( ( bit_se1409905431419307370or_int @ A @ Y )
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 => ( X = Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % bit.complement_unique
% 5.15/5.47 thf(fact_6743_concat__bit__take__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,B: int] :
% 5.15/5.47 ( ( bit_concat_bit @ N2 @ ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.15/5.47 = ( bit_concat_bit @ N2 @ B ) ) ).
% 5.15/5.47
% 5.15/5.47 % concat_bit_take_bit_eq
% 5.15/5.47 thf(fact_6744_concat__bit__eq__iff,axiom,
% 5.15/5.47 ! [N2: nat,K: int,L: int,R2: int,S: int] :
% 5.15/5.47 ( ( ( bit_concat_bit @ N2 @ K @ L )
% 5.15/5.47 = ( bit_concat_bit @ N2 @ R2 @ S ) )
% 5.15/5.47 = ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ R2 ) )
% 5.15/5.47 & ( L = S ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % concat_bit_eq_iff
% 5.15/5.47 thf(fact_6745_and__eq__minus__1__iff,axiom,
% 5.15/5.47 ! [A: code_integer,B: code_integer] :
% 5.15/5.47 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.15/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 = ( ( A
% 5.15/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 & ( B
% 5.15/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_eq_minus_1_iff
% 5.15/5.47 thf(fact_6746_and__eq__minus__1__iff,axiom,
% 5.15/5.47 ! [A: int,B: int] :
% 5.15/5.47 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 = ( ( A
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 & ( B
% 5.15/5.47 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_eq_minus_1_iff
% 5.15/5.47 thf(fact_6747_real__sqrt__gt__zero,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_gt_zero
% 5.15/5.47 thf(fact_6748_exp__total,axiom,
% 5.15/5.47 ! [Y: real] :
% 5.15/5.47 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.47 => ? [X3: real] :
% 5.15/5.47 ( ( exp_real @ X3 )
% 5.15/5.47 = Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_total
% 5.15/5.47 thf(fact_6749_exp__gt__zero,axiom,
% 5.15/5.47 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_gt_zero
% 5.15/5.47 thf(fact_6750_not__exp__less__zero,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.15/5.47
% 5.15/5.47 % not_exp_less_zero
% 5.15/5.47 thf(fact_6751_real__sqrt__eq__zero__cancel,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( ( sqrt @ X )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 => ( X = zero_zero_real ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_eq_zero_cancel
% 5.15/5.47 thf(fact_6752_real__sqrt__ge__zero,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_ge_zero
% 5.15/5.47 thf(fact_6753_exp__ge__zero,axiom,
% 5.15/5.47 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_ge_zero
% 5.15/5.47 thf(fact_6754_not__exp__le__zero,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.15/5.47
% 5.15/5.47 % not_exp_le_zero
% 5.15/5.47 thf(fact_6755_sum__cong__Suc,axiom,
% 5.15/5.47 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.15/5.47 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.15/5.47 => ( ( F @ ( suc @ X3 ) )
% 5.15/5.47 = ( G @ ( suc @ X3 ) ) ) )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.15/5.47 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_cong_Suc
% 5.15/5.47 thf(fact_6756_sum__cong__Suc,axiom,
% 5.15/5.47 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.15/5.47 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.15/5.47 => ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.15/5.47 => ( ( F @ ( suc @ X3 ) )
% 5.15/5.47 = ( G @ ( suc @ X3 ) ) ) )
% 5.15/5.47 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.15/5.47 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_cong_Suc
% 5.15/5.47 thf(fact_6757_real__sqrt__ge__one,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.47 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_ge_one
% 5.15/5.47 thf(fact_6758_or__greater__eq,axiom,
% 5.15/5.47 ! [L: int,K: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.15/5.47 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_greater_eq
% 5.15/5.47 thf(fact_6759_OR__lower,axiom,
% 5.15/5.47 ! [X: int,Y: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.47 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % OR_lower
% 5.15/5.47 thf(fact_6760_take__bit__tightened__less__eq__int,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,K: int] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_tightened_less_eq_int
% 5.15/5.47 thf(fact_6761_AND__upper2_H,axiom,
% 5.15/5.47 ! [Y: int,Z: int,X: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.47 => ( ( ord_less_eq_int @ Y @ Z )
% 5.15/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % AND_upper2'
% 5.15/5.47 thf(fact_6762_AND__upper1_H,axiom,
% 5.15/5.47 ! [Y: int,Z: int,Ya: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.47 => ( ( ord_less_eq_int @ Y @ Z )
% 5.15/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % AND_upper1'
% 5.15/5.47 thf(fact_6763_AND__upper2,axiom,
% 5.15/5.47 ! [Y: int,X: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % AND_upper2
% 5.15/5.47 thf(fact_6764_AND__upper1,axiom,
% 5.15/5.47 ! [X: int,Y: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % AND_upper1
% 5.15/5.47 thf(fact_6765_AND__lower,axiom,
% 5.15/5.47 ! [X: int,Y: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.47 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % AND_lower
% 5.15/5.47 thf(fact_6766_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,A: int,B: int] :
% 5.15/5.47 ( ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 5.15/5.47 = ( bit_ri631733984087533419it_int @ N2 @ B ) )
% 5.15/5.47 = ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % signed_take_bit_eq_iff_take_bit_eq
% 5.15/5.47 thf(fact_6767_take__bit__int__less__eq__self__iff,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.15/5.47 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_int_less_eq_self_iff
% 5.15/5.47 thf(fact_6768_take__bit__nonnegative,axiom,
% 5.15/5.47 ! [N2: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_nonnegative
% 5.15/5.47 thf(fact_6769_take__bit__int__greater__self__iff,axiom,
% 5.15/5.47 ! [K: int,N2: nat] :
% 5.15/5.47 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.15/5.47 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_int_greater_self_iff
% 5.15/5.47 thf(fact_6770_not__take__bit__negative,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 5.15/5.47
% 5.15/5.47 % not_take_bit_negative
% 5.15/5.47 thf(fact_6771_signed__take__bit__take__bit,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,A: int] :
% 5.15/5.47 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.15/5.47 = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.15/5.47
% 5.15/5.47 % signed_take_bit_take_bit
% 5.15/5.47 thf(fact_6772_exp__add__commuting,axiom,
% 5.15/5.47 ! [X: complex,Y: complex] :
% 5.15/5.47 ( ( ( times_times_complex @ X @ Y )
% 5.15/5.47 = ( times_times_complex @ Y @ X ) )
% 5.15/5.47 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.15/5.47 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_add_commuting
% 5.15/5.47 thf(fact_6773_exp__add__commuting,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ( times_times_real @ X @ Y )
% 5.15/5.47 = ( times_times_real @ Y @ X ) )
% 5.15/5.47 => ( ( exp_real @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.47 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_add_commuting
% 5.15/5.47 thf(fact_6774_mult__exp__exp,axiom,
% 5.15/5.47 ! [X: complex,Y: complex] :
% 5.15/5.47 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) )
% 5.15/5.47 = ( exp_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mult_exp_exp
% 5.15/5.47 thf(fact_6775_mult__exp__exp,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.15/5.47 = ( exp_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mult_exp_exp
% 5.15/5.47 thf(fact_6776_exp__diff,axiom,
% 5.15/5.47 ! [X: complex,Y: complex] :
% 5.15/5.47 ( ( exp_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.15/5.47 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_diff
% 5.15/5.47 thf(fact_6777_exp__diff,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( exp_real @ ( minus_minus_real @ X @ Y ) )
% 5.15/5.47 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_diff
% 5.15/5.47 thf(fact_6778_take__bit__unset__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,A: int] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.15/5.47 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_unset_bit_eq
% 5.15/5.47 thf(fact_6779_take__bit__unset__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,A: nat] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.15/5.47 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.15/5.47 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_unset_bit_eq
% 5.15/5.47 thf(fact_6780_take__bit__set__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,A: int] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.15/5.47 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_set_bit_eq
% 5.15/5.47 thf(fact_6781_take__bit__set__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,A: nat] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.15/5.47 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.15/5.47 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_set_bit_eq
% 5.15/5.47 thf(fact_6782_take__bit__flip__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,A: int] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.15/5.47 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_flip_bit_eq
% 5.15/5.47 thf(fact_6783_take__bit__flip__bit__eq,axiom,
% 5.15/5.47 ! [N2: nat,M: nat,A: nat] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.15/5.47 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.47 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.15/5.47 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_flip_bit_eq
% 5.15/5.47 thf(fact_6784_sum__subtractf__nat,axiom,
% 5.15/5.47 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.15/5.47 ( ! [X3: complex] :
% 5.15/5.47 ( ( member_complex @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( groups5693394587270226106ex_nat
% 5.15/5.47 @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_subtractf_nat
% 5.15/5.47 thf(fact_6785_sum__subtractf__nat,axiom,
% 5.15/5.47 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.15/5.47 ( ! [X3: real] :
% 5.15/5.47 ( ( member_real @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( groups1935376822645274424al_nat
% 5.15/5.47 @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_subtractf_nat
% 5.15/5.47 thf(fact_6786_sum__subtractf__nat,axiom,
% 5.15/5.47 ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 5.15/5.47 ( ! [X3: set_nat] :
% 5.15/5.47 ( ( member_set_nat @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( groups8294997508430121362at_nat
% 5.15/5.47 @ ^ [X2: set_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_subtractf_nat
% 5.15/5.47 thf(fact_6787_sum__subtractf__nat,axiom,
% 5.15/5.47 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.15/5.47 ( ! [X3: int] :
% 5.15/5.47 ( ( member_int @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( groups4541462559716669496nt_nat
% 5.15/5.47 @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_subtractf_nat
% 5.15/5.47 thf(fact_6788_sum__subtractf__nat,axiom,
% 5.15/5.47 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.15/5.47 ( ! [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ A2 )
% 5.15/5.47 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat
% 5.15/5.47 @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.47 @ A2 )
% 5.15/5.47 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_subtractf_nat
% 5.15/5.47 thf(fact_6789_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.15/5.47 ! [G: nat > nat,M: nat,N2: nat] :
% 5.15/5.47 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( groups3542108847815614940at_nat
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.shift_bounds_cl_Suc_ivl
% 5.15/5.47 thf(fact_6790_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.15/5.47 ! [G: nat > real,M: nat,N2: nat] :
% 5.15/5.47 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.shift_bounds_cl_Suc_ivl
% 5.15/5.47 thf(fact_6791_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.15/5.47 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.15/5.47 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.15/5.47 = ( groups3542108847815614940at_nat
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.shift_bounds_cl_nat_ivl
% 5.15/5.47 thf(fact_6792_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.15/5.47 ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 5.15/5.47 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.15/5.47 = ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.shift_bounds_cl_nat_ivl
% 5.15/5.47 thf(fact_6793_pow_Osimps_I1_J,axiom,
% 5.15/5.47 ! [X: num] :
% 5.15/5.47 ( ( pow @ X @ one )
% 5.15/5.47 = X ) ).
% 5.15/5.47
% 5.15/5.47 % pow.simps(1)
% 5.15/5.47 thf(fact_6794_sum__eq__Suc0__iff,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.15/5.47 = ( suc @ zero_zero_nat ) )
% 5.15/5.47 = ( ? [X2: complex] :
% 5.15/5.47 ( ( member_complex @ X2 @ A2 )
% 5.15/5.47 & ( ( F @ X2 )
% 5.15/5.47 = ( suc @ zero_zero_nat ) )
% 5.15/5.47 & ! [Y2: complex] :
% 5.15/5.47 ( ( member_complex @ Y2 @ A2 )
% 5.15/5.47 => ( ( X2 != Y2 )
% 5.15/5.47 => ( ( F @ Y2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_eq_Suc0_iff
% 5.15/5.47 thf(fact_6795_sum__eq__Suc0__iff,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.15/5.47 = ( suc @ zero_zero_nat ) )
% 5.15/5.47 = ( ? [X2: int] :
% 5.15/5.47 ( ( member_int @ X2 @ A2 )
% 5.15/5.47 & ( ( F @ X2 )
% 5.15/5.47 = ( suc @ zero_zero_nat ) )
% 5.15/5.47 & ! [Y2: int] :
% 5.15/5.47 ( ( member_int @ Y2 @ A2 )
% 5.15/5.47 => ( ( X2 != Y2 )
% 5.15/5.47 => ( ( F @ Y2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_eq_Suc0_iff
% 5.15/5.47 thf(fact_6796_sum__eq__Suc0__iff,axiom,
% 5.15/5.47 ! [A2: set_nat,F: nat > nat] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.15/5.47 = ( suc @ zero_zero_nat ) )
% 5.15/5.47 = ( ? [X2: nat] :
% 5.15/5.47 ( ( member_nat @ X2 @ A2 )
% 5.15/5.47 & ( ( F @ X2 )
% 5.15/5.47 = ( suc @ zero_zero_nat ) )
% 5.15/5.47 & ! [Y2: nat] :
% 5.15/5.47 ( ( member_nat @ Y2 @ A2 )
% 5.15/5.47 => ( ( X2 != Y2 )
% 5.15/5.47 => ( ( F @ Y2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_eq_Suc0_iff
% 5.15/5.47 thf(fact_6797_sum__SucD,axiom,
% 5.15/5.47 ! [F: nat > nat,A2: set_nat,N2: nat] :
% 5.15/5.47 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.15/5.47 = ( suc @ N2 ) )
% 5.15/5.47 => ? [X3: nat] :
% 5.15/5.47 ( ( member_nat @ X3 @ A2 )
% 5.15/5.47 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_SucD
% 5.15/5.47 thf(fact_6798_sum__eq__1__iff,axiom,
% 5.15/5.47 ! [A2: set_complex,F: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.47 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.15/5.47 = one_one_nat )
% 5.15/5.47 = ( ? [X2: complex] :
% 5.15/5.47 ( ( member_complex @ X2 @ A2 )
% 5.15/5.47 & ( ( F @ X2 )
% 5.15/5.47 = one_one_nat )
% 5.15/5.47 & ! [Y2: complex] :
% 5.15/5.47 ( ( member_complex @ Y2 @ A2 )
% 5.15/5.47 => ( ( X2 != Y2 )
% 5.15/5.47 => ( ( F @ Y2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_eq_1_iff
% 5.15/5.47 thf(fact_6799_sum__eq__1__iff,axiom,
% 5.15/5.47 ! [A2: set_int,F: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ A2 )
% 5.15/5.47 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.15/5.47 = one_one_nat )
% 5.15/5.47 = ( ? [X2: int] :
% 5.15/5.47 ( ( member_int @ X2 @ A2 )
% 5.15/5.47 & ( ( F @ X2 )
% 5.15/5.47 = one_one_nat )
% 5.15/5.47 & ! [Y2: int] :
% 5.15/5.47 ( ( member_int @ Y2 @ A2 )
% 5.15/5.47 => ( ( X2 != Y2 )
% 5.15/5.47 => ( ( F @ Y2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_eq_1_iff
% 5.15/5.47 thf(fact_6800_sum__eq__1__iff,axiom,
% 5.15/5.47 ! [A2: set_nat,F: nat > nat] :
% 5.15/5.47 ( ( finite_finite_nat @ A2 )
% 5.15/5.47 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.15/5.47 = one_one_nat )
% 5.15/5.47 = ( ? [X2: nat] :
% 5.15/5.47 ( ( member_nat @ X2 @ A2 )
% 5.15/5.47 & ( ( F @ X2 )
% 5.15/5.47 = one_one_nat )
% 5.15/5.47 & ! [Y2: nat] :
% 5.15/5.47 ( ( member_nat @ Y2 @ A2 )
% 5.15/5.47 => ( ( X2 != Y2 )
% 5.15/5.47 => ( ( F @ Y2 )
% 5.15/5.47 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_eq_1_iff
% 5.15/5.47 thf(fact_6801_sum__diff__nat,axiom,
% 5.15/5.47 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 5.15/5.47 ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.47 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.15/5.47 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff_nat
% 5.15/5.47 thf(fact_6802_sum__diff__nat,axiom,
% 5.15/5.47 ! [B3: set_int,A2: set_int,F: int > nat] :
% 5.15/5.47 ( ( finite_finite_int @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.15/5.47 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff_nat
% 5.15/5.47 thf(fact_6803_sum__diff__nat,axiom,
% 5.15/5.47 ! [B3: set_nat,A2: set_nat,F: nat > nat] :
% 5.15/5.47 ( ( finite_finite_nat @ B3 )
% 5.15/5.47 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.15/5.47 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B3 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_diff_nat
% 5.15/5.47 thf(fact_6804_exp__gt__one,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_gt_one
% 5.15/5.47 thf(fact_6805_real__div__sqrt,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 5.15/5.47 = ( sqrt @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_div_sqrt
% 5.15/5.47 thf(fact_6806_sqrt__add__le__add__sqrt,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.47 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sqrt_add_le_add_sqrt
% 5.15/5.47 thf(fact_6807_take__bit__signed__take__bit,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,A: int] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 5.15/5.47 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_signed_take_bit
% 5.15/5.47 thf(fact_6808_exp__ge__add__one__self,axiom,
% 5.15/5.47 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_ge_add_one_self
% 5.15/5.47 thf(fact_6809_le__real__sqrt__sumsq,axiom,
% 5.15/5.47 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % le_real_sqrt_sumsq
% 5.15/5.47 thf(fact_6810_and__less__eq,axiom,
% 5.15/5.47 ! [L: int,K: int] :
% 5.15/5.47 ( ( ord_less_int @ L @ zero_zero_int )
% 5.15/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_less_eq
% 5.15/5.47 thf(fact_6811_AND__upper1_H_H,axiom,
% 5.15/5.47 ! [Y: int,Z: int,Ya: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.47 => ( ( ord_less_int @ Y @ Z )
% 5.15/5.47 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % AND_upper1''
% 5.15/5.47 thf(fact_6812_AND__upper2_H_H,axiom,
% 5.15/5.47 ! [Y: int,Z: int,X: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.47 => ( ( ord_less_int @ Y @ Z )
% 5.15/5.47 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % AND_upper2''
% 5.15/5.47 thf(fact_6813_take__bit__eq__mask__iff,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.15/5.47 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.15/5.47 = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.15/5.47 = zero_zero_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_mask_iff
% 5.15/5.47 thf(fact_6814_exp__minus__inverse,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 5.15/5.47 = one_one_real ) ).
% 5.15/5.47
% 5.15/5.47 % exp_minus_inverse
% 5.15/5.47 thf(fact_6815_exp__minus__inverse,axiom,
% 5.15/5.47 ! [X: complex] :
% 5.15/5.47 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 5.15/5.47 = one_one_complex ) ).
% 5.15/5.47
% 5.15/5.47 % exp_minus_inverse
% 5.15/5.47 thf(fact_6816_take__bit__decr__eq,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.15/5.47 != zero_zero_int )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ one_one_int ) )
% 5.15/5.47 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ one_one_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_decr_eq
% 5.15/5.47 thf(fact_6817_sum__power__add,axiom,
% 5.15/5.47 ! [X: complex,M: nat,I5: set_nat] :
% 5.15/5.47 ( ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [I3: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I5 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_power_add
% 5.15/5.47 thf(fact_6818_sum__power__add,axiom,
% 5.15/5.47 ! [X: rat,M: nat,I5: set_nat] :
% 5.15/5.47 ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_power_add
% 5.15/5.47 thf(fact_6819_sum__power__add,axiom,
% 5.15/5.47 ! [X: int,M: nat,I5: set_nat] :
% 5.15/5.47 ( ( groups3539618377306564664at_int
% 5.15/5.47 @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_power_add
% 5.15/5.47 thf(fact_6820_sum__power__add,axiom,
% 5.15/5.47 ! [X: real,M: nat,I5: set_nat] :
% 5.15/5.47 ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I3 ) )
% 5.15/5.47 @ I5 )
% 5.15/5.47 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I5 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_power_add
% 5.15/5.47 thf(fact_6821_sum_OatLeastAtMost__rev,axiom,
% 5.15/5.47 ! [G: nat > nat,N2: nat,M: nat] :
% 5.15/5.47 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.15/5.47 = ( groups3542108847815614940at_nat
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeastAtMost_rev
% 5.15/5.47 thf(fact_6822_sum_OatLeastAtMost__rev,axiom,
% 5.15/5.47 ! [G: nat > real,N2: nat,M: nat] :
% 5.15/5.47 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.15/5.47 = ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeastAtMost_rev
% 5.15/5.47 thf(fact_6823_sum__nth__roots,axiom,
% 5.15/5.47 ! [N2: nat,C: complex] :
% 5.15/5.47 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.15/5.47 => ( ( groups7754918857620584856omplex
% 5.15/5.47 @ ^ [X2: complex] : X2
% 5.15/5.47 @ ( collect_complex
% 5.15/5.47 @ ^ [Z3: complex] :
% 5.15/5.47 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.47 = C ) ) )
% 5.15/5.47 = zero_zero_complex ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_nth_roots
% 5.15/5.47 thf(fact_6824_sum__roots__unity,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.15/5.47 => ( ( groups7754918857620584856omplex
% 5.15/5.47 @ ^ [X2: complex] : X2
% 5.15/5.47 @ ( collect_complex
% 5.15/5.47 @ ^ [Z3: complex] :
% 5.15/5.47 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.47 = one_one_complex ) ) )
% 5.15/5.47 = zero_zero_complex ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_roots_unity
% 5.15/5.47 thf(fact_6825_even__and__iff,axiom,
% 5.15/5.47 ! [A: code_integer,B: code_integer] :
% 5.15/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.15/5.47 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.47 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_and_iff
% 5.15/5.47 thf(fact_6826_even__and__iff,axiom,
% 5.15/5.47 ! [A: int,B: int] :
% 5.15/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.15/5.47 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.47 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_and_iff
% 5.15/5.47 thf(fact_6827_even__and__iff,axiom,
% 5.15/5.47 ! [A: nat,B: nat] :
% 5.15/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.15/5.47 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.47 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_and_iff
% 5.15/5.47 thf(fact_6828_sqrt2__less__2,axiom,
% 5.15/5.47 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.15/5.47
% 5.15/5.47 % sqrt2_less_2
% 5.15/5.47 thf(fact_6829_even__or__iff,axiom,
% 5.15/5.47 ! [A: code_integer,B: code_integer] :
% 5.15/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 5.15/5.47 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.47 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_or_iff
% 5.15/5.47 thf(fact_6830_even__or__iff,axiom,
% 5.15/5.47 ! [A: int,B: int] :
% 5.15/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.15/5.47 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.47 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_or_iff
% 5.15/5.47 thf(fact_6831_even__or__iff,axiom,
% 5.15/5.47 ! [A: nat,B: nat] :
% 5.15/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.15/5.47 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.47 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_or_iff
% 5.15/5.47 thf(fact_6832_exp__ge__add__one__self__aux,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_ge_add_one_self_aux
% 5.15/5.47 thf(fact_6833_sum__shift__lb__Suc0__0,axiom,
% 5.15/5.47 ! [F: nat > complex,K: nat] :
% 5.15/5.47 ( ( ( F @ zero_zero_nat )
% 5.15/5.47 = zero_zero_complex )
% 5.15/5.47 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.15/5.47 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_shift_lb_Suc0_0
% 5.15/5.47 thf(fact_6834_sum__shift__lb__Suc0__0,axiom,
% 5.15/5.47 ! [F: nat > rat,K: nat] :
% 5.15/5.47 ( ( ( F @ zero_zero_nat )
% 5.15/5.47 = zero_zero_rat )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.15/5.47 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_shift_lb_Suc0_0
% 5.15/5.47 thf(fact_6835_sum__shift__lb__Suc0__0,axiom,
% 5.15/5.47 ! [F: nat > int,K: nat] :
% 5.15/5.47 ( ( ( F @ zero_zero_nat )
% 5.15/5.47 = zero_zero_int )
% 5.15/5.47 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.15/5.47 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_shift_lb_Suc0_0
% 5.15/5.47 thf(fact_6836_sum__shift__lb__Suc0__0,axiom,
% 5.15/5.47 ! [F: nat > nat,K: nat] :
% 5.15/5.47 ( ( ( F @ zero_zero_nat )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.15/5.47 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_shift_lb_Suc0_0
% 5.15/5.47 thf(fact_6837_sum__shift__lb__Suc0__0,axiom,
% 5.15/5.47 ! [F: nat > real,K: nat] :
% 5.15/5.47 ( ( ( F @ zero_zero_nat )
% 5.15/5.47 = zero_zero_real )
% 5.15/5.47 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.15/5.47 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_shift_lb_Suc0_0
% 5.15/5.47 thf(fact_6838_sum_OatLeast0__atMost__Suc,axiom,
% 5.15/5.47 ! [G: nat > rat,N2: nat] :
% 5.15/5.47 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast0_atMost_Suc
% 5.15/5.47 thf(fact_6839_sum_OatLeast0__atMost__Suc,axiom,
% 5.15/5.47 ! [G: nat > int,N2: nat] :
% 5.15/5.47 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast0_atMost_Suc
% 5.15/5.47 thf(fact_6840_sum_OatLeast0__atMost__Suc,axiom,
% 5.15/5.47 ! [G: nat > complex,N2: nat] :
% 5.15/5.47 ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast0_atMost_Suc
% 5.15/5.47 thf(fact_6841_sum_OatLeast0__atMost__Suc,axiom,
% 5.15/5.47 ! [G: nat > nat,N2: nat] :
% 5.15/5.47 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast0_atMost_Suc
% 5.15/5.47 thf(fact_6842_sum_OatLeast0__atMost__Suc,axiom,
% 5.15/5.47 ! [G: nat > real,N2: nat] :
% 5.15/5.47 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast0_atMost_Suc
% 5.15/5.47 thf(fact_6843_even__and__iff__int,axiom,
% 5.15/5.47 ! [K: int,L: int] :
% 5.15/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.15/5.47 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.15/5.47 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % even_and_iff_int
% 5.15/5.47 thf(fact_6844_lemma__exp__total,axiom,
% 5.15/5.47 ! [Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.15/5.47 => ? [X3: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.15/5.47 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.15/5.47 & ( ( exp_real @ X3 )
% 5.15/5.47 = Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % lemma_exp_total
% 5.15/5.47 thf(fact_6845_sum_Onat__ivl__Suc_H,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > rat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.nat_ivl_Suc'
% 5.15/5.47 thf(fact_6846_sum_Onat__ivl__Suc_H,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > int] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.nat_ivl_Suc'
% 5.15/5.47 thf(fact_6847_sum_Onat__ivl__Suc_H,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > complex] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_complex @ ( G @ ( suc @ N2 ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.nat_ivl_Suc'
% 5.15/5.47 thf(fact_6848_sum_Onat__ivl__Suc_H,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.nat_ivl_Suc'
% 5.15/5.47 thf(fact_6849_sum_Onat__ivl__Suc_H,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > real] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.nat_ivl_Suc'
% 5.15/5.47 thf(fact_6850_sum_OatLeast__Suc__atMost,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > rat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast_Suc_atMost
% 5.15/5.47 thf(fact_6851_sum_OatLeast__Suc__atMost,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > int] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast_Suc_atMost
% 5.15/5.47 thf(fact_6852_sum_OatLeast__Suc__atMost,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > complex] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( plus_plus_complex @ ( G @ M ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast_Suc_atMost
% 5.15/5.47 thf(fact_6853_sum_OatLeast__Suc__atMost,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast_Suc_atMost
% 5.15/5.47 thf(fact_6854_sum_OatLeast__Suc__atMost,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > real] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.atLeast_Suc_atMost
% 5.15/5.47 thf(fact_6855_ln__ge__iff,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 5.15/5.47 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % ln_ge_iff
% 5.15/5.47 thf(fact_6856_ln__x__over__x__mono,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 5.15/5.47 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.47 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % ln_x_over_x_mono
% 5.15/5.47 thf(fact_6857_sum_OSuc__reindex__ivl,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > rat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_rat @ ( G @ M )
% 5.15/5.47 @ ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.Suc_reindex_ivl
% 5.15/5.47 thf(fact_6858_sum_OSuc__reindex__ivl,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > int] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_int @ ( G @ M )
% 5.15/5.47 @ ( groups3539618377306564664at_int
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.Suc_reindex_ivl
% 5.15/5.47 thf(fact_6859_sum_OSuc__reindex__ivl,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > complex] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_complex @ ( G @ M )
% 5.15/5.47 @ ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.Suc_reindex_ivl
% 5.15/5.47 thf(fact_6860_sum_OSuc__reindex__ivl,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_nat @ ( G @ M )
% 5.15/5.47 @ ( groups3542108847815614940at_nat
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.Suc_reindex_ivl
% 5.15/5.47 thf(fact_6861_sum_OSuc__reindex__ivl,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > real] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.15/5.47 = ( plus_plus_real @ ( G @ M )
% 5.15/5.47 @ ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.Suc_reindex_ivl
% 5.15/5.47 thf(fact_6862_sum__Suc__diff,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > rat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_Suc_diff
% 5.15/5.47 thf(fact_6863_sum__Suc__diff,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > int] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( groups3539618377306564664at_int
% 5.15/5.47 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_Suc_diff
% 5.15/5.47 thf(fact_6864_sum__Suc__diff,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > real] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.47 => ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_Suc_diff
% 5.15/5.47 thf(fact_6865_take__bit__Suc__bit0,axiom,
% 5.15/5.47 ! [N2: nat,K: num] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.15/5.47 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_bit0
% 5.15/5.47 thf(fact_6866_take__bit__Suc__bit0,axiom,
% 5.15/5.47 ! [N2: nat,K: num] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.15/5.47 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_bit0
% 5.15/5.47 thf(fact_6867_take__bit__eq__mod,axiom,
% 5.15/5.47 ( bit_se1745604003318907178nteger
% 5.15/5.47 = ( ^ [N3: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_mod
% 5.15/5.47 thf(fact_6868_take__bit__eq__mod,axiom,
% 5.15/5.47 ( bit_se2923211474154528505it_int
% 5.15/5.47 = ( ^ [N3: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_mod
% 5.15/5.47 thf(fact_6869_take__bit__eq__mod,axiom,
% 5.15/5.47 ( bit_se2925701944663578781it_nat
% 5.15/5.47 = ( ^ [N3: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_mod
% 5.15/5.47 thf(fact_6870_one__and__eq,axiom,
% 5.15/5.47 ! [A: code_integer] :
% 5.15/5.47 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.15/5.47 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % one_and_eq
% 5.15/5.47 thf(fact_6871_one__and__eq,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.15/5.47 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % one_and_eq
% 5.15/5.47 thf(fact_6872_one__and__eq,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.15/5.47 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % one_and_eq
% 5.15/5.47 thf(fact_6873_and__one__eq,axiom,
% 5.15/5.47 ! [A: code_integer] :
% 5.15/5.47 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.15/5.47 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_one_eq
% 5.15/5.47 thf(fact_6874_and__one__eq,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.15/5.47 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_one_eq
% 5.15/5.47 thf(fact_6875_and__one__eq,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.15/5.47 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % and_one_eq
% 5.15/5.47 thf(fact_6876_take__bit__nat__eq__self__iff,axiom,
% 5.15/5.47 ! [N2: nat,M: nat] :
% 5.15/5.47 ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.15/5.47 = M )
% 5.15/5.47 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_nat_eq_self_iff
% 5.15/5.47 thf(fact_6877_take__bit__nat__less__exp,axiom,
% 5.15/5.47 ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_nat_less_exp
% 5.15/5.47 thf(fact_6878_take__bit__nat__eq__self,axiom,
% 5.15/5.47 ! [M: nat,N2: nat] :
% 5.15/5.47 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.47 => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.15/5.47 = M ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_nat_eq_self
% 5.15/5.47 thf(fact_6879_real__less__rsqrt,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.15/5.47 => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_less_rsqrt
% 5.15/5.47 thf(fact_6880_real__le__rsqrt,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.15/5.47 => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_le_rsqrt
% 5.15/5.47 thf(fact_6881_sqrt__le__D,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 5.15/5.47 => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sqrt_le_D
% 5.15/5.47 thf(fact_6882_take__bit__nat__def,axiom,
% 5.15/5.47 ( bit_se2925701944663578781it_nat
% 5.15/5.47 = ( ^ [N3: nat,M5: nat] : ( modulo_modulo_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_nat_def
% 5.15/5.47 thf(fact_6883_exp__le,axiom,
% 5.15/5.47 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_le
% 5.15/5.47 thf(fact_6884_sum_Oub__add__nat,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > rat,P2: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.15/5.47 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.ub_add_nat
% 5.15/5.47 thf(fact_6885_sum_Oub__add__nat,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > int,P2: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.15/5.47 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.15/5.47 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.ub_add_nat
% 5.15/5.47 thf(fact_6886_sum_Oub__add__nat,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > complex,P2: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.15/5.47 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.15/5.47 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.ub_add_nat
% 5.15/5.47 thf(fact_6887_sum_Oub__add__nat,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > nat,P2: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.15/5.47 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.15/5.47 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.ub_add_nat
% 5.15/5.47 thf(fact_6888_sum_Oub__add__nat,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,G: nat > real,P2: nat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.15/5.47 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.15/5.47 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.ub_add_nat
% 5.15/5.47 thf(fact_6889_take__bit__int__less__exp,axiom,
% 5.15/5.47 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_int_less_exp
% 5.15/5.47 thf(fact_6890_take__bit__int__def,axiom,
% 5.15/5.47 ( bit_se2923211474154528505it_int
% 5.15/5.47 = ( ^ [N3: nat,K2: int] : ( modulo_modulo_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_int_def
% 5.15/5.47 thf(fact_6891_set__encode__def,axiom,
% 5.15/5.47 ( nat_set_encode
% 5.15/5.47 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % set_encode_def
% 5.15/5.47 thf(fact_6892_tanh__altdef,axiom,
% 5.15/5.47 ( tanh_real
% 5.15/5.47 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % tanh_altdef
% 5.15/5.47 thf(fact_6893_tanh__altdef,axiom,
% 5.15/5.47 ( tanh_complex
% 5.15/5.47 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % tanh_altdef
% 5.15/5.47 thf(fact_6894_take__bit__eq__0__iff,axiom,
% 5.15/5.47 ! [N2: nat,A: code_integer] :
% 5.15/5.47 ( ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.15/5.47 = zero_z3403309356797280102nteger )
% 5.15/5.47 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_0_iff
% 5.15/5.47 thf(fact_6895_take__bit__eq__0__iff,axiom,
% 5.15/5.47 ! [N2: nat,A: int] :
% 5.15/5.47 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.15/5.47 = zero_zero_int )
% 5.15/5.47 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_0_iff
% 5.15/5.47 thf(fact_6896_take__bit__eq__0__iff,axiom,
% 5.15/5.47 ! [N2: nat,A: nat] :
% 5.15/5.47 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.15/5.47 = zero_zero_nat )
% 5.15/5.47 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_0_iff
% 5.15/5.47 thf(fact_6897_take__bit__numeral__bit0,axiom,
% 5.15/5.47 ! [L: num,K: num] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.15/5.47 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_numeral_bit0
% 5.15/5.47 thf(fact_6898_take__bit__numeral__bit0,axiom,
% 5.15/5.47 ! [L: num,K: num] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.15/5.47 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_numeral_bit0
% 5.15/5.47 thf(fact_6899_take__bit__nat__less__self__iff,axiom,
% 5.15/5.47 ! [N2: nat,M: nat] :
% 5.15/5.47 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 5.15/5.47 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_nat_less_self_iff
% 5.15/5.47 thf(fact_6900_real__sqrt__unique,axiom,
% 5.15/5.47 ! [Y: real,X: real] :
% 5.15/5.47 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.47 = X )
% 5.15/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.47 => ( ( sqrt @ X )
% 5.15/5.47 = Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_unique
% 5.15/5.47 thf(fact_6901_real__le__lsqrt,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.47 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_le_lsqrt
% 5.15/5.47 thf(fact_6902_lemma__real__divide__sqrt__less,axiom,
% 5.15/5.47 ! [U: real] :
% 5.15/5.47 ( ( ord_less_real @ zero_zero_real @ U )
% 5.15/5.47 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.15/5.47
% 5.15/5.47 % lemma_real_divide_sqrt_less
% 5.15/5.47 thf(fact_6903_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.47 = Y )
% 5.15/5.47 => ( X = zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_sum_squares_eq_cancel2
% 5.15/5.47 thf(fact_6904_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.47 = X )
% 5.15/5.47 => ( Y = zero_zero_real ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_sum_squares_eq_cancel
% 5.15/5.47 thf(fact_6905_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.15/5.47 ! [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 ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_sum_squares_triangle_ineq
% 5.15/5.47 thf(fact_6906_real__sqrt__sum__squares__ge2,axiom,
% 5.15/5.47 ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_sum_squares_ge2
% 5.15/5.47 thf(fact_6907_real__sqrt__sum__squares__ge1,axiom,
% 5.15/5.47 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_sum_squares_ge1
% 5.15/5.47 thf(fact_6908_exp__half__le2,axiom,
% 5.15/5.47 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_half_le2
% 5.15/5.47 thf(fact_6909_sqrt__ge__absD,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 5.15/5.47 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 5.15/5.47
% 5.15/5.47 % sqrt_ge_absD
% 5.15/5.47 thf(fact_6910_take__bit__Suc__minus__bit0,axiom,
% 5.15/5.47 ! [N2: nat,K: num] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.15/5.47 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_minus_bit0
% 5.15/5.47 thf(fact_6911_mask__Suc__exp,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N2 ) )
% 5.15/5.47 = ( bit_se1412395901928357646or_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_Suc_exp
% 5.15/5.47 thf(fact_6912_mask__Suc__exp,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2000444600071755411sk_int @ ( suc @ N2 ) )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_Suc_exp
% 5.15/5.47 thf(fact_6913_take__bit__int__less__self__iff,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.15/5.47 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_int_less_self_iff
% 5.15/5.47 thf(fact_6914_take__bit__int__greater__eq__self__iff,axiom,
% 5.15/5.47 ! [K: int,N2: nat] :
% 5.15/5.47 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.15/5.47 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_int_greater_eq_self_iff
% 5.15/5.47 thf(fact_6915_exp__double,axiom,
% 5.15/5.47 ! [Z: complex] :
% 5.15/5.47 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.15/5.47 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_double
% 5.15/5.47 thf(fact_6916_exp__double,axiom,
% 5.15/5.47 ! [Z: real] :
% 5.15/5.47 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.15/5.47 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_double
% 5.15/5.47 thf(fact_6917_sum__natinterval__diff,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > complex] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = zero_zero_complex ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_natinterval_diff
% 5.15/5.47 thf(fact_6918_sum__natinterval__diff,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > rat] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = zero_zero_rat ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_natinterval_diff
% 5.15/5.47 thf(fact_6919_sum__natinterval__diff,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > int] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups3539618377306564664at_int
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups3539618377306564664at_int
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = zero_zero_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_natinterval_diff
% 5.15/5.47 thf(fact_6920_sum__natinterval__diff,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > real] :
% 5.15/5.47 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.15/5.47 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.47 = zero_zero_real ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_natinterval_diff
% 5.15/5.47 thf(fact_6921_sum__telescope_H_H,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > rat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.15/5.47 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_telescope''
% 5.15/5.47 thf(fact_6922_sum__telescope_H_H,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > int] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups3539618377306564664at_int
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.15/5.47 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_telescope''
% 5.15/5.47 thf(fact_6923_sum__telescope_H_H,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,F: nat > real] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.15/5.47 = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_telescope''
% 5.15/5.47 thf(fact_6924_real__less__lsqrt,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.47 => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.47 => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_less_lsqrt
% 5.15/5.47 thf(fact_6925_sqrt__sum__squares__le__sum,axiom,
% 5.15/5.47 ! [X: real,Y: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.47 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sqrt_sum_squares_le_sum
% 5.15/5.47 thf(fact_6926_or__one__eq,axiom,
% 5.15/5.47 ! [A: code_integer] :
% 5.15/5.47 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 5.15/5.47 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_one_eq
% 5.15/5.47 thf(fact_6927_or__one__eq,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 5.15/5.47 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_one_eq
% 5.15/5.47 thf(fact_6928_or__one__eq,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 5.15/5.47 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % or_one_eq
% 5.15/5.47 thf(fact_6929_one__or__eq,axiom,
% 5.15/5.47 ! [A: code_integer] :
% 5.15/5.47 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 5.15/5.47 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % one_or_eq
% 5.15/5.47 thf(fact_6930_one__or__eq,axiom,
% 5.15/5.47 ! [A: int] :
% 5.15/5.47 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 5.15/5.47 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % one_or_eq
% 5.15/5.47 thf(fact_6931_one__or__eq,axiom,
% 5.15/5.47 ! [A: nat] :
% 5.15/5.47 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 5.15/5.47 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % one_or_eq
% 5.15/5.47 thf(fact_6932_sqrt__even__pow2,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.47 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.47 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sqrt_even_pow2
% 5.15/5.47 thf(fact_6933_mask__Suc__double,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N2 ) )
% 5.15/5.47 = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_Suc_double
% 5.15/5.47 thf(fact_6934_mask__Suc__double,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2000444600071755411sk_int @ ( suc @ N2 ) )
% 5.15/5.47 = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_Suc_double
% 5.15/5.47 thf(fact_6935_real__sqrt__ge__abs1,axiom,
% 5.15/5.47 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_ge_abs1
% 5.15/5.47 thf(fact_6936_real__sqrt__ge__abs2,axiom,
% 5.15/5.47 ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_ge_abs2
% 5.15/5.47 thf(fact_6937_sqrt__sum__squares__le__sum__abs,axiom,
% 5.15/5.47 ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sqrt_sum_squares_le_sum_abs
% 5.15/5.47 thf(fact_6938_ln__sqrt,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 5.15/5.47 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % ln_sqrt
% 5.15/5.47 thf(fact_6939_OR__upper,axiom,
% 5.15/5.47 ! [X: int,N2: nat,Y: int] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.47 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.47 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.47 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % OR_upper
% 5.15/5.47 thf(fact_6940_take__bit__int__eq__self__iff,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.15/5.47 = K )
% 5.15/5.47 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.47 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_int_eq_self_iff
% 5.15/5.47 thf(fact_6941_take__bit__int__eq__self,axiom,
% 5.15/5.47 ! [K: int,N2: nat] :
% 5.15/5.47 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.47 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.15/5.47 = K ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_int_eq_self
% 5.15/5.47 thf(fact_6942_take__bit__numeral__minus__bit0,axiom,
% 5.15/5.47 ! [L: num,K: num] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.15/5.47 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_numeral_minus_bit0
% 5.15/5.47 thf(fact_6943_take__bit__incr__eq,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.15/5.47 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.15/5.47 => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.15/5.47 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_incr_eq
% 5.15/5.47 thf(fact_6944_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.15/5.47 ! [N2: nat,K: int] :
% 5.15/5.47 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.15/5.47 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.15/5.47 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_eq_mask_iff_exp_dvd
% 5.15/5.47 thf(fact_6945_mask__eq__sum__exp,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 5.15/5.47 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.47 @ ( collect_nat
% 5.15/5.47 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_eq_sum_exp
% 5.15/5.47 thf(fact_6946_mask__eq__sum__exp,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 5.15/5.47 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.47 @ ( collect_nat
% 5.15/5.47 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % mask_eq_sum_exp
% 5.15/5.47 thf(fact_6947_sum__gp__multiplied,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,X: complex] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.15/5.47 = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_gp_multiplied
% 5.15/5.47 thf(fact_6948_sum__gp__multiplied,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,X: rat] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.15/5.47 = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_gp_multiplied
% 5.15/5.47 thf(fact_6949_sum__gp__multiplied,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,X: int] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.15/5.47 = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_gp_multiplied
% 5.15/5.47 thf(fact_6950_sum__gp__multiplied,axiom,
% 5.15/5.47 ! [M: nat,N2: nat,X: real] :
% 5.15/5.47 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.47 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.15/5.47 = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum_gp_multiplied
% 5.15/5.47 thf(fact_6951_sum_Oin__pairs,axiom,
% 5.15/5.47 ! [G: nat > rat,M: nat,N2: nat] :
% 5.15/5.47 ( ( 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 ) ) ) )
% 5.15/5.47 = ( groups2906978787729119204at_rat
% 5.15/5.47 @ ^ [I3: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.in_pairs
% 5.15/5.47 thf(fact_6952_sum_Oin__pairs,axiom,
% 5.15/5.47 ! [G: nat > int,M: nat,N2: nat] :
% 5.15/5.47 ( ( 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 ) ) ) )
% 5.15/5.47 = ( groups3539618377306564664at_int
% 5.15/5.47 @ ^ [I3: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.in_pairs
% 5.15/5.47 thf(fact_6953_sum_Oin__pairs,axiom,
% 5.15/5.47 ! [G: nat > complex,M: nat,N2: nat] :
% 5.15/5.47 ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.15/5.47 = ( groups2073611262835488442omplex
% 5.15/5.47 @ ^ [I3: nat] : ( plus_plus_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.in_pairs
% 5.15/5.47 thf(fact_6954_sum_Oin__pairs,axiom,
% 5.15/5.47 ! [G: nat > nat,M: nat,N2: nat] :
% 5.15/5.47 ( ( 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 ) ) ) )
% 5.15/5.47 = ( groups3542108847815614940at_nat
% 5.15/5.47 @ ^ [I3: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.in_pairs
% 5.15/5.47 thf(fact_6955_sum_Oin__pairs,axiom,
% 5.15/5.47 ! [G: nat > real,M: nat,N2: nat] :
% 5.15/5.47 ( ( 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 ) ) ) )
% 5.15/5.47 = ( groups6591440286371151544t_real
% 5.15/5.47 @ ^ [I3: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 5.15/5.47 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % sum.in_pairs
% 5.15/5.47 thf(fact_6956_take__bit__Suc__minus__1__eq,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_minus_1_eq
% 5.15/5.47 thf(fact_6957_take__bit__Suc__minus__1__eq,axiom,
% 5.15/5.47 ! [N2: nat] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_minus_1_eq
% 5.15/5.47 thf(fact_6958_take__bit__Suc__bit1,axiom,
% 5.15/5.47 ! [N2: nat,K: num] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.15/5.47 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_bit1
% 5.15/5.47 thf(fact_6959_take__bit__Suc__bit1,axiom,
% 5.15/5.47 ! [N2: nat,K: num] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.15/5.47 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc_bit1
% 5.15/5.47 thf(fact_6960_take__bit__numeral__minus__1__eq,axiom,
% 5.15/5.47 ! [K: num] :
% 5.15/5.47 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.47 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_numeral_minus_1_eq
% 5.15/5.47 thf(fact_6961_take__bit__numeral__minus__1__eq,axiom,
% 5.15/5.47 ! [K: num] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.47 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_numeral_minus_1_eq
% 5.15/5.47 thf(fact_6962_take__bit__Suc,axiom,
% 5.15/5.47 ! [N2: nat,A: code_integer] :
% 5.15/5.47 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 5.15/5.47 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc
% 5.15/5.47 thf(fact_6963_take__bit__Suc,axiom,
% 5.15/5.47 ! [N2: nat,A: int] :
% 5.15/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.15/5.47 = ( 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 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc
% 5.15/5.47 thf(fact_6964_take__bit__Suc,axiom,
% 5.15/5.47 ! [N2: nat,A: nat] :
% 5.15/5.47 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 5.15/5.47 = ( 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 ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % take_bit_Suc
% 5.15/5.47 thf(fact_6965_arsinh__real__aux,axiom,
% 5.15/5.47 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % arsinh_real_aux
% 5.15/5.47 thf(fact_6966_exp__bound,axiom,
% 5.15/5.47 ! [X: real] :
% 5.15/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.47 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % exp_bound
% 5.15/5.47 thf(fact_6967_real__sqrt__power__even,axiom,
% 5.15/5.47 ! [N2: nat,X: real] :
% 5.15/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.47 => ( ( power_power_real @ ( sqrt @ X ) @ N2 )
% 5.15/5.47 = ( power_power_real @ X @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.47
% 5.15/5.47 % real_sqrt_power_even
% 5.15/5.47 thf(fact_6968_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.15/5.47 ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_sqrt_sum_squares_mult_ge_zero
% 5.15/5.48 thf(fact_6969_arith__geo__mean__sqrt,axiom,
% 5.15/5.48 ! [X: real,Y: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.48 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % arith_geo_mean_sqrt
% 5.15/5.48 thf(fact_6970_take__bit__int__less__eq,axiom,
% 5.15/5.48 ! [N2: nat,K: int] :
% 5.15/5.48 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.48 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_int_less_eq
% 5.15/5.48 thf(fact_6971_take__bit__int__greater__eq,axiom,
% 5.15/5.48 ! [K: int,N2: nat] :
% 5.15/5.48 ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_int_greater_eq
% 5.15/5.48 thf(fact_6972_or__int__rec,axiom,
% 5.15/5.48 ( bit_se1409905431419307370or_int
% 5.15/5.48 = ( ^ [K2: int,L2: int] :
% 5.15/5.48 ( plus_plus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.15/5.48 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.15/5.48 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_int_rec
% 5.15/5.48 thf(fact_6973_signed__take__bit__eq__take__bit__shift,axiom,
% 5.15/5.48 ( bit_ri631733984087533419it_int
% 5.15/5.48 = ( ^ [N3: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % signed_take_bit_eq_take_bit_shift
% 5.15/5.48 thf(fact_6974_mask__eq__sum__exp__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.48 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.48 @ ( collect_nat
% 5.15/5.48 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mask_eq_sum_exp_nat
% 5.15/5.48 thf(fact_6975_and__int__rec,axiom,
% 5.15/5.48 ( bit_se725231765392027082nd_int
% 5.15/5.48 = ( ^ [K2: int,L2: int] :
% 5.15/5.48 ( plus_plus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.15/5.48 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_int_rec
% 5.15/5.48 thf(fact_6976_stable__imp__take__bit__eq,axiom,
% 5.15/5.48 ! [A: code_integer,N2: nat] :
% 5.15/5.48 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.48 = A )
% 5.15/5.48 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.48 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.15/5.48 = zero_z3403309356797280102nteger ) )
% 5.15/5.48 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.15/5.48 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.15/5.48 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % stable_imp_take_bit_eq
% 5.15/5.48 thf(fact_6977_stable__imp__take__bit__eq,axiom,
% 5.15/5.48 ! [A: int,N2: nat] :
% 5.15/5.48 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.48 = A )
% 5.15/5.48 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.48 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.15/5.48 = zero_zero_int ) )
% 5.15/5.48 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.15/5.48 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.15/5.48 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % stable_imp_take_bit_eq
% 5.15/5.48 thf(fact_6978_stable__imp__take__bit__eq,axiom,
% 5.15/5.48 ! [A: nat,N2: nat] :
% 5.15/5.48 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.48 = A )
% 5.15/5.48 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.48 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.15/5.48 = zero_zero_nat ) )
% 5.15/5.48 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.15/5.48 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.15/5.48 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % stable_imp_take_bit_eq
% 5.15/5.48 thf(fact_6979_gauss__sum__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( groups3542108847815614940at_nat
% 5.15/5.48 @ ^ [X2: nat] : X2
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.48 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % gauss_sum_nat
% 5.15/5.48 thf(fact_6980_take__bit__numeral__bit1,axiom,
% 5.15/5.48 ! [L: num,K: num] :
% 5.15/5.48 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.15/5.48 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_numeral_bit1
% 5.15/5.48 thf(fact_6981_take__bit__numeral__bit1,axiom,
% 5.15/5.48 ! [L: num,K: num] :
% 5.15/5.48 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.15/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_numeral_bit1
% 5.15/5.48 thf(fact_6982_real__exp__bound__lemma,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_exp_bound_lemma
% 5.15/5.48 thf(fact_6983_cos__x__y__le__one,axiom,
% 5.15/5.48 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.15/5.48
% 5.15/5.48 % cos_x_y_le_one
% 5.15/5.48 thf(fact_6984_real__sqrt__sum__squares__less,axiom,
% 5.15/5.48 ! [X: real,U: real,Y: real] :
% 5.15/5.48 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.15/5.48 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.15/5.48 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_sqrt_sum_squares_less
% 5.15/5.48 thf(fact_6985_arcosh__real__def,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.48 => ( ( arcosh_real @ X )
% 5.15/5.48 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % arcosh_real_def
% 5.15/5.48 thf(fact_6986_take__bit__minus__small__eq,axiom,
% 5.15/5.48 ! [K: int,N2: nat] :
% 5.15/5.48 ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.48 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.48 => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 5.15/5.48 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_minus_small_eq
% 5.15/5.48 thf(fact_6987_arith__series__nat,axiom,
% 5.15/5.48 ! [A: nat,D: nat,N2: nat] :
% 5.15/5.48 ( ( groups3542108847815614940at_nat
% 5.15/5.48 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % arith_series_nat
% 5.15/5.48 thf(fact_6988_Sum__Icc__nat,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( groups3542108847815614940at_nat
% 5.15/5.48 @ ^ [X2: nat] : X2
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Sum_Icc_nat
% 5.15/5.48 thf(fact_6989_sqrt__sum__squares__half__less,axiom,
% 5.15/5.48 ! [X: real,U: real,Y: real] :
% 5.15/5.48 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.48 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.48 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sqrt_sum_squares_half_less
% 5.15/5.48 thf(fact_6990_exp__lower__Taylor__quadratic,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_lower_Taylor_quadratic
% 5.15/5.48 thf(fact_6991_take__bit__numeral__minus__bit1,axiom,
% 5.15/5.48 ! [L: num,K: num] :
% 5.15/5.48 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.15/5.48 = ( 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 ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_numeral_minus_bit1
% 5.15/5.48 thf(fact_6992_and__int_Oelims,axiom,
% 5.15/5.48 ! [X: int,Xa2: int,Y: int] :
% 5.15/5.48 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.15/5.48 = Y )
% 5.15/5.48 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 = ( uminus_uminus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 = ( plus_plus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.15/5.48 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_int.elims
% 5.15/5.48 thf(fact_6993_and__int_Osimps,axiom,
% 5.15/5.48 ( bit_se725231765392027082nd_int
% 5.15/5.48 = ( ^ [K2: int,L2: int] :
% 5.15/5.48 ( if_int
% 5.15/5.48 @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.15/5.48 @ ( uminus_uminus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.15/5.48 @ ( plus_plus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.15/5.48 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_int.simps
% 5.15/5.48 thf(fact_6994_arsinh__real__def,axiom,
% 5.15/5.48 ( arsinh_real
% 5.15/5.48 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % arsinh_real_def
% 5.15/5.48 thf(fact_6995_take__bit__Suc__minus__bit1,axiom,
% 5.15/5.48 ! [N2: nat,K: num] :
% 5.15/5.48 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.15/5.48 = ( 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 ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_Suc_minus_bit1
% 5.15/5.48 thf(fact_6996_or__minus__numerals_I1_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_minus_numerals(1)
% 5.15/5.48 thf(fact_6997_pred__numeral__inc,axiom,
% 5.15/5.48 ! [K: num] :
% 5.15/5.48 ( ( pred_numeral @ ( inc @ K ) )
% 5.15/5.48 = ( numeral_numeral_nat @ K ) ) ).
% 5.15/5.48
% 5.15/5.48 % pred_numeral_inc
% 5.15/5.48 thf(fact_6998_and__nat__numerals_I3_J,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.48 = zero_zero_nat ) ).
% 5.15/5.48
% 5.15/5.48 % and_nat_numerals(3)
% 5.15/5.48 thf(fact_6999_and__nat__numerals_I1_J,axiom,
% 5.15/5.48 ! [Y: num] :
% 5.15/5.48 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.48 = zero_zero_nat ) ).
% 5.15/5.48
% 5.15/5.48 % and_nat_numerals(1)
% 5.15/5.48 thf(fact_7000_or__nat__numerals_I4_J,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.48 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_nat_numerals(4)
% 5.15/5.48 thf(fact_7001_or__nat__numerals_I2_J,axiom,
% 5.15/5.48 ! [Y: num] :
% 5.15/5.48 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.48 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_nat_numerals(2)
% 5.15/5.48 thf(fact_7002_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7003_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_real,X: real,G: real > real] :
% 5.15/5.48 ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ~ ( member_real @ X @ A2 )
% 5.15/5.48 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7004_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ~ ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7005_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_int,X: int,G: int > real] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ~ ( member_int @ X @ A2 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7006_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7007_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_real,X: real,G: real > rat] :
% 5.15/5.48 ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ~ ( member_real @ X @ A2 )
% 5.15/5.48 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7008_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_nat,X: nat,G: nat > rat] :
% 5.15/5.48 ( ( finite_finite_nat @ A2 )
% 5.15/5.48 => ( ~ ( member_nat @ X @ A2 )
% 5.15/5.48 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7009_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_complex,X: complex,G: complex > rat] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ~ ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7010_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_int,X: int,G: int > rat] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ~ ( member_int @ X @ A2 )
% 5.15/5.48 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7011_sum_Oinsert,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert
% 5.15/5.48 thf(fact_7012_or__nat__numerals_I3_J,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.48 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_nat_numerals(3)
% 5.15/5.48 thf(fact_7013_or__nat__numerals_I1_J,axiom,
% 5.15/5.48 ! [Y: num] :
% 5.15/5.48 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.48 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_nat_numerals(1)
% 5.15/5.48 thf(fact_7014_and__nat__numerals_I4_J,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.48 = one_one_nat ) ).
% 5.15/5.48
% 5.15/5.48 % and_nat_numerals(4)
% 5.15/5.48 thf(fact_7015_and__nat__numerals_I2_J,axiom,
% 5.15/5.48 ! [Y: num] :
% 5.15/5.48 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.48 = one_one_nat ) ).
% 5.15/5.48
% 5.15/5.48 % and_nat_numerals(2)
% 5.15/5.48 thf(fact_7016_set__replicate,axiom,
% 5.15/5.48 ! [N2: nat,X: vEBT_VEBT] :
% 5.15/5.48 ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.15/5.48 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate
% 5.15/5.48 thf(fact_7017_set__replicate,axiom,
% 5.15/5.48 ! [N2: nat,X: nat] :
% 5.15/5.48 ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 5.15/5.48 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate
% 5.15/5.48 thf(fact_7018_set__replicate,axiom,
% 5.15/5.48 ! [N2: nat,X: int] :
% 5.15/5.48 ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 5.15/5.48 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate
% 5.15/5.48 thf(fact_7019_set__replicate,axiom,
% 5.15/5.48 ! [N2: nat,X: real] :
% 5.15/5.48 ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 5.15/5.48 = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate
% 5.15/5.48 thf(fact_7020_add__neg__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(6)
% 5.15/5.48 thf(fact_7021_add__neg__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.48 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(6)
% 5.15/5.48 thf(fact_7022_add__neg__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.48 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(6)
% 5.15/5.48 thf(fact_7023_add__neg__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.48 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(6)
% 5.15/5.48 thf(fact_7024_add__neg__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.48 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(6)
% 5.15/5.48 thf(fact_7025_add__neg__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(5)
% 5.15/5.48 thf(fact_7026_add__neg__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.48 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(5)
% 5.15/5.48 thf(fact_7027_add__neg__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.15/5.48 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(5)
% 5.15/5.48 thf(fact_7028_add__neg__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.15/5.48 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(5)
% 5.15/5.48 thf(fact_7029_add__neg__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.15/5.48 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_neg_numeral_special(5)
% 5.15/5.48 thf(fact_7030_diff__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.48 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(6)
% 5.15/5.48 thf(fact_7031_diff__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.48 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(6)
% 5.15/5.48 thf(fact_7032_diff__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.48 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(6)
% 5.15/5.48 thf(fact_7033_diff__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.48 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(6)
% 5.15/5.48 thf(fact_7034_diff__numeral__special_I6_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.15/5.48 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(6)
% 5.15/5.48 thf(fact_7035_diff__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(5)
% 5.15/5.48 thf(fact_7036_diff__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.48 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(5)
% 5.15/5.48 thf(fact_7037_diff__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.15/5.48 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(5)
% 5.15/5.48 thf(fact_7038_diff__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 5.15/5.48 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(5)
% 5.15/5.48 thf(fact_7039_diff__numeral__special_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.15/5.48 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % diff_numeral_special(5)
% 5.15/5.48 thf(fact_7040_Suc__0__and__eq,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.48 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Suc_0_and_eq
% 5.15/5.48 thf(fact_7041_and__Suc__0__eq,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.15/5.48 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_Suc_0_eq
% 5.15/5.48 thf(fact_7042_or__minus__numerals_I4_J,axiom,
% 5.15/5.48 ! [M: num,N2: num] :
% 5.15/5.48 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_minus_numerals(4)
% 5.15/5.48 thf(fact_7043_or__minus__numerals_I8_J,axiom,
% 5.15/5.48 ! [N2: num,M: num] :
% 5.15/5.48 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_minus_numerals(8)
% 5.15/5.48 thf(fact_7044_or__minus__numerals_I7_J,axiom,
% 5.15/5.48 ! [N2: num,M: num] :
% 5.15/5.48 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_minus_numerals(7)
% 5.15/5.48 thf(fact_7045_or__minus__numerals_I3_J,axiom,
% 5.15/5.48 ! [M: num,N2: num] :
% 5.15/5.48 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_minus_numerals(3)
% 5.15/5.48 thf(fact_7046_or__minus__numerals_I5_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.15/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_minus_numerals(5)
% 5.15/5.48 thf(fact_7047_or__not__num__neg_Osimps_I1_J,axiom,
% 5.15/5.48 ( ( bit_or_not_num_neg @ one @ one )
% 5.15/5.48 = one ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(1)
% 5.15/5.48 thf(fact_7048_num__induct,axiom,
% 5.15/5.48 ! [P: num > $o,X: num] :
% 5.15/5.48 ( ( P @ one )
% 5.15/5.48 => ( ! [X3: num] :
% 5.15/5.48 ( ( P @ X3 )
% 5.15/5.48 => ( P @ ( inc @ X3 ) ) )
% 5.15/5.48 => ( P @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % num_induct
% 5.15/5.48 thf(fact_7049_add__inc,axiom,
% 5.15/5.48 ! [X: num,Y: num] :
% 5.15/5.48 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 5.15/5.48 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_inc
% 5.15/5.48 thf(fact_7050_or__not__num__neg_Osimps_I4_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
% 5.15/5.48 = ( bit0 @ one ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(4)
% 5.15/5.48 thf(fact_7051_or__not__num__neg_Osimps_I6_J,axiom,
% 5.15/5.48 ! [N2: num,M: num] :
% 5.15/5.48 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit1 @ M ) )
% 5.15/5.48 = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(6)
% 5.15/5.48 thf(fact_7052_or__not__num__neg_Osimps_I7_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ one )
% 5.15/5.48 = one ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(7)
% 5.15/5.48 thf(fact_7053_or__not__num__neg_Osimps_I3_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.15/5.48 = ( bit1 @ M ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(3)
% 5.15/5.48 thf(fact_7054_inc_Osimps_I1_J,axiom,
% 5.15/5.48 ( ( inc @ one )
% 5.15/5.48 = ( bit0 @ one ) ) ).
% 5.15/5.48
% 5.15/5.48 % inc.simps(1)
% 5.15/5.48 thf(fact_7055_inc_Osimps_I3_J,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( inc @ ( bit1 @ X ) )
% 5.15/5.48 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % inc.simps(3)
% 5.15/5.48 thf(fact_7056_inc_Osimps_I2_J,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( inc @ ( bit0 @ X ) )
% 5.15/5.48 = ( bit1 @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % inc.simps(2)
% 5.15/5.48 thf(fact_7057_or__not__num__neg_Osimps_I5_J,axiom,
% 5.15/5.48 ! [N2: num,M: num] :
% 5.15/5.48 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit0 @ M ) )
% 5.15/5.48 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(5)
% 5.15/5.48 thf(fact_7058_or__not__num__neg_Osimps_I9_J,axiom,
% 5.15/5.48 ! [N2: num,M: num] :
% 5.15/5.48 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit1 @ M ) )
% 5.15/5.48 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(9)
% 5.15/5.48 thf(fact_7059_add__One,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( plus_plus_num @ X @ one )
% 5.15/5.48 = ( inc @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % add_One
% 5.15/5.48 thf(fact_7060_inc__BitM__eq,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( inc @ ( bitM @ N2 ) )
% 5.15/5.48 = ( bit0 @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % inc_BitM_eq
% 5.15/5.48 thf(fact_7061_BitM__inc__eq,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( bitM @ ( inc @ N2 ) )
% 5.15/5.48 = ( bit1 @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % BitM_inc_eq
% 5.15/5.48 thf(fact_7062_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.15/5.48 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.15/5.48 => ( ! [X3: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S4 )
% 5.15/5.48 => ( ! [Y4: vEBT_VEBT] :
% 5.15/5.48 ( ( member_VEBT_VEBT @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_VEBT_VEBT @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7063_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_complex,P: set_complex > $o,F: complex > rat] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.48 => ( ( P @ bot_bot_set_complex )
% 5.15/5.48 => ( ! [X3: complex,S4: set_complex] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ S4 )
% 5.15/5.48 => ( ! [Y4: complex] :
% 5.15/5.48 ( ( member_complex @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7064_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_nat,P: set_nat > $o,F: nat > rat] :
% 5.15/5.48 ( ( finite_finite_nat @ S3 )
% 5.15/5.48 => ( ( P @ bot_bot_set_nat )
% 5.15/5.48 => ( ! [X3: nat,S4: set_nat] :
% 5.15/5.48 ( ( finite_finite_nat @ S4 )
% 5.15/5.48 => ( ! [Y4: nat] :
% 5.15/5.48 ( ( member_nat @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7065_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_int,P: set_int > $o,F: int > rat] :
% 5.15/5.48 ( ( finite_finite_int @ S3 )
% 5.15/5.48 => ( ( P @ bot_bot_set_int )
% 5.15/5.48 => ( ! [X3: int,S4: set_int] :
% 5.15/5.48 ( ( finite_finite_int @ S4 )
% 5.15/5.48 => ( ! [Y4: int] :
% 5.15/5.48 ( ( member_int @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7066_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_real,P: set_real > $o,F: real > rat] :
% 5.15/5.48 ( ( finite_finite_real @ S3 )
% 5.15/5.48 => ( ( P @ bot_bot_set_real )
% 5.15/5.48 => ( ! [X3: real,S4: set_real] :
% 5.15/5.48 ( ( finite_finite_real @ S4 )
% 5.15/5.48 => ( ! [Y4: real] :
% 5.15/5.48 ( ( member_real @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7067_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.15/5.48 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.15/5.48 => ( ! [X3: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S4 )
% 5.15/5.48 => ( ! [Y4: vEBT_VEBT] :
% 5.15/5.48 ( ( member_VEBT_VEBT @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_VEBT_VEBT @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7068_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_complex,P: set_complex > $o,F: complex > num] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.48 => ( ( P @ bot_bot_set_complex )
% 5.15/5.48 => ( ! [X3: complex,S4: set_complex] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ S4 )
% 5.15/5.48 => ( ! [Y4: complex] :
% 5.15/5.48 ( ( member_complex @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7069_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_nat,P: set_nat > $o,F: nat > num] :
% 5.15/5.48 ( ( finite_finite_nat @ S3 )
% 5.15/5.48 => ( ( P @ bot_bot_set_nat )
% 5.15/5.48 => ( ! [X3: nat,S4: set_nat] :
% 5.15/5.48 ( ( finite_finite_nat @ S4 )
% 5.15/5.48 => ( ! [Y4: nat] :
% 5.15/5.48 ( ( member_nat @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7070_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_int,P: set_int > $o,F: int > num] :
% 5.15/5.48 ( ( finite_finite_int @ S3 )
% 5.15/5.48 => ( ( P @ bot_bot_set_int )
% 5.15/5.48 => ( ! [X3: int,S4: set_int] :
% 5.15/5.48 ( ( finite_finite_int @ S4 )
% 5.15/5.48 => ( ! [Y4: int] :
% 5.15/5.48 ( ( member_int @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7071_finite__ranking__induct,axiom,
% 5.15/5.48 ! [S3: set_real,P: set_real > $o,F: real > num] :
% 5.15/5.48 ( ( finite_finite_real @ S3 )
% 5.15/5.48 => ( ( P @ bot_bot_set_real )
% 5.15/5.48 => ( ! [X3: real,S4: set_real] :
% 5.15/5.48 ( ( finite_finite_real @ S4 )
% 5.15/5.48 => ( ! [Y4: real] :
% 5.15/5.48 ( ( member_real @ Y4 @ S4 )
% 5.15/5.48 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( P @ S4 )
% 5.15/5.48 => ( P @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 5.15/5.48 => ( P @ S3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_ranking_induct
% 5.15/5.48 thf(fact_7072_finite__linorder__min__induct,axiom,
% 5.15/5.48 ! [A2: set_real,P: set_real > $o] :
% 5.15/5.48 ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_real )
% 5.15/5.48 => ( ! [B6: real,A6: set_real] :
% 5.15/5.48 ( ( finite_finite_real @ A6 )
% 5.15/5.48 => ( ! [X5: real] :
% 5.15/5.48 ( ( member_real @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_real @ B6 @ X5 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_real @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_min_induct
% 5.15/5.48 thf(fact_7073_finite__linorder__min__induct,axiom,
% 5.15/5.48 ! [A2: set_rat,P: set_rat > $o] :
% 5.15/5.48 ( ( finite_finite_rat @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_rat )
% 5.15/5.48 => ( ! [B6: rat,A6: set_rat] :
% 5.15/5.48 ( ( finite_finite_rat @ A6 )
% 5.15/5.48 => ( ! [X5: rat] :
% 5.15/5.48 ( ( member_rat @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_rat @ B6 @ X5 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_rat @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_min_induct
% 5.15/5.48 thf(fact_7074_finite__linorder__min__induct,axiom,
% 5.15/5.48 ! [A2: set_num,P: set_num > $o] :
% 5.15/5.48 ( ( finite_finite_num @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_num )
% 5.15/5.48 => ( ! [B6: num,A6: set_num] :
% 5.15/5.48 ( ( finite_finite_num @ A6 )
% 5.15/5.48 => ( ! [X5: num] :
% 5.15/5.48 ( ( member_num @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_num @ B6 @ X5 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_num @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_min_induct
% 5.15/5.48 thf(fact_7075_finite__linorder__min__induct,axiom,
% 5.15/5.48 ! [A2: set_nat,P: set_nat > $o] :
% 5.15/5.48 ( ( finite_finite_nat @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_nat )
% 5.15/5.48 => ( ! [B6: nat,A6: set_nat] :
% 5.15/5.48 ( ( finite_finite_nat @ A6 )
% 5.15/5.48 => ( ! [X5: nat] :
% 5.15/5.48 ( ( member_nat @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_nat @ B6 @ X5 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_nat @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_min_induct
% 5.15/5.48 thf(fact_7076_finite__linorder__min__induct,axiom,
% 5.15/5.48 ! [A2: set_int,P: set_int > $o] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_int )
% 5.15/5.48 => ( ! [B6: int,A6: set_int] :
% 5.15/5.48 ( ( finite_finite_int @ A6 )
% 5.15/5.48 => ( ! [X5: int] :
% 5.15/5.48 ( ( member_int @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_int @ B6 @ X5 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_int @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_min_induct
% 5.15/5.48 thf(fact_7077_finite__linorder__max__induct,axiom,
% 5.15/5.48 ! [A2: set_real,P: set_real > $o] :
% 5.15/5.48 ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_real )
% 5.15/5.48 => ( ! [B6: real,A6: set_real] :
% 5.15/5.48 ( ( finite_finite_real @ A6 )
% 5.15/5.48 => ( ! [X5: real] :
% 5.15/5.48 ( ( member_real @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_real @ X5 @ B6 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_real @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_max_induct
% 5.15/5.48 thf(fact_7078_finite__linorder__max__induct,axiom,
% 5.15/5.48 ! [A2: set_rat,P: set_rat > $o] :
% 5.15/5.48 ( ( finite_finite_rat @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_rat )
% 5.15/5.48 => ( ! [B6: rat,A6: set_rat] :
% 5.15/5.48 ( ( finite_finite_rat @ A6 )
% 5.15/5.48 => ( ! [X5: rat] :
% 5.15/5.48 ( ( member_rat @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_rat @ X5 @ B6 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_rat @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_max_induct
% 5.15/5.48 thf(fact_7079_finite__linorder__max__induct,axiom,
% 5.15/5.48 ! [A2: set_num,P: set_num > $o] :
% 5.15/5.48 ( ( finite_finite_num @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_num )
% 5.15/5.48 => ( ! [B6: num,A6: set_num] :
% 5.15/5.48 ( ( finite_finite_num @ A6 )
% 5.15/5.48 => ( ! [X5: num] :
% 5.15/5.48 ( ( member_num @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_num @ X5 @ B6 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_num @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_max_induct
% 5.15/5.48 thf(fact_7080_finite__linorder__max__induct,axiom,
% 5.15/5.48 ! [A2: set_nat,P: set_nat > $o] :
% 5.15/5.48 ( ( finite_finite_nat @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_nat )
% 5.15/5.48 => ( ! [B6: nat,A6: set_nat] :
% 5.15/5.48 ( ( finite_finite_nat @ A6 )
% 5.15/5.48 => ( ! [X5: nat] :
% 5.15/5.48 ( ( member_nat @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_nat @ X5 @ B6 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_nat @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_max_induct
% 5.15/5.48 thf(fact_7081_finite__linorder__max__induct,axiom,
% 5.15/5.48 ! [A2: set_int,P: set_int > $o] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ( P @ bot_bot_set_int )
% 5.15/5.48 => ( ! [B6: int,A6: set_int] :
% 5.15/5.48 ( ( finite_finite_int @ A6 )
% 5.15/5.48 => ( ! [X5: int] :
% 5.15/5.48 ( ( member_int @ X5 @ A6 )
% 5.15/5.48 => ( ord_less_int @ X5 @ B6 ) )
% 5.15/5.48 => ( ( P @ A6 )
% 5.15/5.48 => ( P @ ( insert_int @ B6 @ A6 ) ) ) ) )
% 5.15/5.48 => ( P @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % finite_linorder_max_induct
% 5.15/5.48 thf(fact_7082_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( groups2240296850493347238T_real @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7083_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_real,X: real,G: real > real] :
% 5.15/5.48 ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ( ( member_real @ X @ A2 )
% 5.15/5.48 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.15/5.48 = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_real @ X @ A2 )
% 5.15/5.48 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7084_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7085_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_int,X: int,G: int > real] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ( ( member_int @ X @ A2 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.48 = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_int @ X @ A2 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7086_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( groups136491112297645522BT_rat @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7087_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_real,X: real,G: real > rat] :
% 5.15/5.48 ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ( ( member_real @ X @ A2 )
% 5.15/5.48 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 5.15/5.48 = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_real @ X @ A2 )
% 5.15/5.48 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7088_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_nat,X: nat,G: nat > rat] :
% 5.15/5.48 ( ( finite_finite_nat @ A2 )
% 5.15/5.48 => ( ( ( member_nat @ X @ A2 )
% 5.15/5.48 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 5.15/5.48 = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_nat @ X @ A2 )
% 5.15/5.48 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7089_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_complex,X: complex,G: complex > rat] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7090_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_int,X: int,G: int > rat] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ( ( member_int @ X @ A2 )
% 5.15/5.48 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.48 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_int @ X @ A2 )
% 5.15/5.48 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7091_sum_Oinsert__if,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( groups771621172384141258BT_nat @ G @ A2 ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_if
% 5.15/5.48 thf(fact_7092_sum__diff1__nat,axiom,
% 5.15/5.48 ! [A: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.15/5.48 ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 = ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1_nat
% 5.15/5.48 thf(fact_7093_sum__diff1__nat,axiom,
% 5.15/5.48 ! [A: complex,A2: set_complex,F: complex > nat] :
% 5.15/5.48 ( ( ( member_complex @ A @ A2 )
% 5.15/5.48 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ A @ A2 )
% 5.15/5.48 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 = ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1_nat
% 5.15/5.48 thf(fact_7094_sum__diff1__nat,axiom,
% 5.15/5.48 ! [A: set_nat,A2: set_set_nat,F: set_nat > nat] :
% 5.15/5.48 ( ( ( member_set_nat @ A @ A2 )
% 5.15/5.48 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.15/5.48 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_set_nat @ A @ A2 )
% 5.15/5.48 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.15/5.48 = ( groups8294997508430121362at_nat @ F @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1_nat
% 5.15/5.48 thf(fact_7095_sum__diff1__nat,axiom,
% 5.15/5.48 ! [A: int,A2: set_int,F: int > nat] :
% 5.15/5.48 ( ( ( member_int @ A @ A2 )
% 5.15/5.48 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.15/5.48 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_int @ A @ A2 )
% 5.15/5.48 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.15/5.48 = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1_nat
% 5.15/5.48 thf(fact_7096_sum__diff1__nat,axiom,
% 5.15/5.48 ! [A: real,A2: set_real,F: real > nat] :
% 5.15/5.48 ( ( ( member_real @ A @ A2 )
% 5.15/5.48 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.15/5.48 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_real @ A @ A2 )
% 5.15/5.48 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.15/5.48 = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1_nat
% 5.15/5.48 thf(fact_7097_sum__diff1__nat,axiom,
% 5.15/5.48 ! [A: nat,A2: set_nat,F: nat > nat] :
% 5.15/5.48 ( ( ( member_nat @ A @ A2 )
% 5.15/5.48 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.15/5.48 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_nat @ A @ A2 )
% 5.15/5.48 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.15/5.48 = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1_nat
% 5.15/5.48 thf(fact_7098_mult__inc,axiom,
% 5.15/5.48 ! [X: num,Y: num] :
% 5.15/5.48 ( ( times_times_num @ X @ ( inc @ Y ) )
% 5.15/5.48 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % mult_inc
% 5.15/5.48 thf(fact_7099_set__update__subset__insert,axiom,
% 5.15/5.48 ! [Xs2: list_real,I: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_update_subset_insert
% 5.15/5.48 thf(fact_7100_set__update__subset__insert,axiom,
% 5.15/5.48 ! [Xs2: list_int,I: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_update_subset_insert
% 5.15/5.48 thf(fact_7101_set__update__subset__insert,axiom,
% 5.15/5.48 ! [Xs2: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_update_subset_insert
% 5.15/5.48 thf(fact_7102_set__update__subset__insert,axiom,
% 5.15/5.48 ! [Xs2: list_nat,I: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_update_subset_insert
% 5.15/5.48 thf(fact_7103_or__not__num__neg_Osimps_I2_J,axiom,
% 5.15/5.48 ! [M: num] :
% 5.15/5.48 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.15/5.48 = ( bit1 @ M ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(2)
% 5.15/5.48 thf(fact_7104_numeral__inc,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 5.15/5.48 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_inc
% 5.15/5.48 thf(fact_7105_numeral__inc,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( numeral_numeral_real @ ( inc @ X ) )
% 5.15/5.48 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_inc
% 5.15/5.48 thf(fact_7106_numeral__inc,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 5.15/5.48 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_inc
% 5.15/5.48 thf(fact_7107_numeral__inc,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 5.15/5.48 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_inc
% 5.15/5.48 thf(fact_7108_numeral__inc,axiom,
% 5.15/5.48 ! [X: num] :
% 5.15/5.48 ( ( numeral_numeral_int @ ( inc @ X ) )
% 5.15/5.48 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_inc
% 5.15/5.48 thf(fact_7109_or__not__num__neg_Osimps_I8_J,axiom,
% 5.15/5.48 ! [N2: num,M: num] :
% 5.15/5.48 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit0 @ M ) )
% 5.15/5.48 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.simps(8)
% 5.15/5.48 thf(fact_7110_set__replicate__Suc,axiom,
% 5.15/5.48 ! [N2: nat,X: vEBT_VEBT] :
% 5.15/5.48 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N2 ) @ X ) )
% 5.15/5.48 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate_Suc
% 5.15/5.48 thf(fact_7111_set__replicate__Suc,axiom,
% 5.15/5.48 ! [N2: nat,X: nat] :
% 5.15/5.48 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N2 ) @ X ) )
% 5.15/5.48 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate_Suc
% 5.15/5.48 thf(fact_7112_set__replicate__Suc,axiom,
% 5.15/5.48 ! [N2: nat,X: int] :
% 5.15/5.48 ( ( set_int2 @ ( replicate_int @ ( suc @ N2 ) @ X ) )
% 5.15/5.48 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate_Suc
% 5.15/5.48 thf(fact_7113_set__replicate__Suc,axiom,
% 5.15/5.48 ! [N2: nat,X: real] :
% 5.15/5.48 ( ( set_real2 @ ( replicate_real @ ( suc @ N2 ) @ X ) )
% 5.15/5.48 = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate_Suc
% 5.15/5.48 thf(fact_7114_set__replicate__conv__if,axiom,
% 5.15/5.48 ! [N2: nat,X: vEBT_VEBT] :
% 5.15/5.48 ( ( ( N2 = zero_zero_nat )
% 5.15/5.48 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.15/5.48 = bot_bo8194388402131092736T_VEBT ) )
% 5.15/5.48 & ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.15/5.48 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate_conv_if
% 5.15/5.48 thf(fact_7115_set__replicate__conv__if,axiom,
% 5.15/5.48 ! [N2: nat,X: nat] :
% 5.15/5.48 ( ( ( N2 = zero_zero_nat )
% 5.15/5.48 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 5.15/5.48 = bot_bot_set_nat ) )
% 5.15/5.48 & ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X ) )
% 5.15/5.48 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate_conv_if
% 5.15/5.48 thf(fact_7116_set__replicate__conv__if,axiom,
% 5.15/5.48 ! [N2: nat,X: int] :
% 5.15/5.48 ( ( ( N2 = zero_zero_nat )
% 5.15/5.48 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 5.15/5.48 = bot_bot_set_int ) )
% 5.15/5.48 & ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ( set_int2 @ ( replicate_int @ N2 @ X ) )
% 5.15/5.48 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate_conv_if
% 5.15/5.48 thf(fact_7117_set__replicate__conv__if,axiom,
% 5.15/5.48 ! [N2: nat,X: real] :
% 5.15/5.48 ( ( ( N2 = zero_zero_nat )
% 5.15/5.48 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 5.15/5.48 = bot_bot_set_real ) )
% 5.15/5.48 & ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ( set_real2 @ ( replicate_real @ N2 @ X ) )
% 5.15/5.48 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_replicate_conv_if
% 5.15/5.48 thf(fact_7118_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X: vEBT_VEBT] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7119_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_complex,G: complex > real,X: complex] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7120_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > rat,X: vEBT_VEBT] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7121_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_complex,G: complex > rat,X: complex] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7122_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > nat,X: vEBT_VEBT] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7123_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_complex,G: complex > nat,X: complex] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7124_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > int,X: vEBT_VEBT] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_int @ ( G @ X ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7125_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_complex,G: complex > int,X: complex] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7126_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > complex,X: vEBT_VEBT] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( groups1794756597179926696omplex @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_complex @ ( G @ X ) @ ( groups1794756597179926696omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7127_sum_Oinsert__remove,axiom,
% 5.15/5.48 ! [A2: set_int,G: int > real,X: int] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.insert_remove
% 5.15/5.48 thf(fact_7128_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real @ G @ A2 )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7129_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7130_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat @ G @ A2 )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7131_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_complex,X: complex,G: complex > rat] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.15/5.48 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7132_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat @ G @ A2 )
% 5.15/5.48 = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7133_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_complex,X: complex,G: complex > nat] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.15/5.48 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7134_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > int] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups769130701875090982BT_int @ G @ A2 )
% 5.15/5.48 = ( plus_plus_int @ ( G @ X ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7135_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_complex,X: complex,G: complex > int] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( member_complex @ X @ A2 )
% 5.15/5.48 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.15/5.48 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7136_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > complex] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.48 => ( ( groups1794756597179926696omplex @ G @ A2 )
% 5.15/5.48 = ( plus_plus_complex @ ( G @ X ) @ ( groups1794756597179926696omplex @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7137_sum_Oremove,axiom,
% 5.15/5.48 ! [A2: set_int,X: int,G: int > real] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ( member_int @ X @ A2 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.15/5.48 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.remove
% 5.15/5.48 thf(fact_7138_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > real] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 = ( minus_minus_real @ ( groups2240296850493347238T_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 = ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7139_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_complex,A: complex,F: complex > real] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( ( member_complex @ A @ A2 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ A @ A2 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 = ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7140_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_int,A: int,F: int > real] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ( ( member_int @ A @ A2 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.15/5.48 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_int @ A @ A2 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.15/5.48 = ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7141_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_real,A: real,F: real > real] :
% 5.15/5.48 ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ( ( member_real @ A @ A2 )
% 5.15/5.48 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.15/5.48 = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_real @ A @ A2 )
% 5.15/5.48 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.15/5.48 = ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7142_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 = ( minus_minus_rat @ ( groups136491112297645522BT_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 = ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7143_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_complex,A: complex,F: complex > rat] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( ( member_complex @ A @ A2 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ A @ A2 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7144_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_int,A: int,F: int > rat] :
% 5.15/5.48 ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ( ( member_int @ A @ A2 )
% 5.15/5.48 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.15/5.48 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_int @ A @ A2 )
% 5.15/5.48 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.15/5.48 = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7145_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_real,A: real,F: real > rat] :
% 5.15/5.48 ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ( ( member_real @ A @ A2 )
% 5.15/5.48 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.15/5.48 = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_real @ A @ A2 )
% 5.15/5.48 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.15/5.48 = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7146_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 5.15/5.48 => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 = ( minus_minus_int @ ( groups769130701875090982BT_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 5.15/5.48 => ( ( groups769130701875090982BT_int @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 = ( groups769130701875090982BT_int @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7147_sum__diff1,axiom,
% 5.15/5.48 ! [A2: set_complex,A: complex,F: complex > int] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ( ( member_complex @ A @ A2 )
% 5.15/5.48 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ A @ A2 )
% 5.15/5.48 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_diff1
% 5.15/5.48 thf(fact_7148_or__not__num__neg_Oelims,axiom,
% 5.15/5.48 ! [X: num,Xa2: num,Y: num] :
% 5.15/5.48 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.15/5.48 = Y )
% 5.15/5.48 => ( ( ( X = one )
% 5.15/5.48 => ( ( Xa2 = one )
% 5.15/5.48 => ( Y != one ) ) )
% 5.15/5.48 => ( ( ( X = one )
% 5.15/5.48 => ! [M3: num] :
% 5.15/5.48 ( ( Xa2
% 5.15/5.48 = ( bit0 @ M3 ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 != ( bit1 @ M3 ) ) ) )
% 5.15/5.48 => ( ( ( X = one )
% 5.15/5.48 => ! [M3: num] :
% 5.15/5.48 ( ( Xa2
% 5.15/5.48 = ( bit1 @ M3 ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 != ( bit1 @ M3 ) ) ) )
% 5.15/5.48 => ( ( ? [N: num] :
% 5.15/5.48 ( X
% 5.15/5.48 = ( bit0 @ N ) )
% 5.15/5.48 => ( ( Xa2 = one )
% 5.15/5.48 => ( Y
% 5.15/5.48 != ( bit0 @ one ) ) ) )
% 5.15/5.48 => ( ! [N: num] :
% 5.15/5.48 ( ( X
% 5.15/5.48 = ( bit0 @ N ) )
% 5.15/5.48 => ! [M3: num] :
% 5.15/5.48 ( ( Xa2
% 5.15/5.48 = ( bit0 @ M3 ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 != ( bitM @ ( bit_or_not_num_neg @ N @ M3 ) ) ) ) )
% 5.15/5.48 => ( ! [N: num] :
% 5.15/5.48 ( ( X
% 5.15/5.48 = ( bit0 @ N ) )
% 5.15/5.48 => ! [M3: num] :
% 5.15/5.48 ( ( Xa2
% 5.15/5.48 = ( bit1 @ M3 ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 != ( bit0 @ ( bit_or_not_num_neg @ N @ M3 ) ) ) ) )
% 5.15/5.48 => ( ( ? [N: num] :
% 5.15/5.48 ( X
% 5.15/5.48 = ( bit1 @ N ) )
% 5.15/5.48 => ( ( Xa2 = one )
% 5.15/5.48 => ( Y != one ) ) )
% 5.15/5.48 => ( ! [N: num] :
% 5.15/5.48 ( ( X
% 5.15/5.48 = ( bit1 @ N ) )
% 5.15/5.48 => ! [M3: num] :
% 5.15/5.48 ( ( Xa2
% 5.15/5.48 = ( bit0 @ M3 ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 != ( bitM @ ( bit_or_not_num_neg @ N @ M3 ) ) ) ) )
% 5.15/5.48 => ~ ! [N: num] :
% 5.15/5.48 ( ( X
% 5.15/5.48 = ( bit1 @ N ) )
% 5.15/5.48 => ! [M3: num] :
% 5.15/5.48 ( ( Xa2
% 5.15/5.48 = ( bit1 @ M3 ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 != ( bitM @ ( bit_or_not_num_neg @ N @ M3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_not_num_neg.elims
% 5.15/5.48 thf(fact_7149_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups2240296850493347238T_real
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7150_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_complex,A: complex,B: complex > real,C: complex > real] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.48 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real
% 5.15/5.48 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.48 => ( ( groups5808333547571424918x_real
% 5.15/5.48 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7151_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups136491112297645522BT_rat
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7152_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.48 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat
% 5.15/5.48 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.48 => ( ( groups5058264527183730370ex_rat
% 5.15/5.48 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7153_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C: vEBT_VEBT > nat] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups771621172384141258BT_nat
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7154_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.48 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.48 => ( ( groups5693394587270226106ex_nat
% 5.15/5.48 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.48 => ( ( groups5693394587270226106ex_nat
% 5.15/5.48 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7155_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > int,C: vEBT_VEBT > int] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups769130701875090982BT_int
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_int @ ( B @ A ) @ ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups769130701875090982BT_int
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7156_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_complex,A: complex,B: complex > int,C: complex > int] :
% 5.15/5.48 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.48 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.48 => ( ( groups5690904116761175830ex_int
% 5.15/5.48 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.48 => ( ( groups5690904116761175830ex_int
% 5.15/5.48 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7157_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > complex,C: vEBT_VEBT > complex] :
% 5.15/5.48 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.15/5.48 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups1794756597179926696omplex
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_complex @ ( B @ A ) @ ( groups1794756597179926696omplex @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.15/5.48 => ( ( groups1794756597179926696omplex
% 5.15/5.48 @ ^ [K2: vEBT_VEBT] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups1794756597179926696omplex @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7158_sum_Odelta__remove,axiom,
% 5.15/5.48 ! [S3: set_int,A: int,B: int > real,C: int > real] :
% 5.15/5.48 ( ( finite_finite_int @ S3 )
% 5.15/5.48 => ( ( ( member_int @ A @ S3 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real
% 5.15/5.48 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.48 => ( ( groups8778361861064173332t_real
% 5.15/5.48 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.15/5.48 @ S3 )
% 5.15/5.48 = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum.delta_remove
% 5.15/5.48 thf(fact_7159_member__le__sum,axiom,
% 5.15/5.48 ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.15/5.48 ( ( member_VEBT_VEBT @ I @ A2 )
% 5.15/5.48 => ( ! [X3: vEBT_VEBT] :
% 5.15/5.48 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ord_less_eq_real @ ( F @ I ) @ ( groups2240296850493347238T_real @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7160_member__le__sum,axiom,
% 5.15/5.48 ! [I: complex,A2: set_complex,F: complex > real] :
% 5.15/5.48 ( ( member_complex @ I @ A2 )
% 5.15/5.48 => ( ! [X3: complex] :
% 5.15/5.48 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7161_member__le__sum,axiom,
% 5.15/5.48 ! [I: int,A2: set_int,F: int > real] :
% 5.15/5.48 ( ( member_int @ I @ A2 )
% 5.15/5.48 => ( ! [X3: int] :
% 5.15/5.48 ( ( member_int @ X3 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7162_member__le__sum,axiom,
% 5.15/5.48 ! [I: real,A2: set_real,F: real > real] :
% 5.15/5.48 ( ( member_real @ I @ A2 )
% 5.15/5.48 => ( ! [X3: real] :
% 5.15/5.48 ( ( member_real @ X3 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7163_member__le__sum,axiom,
% 5.15/5.48 ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.15/5.48 ( ( member_VEBT_VEBT @ I @ A2 )
% 5.15/5.48 => ( ! [X3: vEBT_VEBT] :
% 5.15/5.48 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7164_member__le__sum,axiom,
% 5.15/5.48 ! [I: complex,A2: set_complex,F: complex > rat] :
% 5.15/5.48 ( ( member_complex @ I @ A2 )
% 5.15/5.48 => ( ! [X3: complex] :
% 5.15/5.48 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.15/5.48 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7165_member__le__sum,axiom,
% 5.15/5.48 ! [I: int,A2: set_int,F: int > rat] :
% 5.15/5.48 ( ( member_int @ I @ A2 )
% 5.15/5.48 => ( ! [X3: int] :
% 5.15/5.48 ( ( member_int @ X3 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.15/5.48 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite_finite_int @ A2 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7166_member__le__sum,axiom,
% 5.15/5.48 ! [I: real,A2: set_real,F: real > rat] :
% 5.15/5.48 ( ( member_real @ I @ A2 )
% 5.15/5.48 => ( ! [X3: real] :
% 5.15/5.48 ( ( member_real @ X3 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.15/5.48 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite_finite_real @ A2 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7167_member__le__sum,axiom,
% 5.15/5.48 ! [I: nat,A2: set_nat,F: nat > rat] :
% 5.15/5.48 ( ( member_nat @ I @ A2 )
% 5.15/5.48 => ( ! [X3: nat] :
% 5.15/5.48 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 5.15/5.48 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite_finite_nat @ A2 )
% 5.15/5.48 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7168_member__le__sum,axiom,
% 5.15/5.48 ! [I: vEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.15/5.48 ( ( member_VEBT_VEBT @ I @ A2 )
% 5.15/5.48 => ( ! [X3: vEBT_VEBT] :
% 5.15/5.48 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.48 => ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.48 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups771621172384141258BT_nat @ F @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_le_sum
% 5.15/5.48 thf(fact_7169_and__nat__unfold,axiom,
% 5.15/5.48 ( bit_se727722235901077358nd_nat
% 5.15/5.48 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.48 ( if_nat
% 5.15/5.48 @ ( ( M5 = zero_zero_nat )
% 5.15/5.48 | ( N3 = zero_zero_nat ) )
% 5.15/5.48 @ zero_zero_nat
% 5.15/5.48 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M5 @ ( 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 @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_nat_unfold
% 5.15/5.48 thf(fact_7170_Suc__0__or__eq,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.48 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Suc_0_or_eq
% 5.15/5.48 thf(fact_7171_or__Suc__0__eq,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.15/5.48 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_Suc_0_eq
% 5.15/5.48 thf(fact_7172_or__nat__rec,axiom,
% 5.15/5.48 ( bit_se1412395901928357646or_nat
% 5.15/5.48 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.48 ( plus_plus_nat
% 5.15/5.48 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.48 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 )
% 5.15/5.48 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.15/5.48 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_nat_rec
% 5.15/5.48 thf(fact_7173_and__nat__rec,axiom,
% 5.15/5.48 ( bit_se727722235901077358nd_nat
% 5.15/5.48 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.48 ( plus_plus_nat
% 5.15/5.48 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.48 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 )
% 5.15/5.48 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.15/5.48 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_nat_rec
% 5.15/5.48 thf(fact_7174_or__nat__unfold,axiom,
% 5.15/5.48 ( bit_se1412395901928357646or_nat
% 5.15/5.48 = ( ^ [M5: nat,N3: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M5 @ ( 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 @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % or_nat_unfold
% 5.15/5.48 thf(fact_7175_singleton__conv,axiom,
% 5.15/5.48 ! [A: vEBT_VEBT] :
% 5.15/5.48 ( ( collect_VEBT_VEBT
% 5.15/5.48 @ ^ [X2: vEBT_VEBT] : ( X2 = A ) )
% 5.15/5.48 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv
% 5.15/5.48 thf(fact_7176_singleton__conv,axiom,
% 5.15/5.48 ! [A: product_prod_int_int] :
% 5.15/5.48 ( ( collec213857154873943460nt_int
% 5.15/5.48 @ ^ [X2: product_prod_int_int] : ( X2 = A ) )
% 5.15/5.48 = ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv
% 5.15/5.48 thf(fact_7177_singleton__conv,axiom,
% 5.15/5.48 ! [A: complex] :
% 5.15/5.48 ( ( collect_complex
% 5.15/5.48 @ ^ [X2: complex] : ( X2 = A ) )
% 5.15/5.48 = ( insert_complex @ A @ bot_bot_set_complex ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv
% 5.15/5.48 thf(fact_7178_singleton__conv,axiom,
% 5.15/5.48 ! [A: set_nat] :
% 5.15/5.48 ( ( collect_set_nat
% 5.15/5.48 @ ^ [X2: set_nat] : ( X2 = A ) )
% 5.15/5.48 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv
% 5.15/5.48 thf(fact_7179_singleton__conv,axiom,
% 5.15/5.48 ! [A: nat] :
% 5.15/5.48 ( ( collect_nat
% 5.15/5.48 @ ^ [X2: nat] : ( X2 = A ) )
% 5.15/5.48 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv
% 5.15/5.48 thf(fact_7180_singleton__conv,axiom,
% 5.15/5.48 ! [A: int] :
% 5.15/5.48 ( ( collect_int
% 5.15/5.48 @ ^ [X2: int] : ( X2 = A ) )
% 5.15/5.48 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv
% 5.15/5.48 thf(fact_7181_singleton__conv,axiom,
% 5.15/5.48 ! [A: real] :
% 5.15/5.48 ( ( collect_real
% 5.15/5.48 @ ^ [X2: real] : ( X2 = A ) )
% 5.15/5.48 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv
% 5.15/5.48 thf(fact_7182_singleton__conv2,axiom,
% 5.15/5.48 ! [A: vEBT_VEBT] :
% 5.15/5.48 ( ( collect_VEBT_VEBT
% 5.15/5.48 @ ( ^ [Y5: vEBT_VEBT,Z5: vEBT_VEBT] : ( Y5 = Z5 )
% 5.15/5.48 @ A ) )
% 5.15/5.48 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv2
% 5.15/5.48 thf(fact_7183_singleton__conv2,axiom,
% 5.15/5.48 ! [A: product_prod_int_int] :
% 5.15/5.48 ( ( collec213857154873943460nt_int
% 5.15/5.48 @ ( ^ [Y5: product_prod_int_int,Z5: product_prod_int_int] : ( Y5 = Z5 )
% 5.15/5.48 @ A ) )
% 5.15/5.48 = ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv2
% 5.15/5.48 thf(fact_7184_singleton__conv2,axiom,
% 5.15/5.48 ! [A: complex] :
% 5.15/5.48 ( ( collect_complex
% 5.15/5.48 @ ( ^ [Y5: complex,Z5: complex] : ( Y5 = Z5 )
% 5.15/5.48 @ A ) )
% 5.15/5.48 = ( insert_complex @ A @ bot_bot_set_complex ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv2
% 5.15/5.48 thf(fact_7185_singleton__conv2,axiom,
% 5.15/5.48 ! [A: set_nat] :
% 5.15/5.48 ( ( collect_set_nat
% 5.15/5.48 @ ( ^ [Y5: set_nat,Z5: set_nat] : ( Y5 = Z5 )
% 5.15/5.48 @ A ) )
% 5.15/5.48 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv2
% 5.15/5.48 thf(fact_7186_singleton__conv2,axiom,
% 5.15/5.48 ! [A: nat] :
% 5.15/5.48 ( ( collect_nat
% 5.15/5.48 @ ( ^ [Y5: nat,Z5: nat] : ( Y5 = Z5 )
% 5.15/5.48 @ A ) )
% 5.15/5.48 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv2
% 5.15/5.48 thf(fact_7187_singleton__conv2,axiom,
% 5.15/5.48 ! [A: int] :
% 5.15/5.48 ( ( collect_int
% 5.15/5.48 @ ( ^ [Y5: int,Z5: int] : ( Y5 = Z5 )
% 5.15/5.48 @ A ) )
% 5.15/5.48 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv2
% 5.15/5.48 thf(fact_7188_singleton__conv2,axiom,
% 5.15/5.48 ! [A: real] :
% 5.15/5.48 ( ( collect_real
% 5.15/5.48 @ ( ^ [Y5: real,Z5: real] : ( Y5 = Z5 )
% 5.15/5.48 @ A ) )
% 5.15/5.48 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 5.15/5.48
% 5.15/5.48 % singleton_conv2
% 5.15/5.48 thf(fact_7189_and__int_Opelims,axiom,
% 5.15/5.48 ! [X: int,Xa2: int,Y: int] :
% 5.15/5.48 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.15/5.48 = Y )
% 5.15/5.48 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.15/5.48 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 = ( uminus_uminus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.15/5.48 => ( Y
% 5.15/5.48 = ( plus_plus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.15/5.48 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.15/5.48 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_int.pelims
% 5.15/5.48 thf(fact_7190_and__int_Opsimps,axiom,
% 5.15/5.48 ! [K: int,L: int] :
% 5.15/5.48 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.15/5.48 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.15/5.48 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.15/5.48 = ( uminus_uminus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.15/5.48 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.15/5.48 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.15/5.48 = ( plus_plus_int
% 5.15/5.48 @ ( zero_n2684676970156552555ol_int
% 5.15/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.15/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.15/5.48 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_int.psimps
% 5.15/5.48 thf(fact_7191_sum__gp,axiom,
% 5.15/5.48 ! [N2: nat,M: nat,X: rat] :
% 5.15/5.48 ( ( ( ord_less_nat @ N2 @ M )
% 5.15/5.48 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = zero_zero_rat ) )
% 5.15/5.48 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.15/5.48 => ( ( ( X = one_one_rat )
% 5.15/5.48 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.15/5.48 & ( ( X != one_one_rat )
% 5.15/5.48 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_gp
% 5.15/5.48 thf(fact_7192_sum__gp,axiom,
% 5.15/5.48 ! [N2: nat,M: nat,X: complex] :
% 5.15/5.48 ( ( ( ord_less_nat @ N2 @ M )
% 5.15/5.48 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = zero_zero_complex ) )
% 5.15/5.48 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.15/5.48 => ( ( ( X = one_one_complex )
% 5.15/5.48 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.15/5.48 & ( ( X != one_one_complex )
% 5.15/5.48 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_gp
% 5.15/5.48 thf(fact_7193_sum__gp,axiom,
% 5.15/5.48 ! [N2: nat,M: nat,X: real] :
% 5.15/5.48 ( ( ( ord_less_nat @ N2 @ M )
% 5.15/5.48 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = zero_zero_real ) )
% 5.15/5.48 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.15/5.48 => ( ( ( X = one_one_real )
% 5.15/5.48 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.15/5.48 & ( ( X != one_one_real )
% 5.15/5.48 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.15/5.48 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_gp
% 5.15/5.48 thf(fact_7194_of__nat__eq__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ( semiri1314217659103216013at_int @ M )
% 5.15/5.48 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( M = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_iff
% 5.15/5.48 thf(fact_7195_of__nat__eq__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ( semiri5074537144036343181t_real @ M )
% 5.15/5.48 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 = ( M = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_iff
% 5.15/5.48 thf(fact_7196_of__nat__eq__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.15/5.48 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 = ( M = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_iff
% 5.15/5.48 thf(fact_7197_of__nat__eq__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ( semiri8010041392384452111omplex @ M )
% 5.15/5.48 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.15/5.48 = ( M = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_iff
% 5.15/5.48 thf(fact_7198_int__eq__iff__numeral,axiom,
% 5.15/5.48 ! [M: nat,V: num] :
% 5.15/5.48 ( ( ( semiri1314217659103216013at_int @ M )
% 5.15/5.48 = ( numeral_numeral_int @ V ) )
% 5.15/5.48 = ( M
% 5.15/5.48 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_eq_iff_numeral
% 5.15/5.48 thf(fact_7199_abs__of__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.15/5.48 = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % abs_of_nat
% 5.15/5.48 thf(fact_7200_abs__of__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.15/5.48 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % abs_of_nat
% 5.15/5.48 thf(fact_7201_abs__of__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % abs_of_nat
% 5.15/5.48 thf(fact_7202_abs__of__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % abs_of_nat
% 5.15/5.48 thf(fact_7203_of__nat__eq__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ( semiri681578069525770553at_rat @ M )
% 5.15/5.48 = zero_zero_rat )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_0_iff
% 5.15/5.48 thf(fact_7204_of__nat__eq__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ( semiri1314217659103216013at_int @ M )
% 5.15/5.48 = zero_zero_int )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_0_iff
% 5.15/5.48 thf(fact_7205_of__nat__eq__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ( semiri5074537144036343181t_real @ M )
% 5.15/5.48 = zero_zero_real )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_0_iff
% 5.15/5.48 thf(fact_7206_of__nat__eq__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.15/5.48 = zero_zero_nat )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_0_iff
% 5.15/5.48 thf(fact_7207_of__nat__eq__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ( semiri8010041392384452111omplex @ M )
% 5.15/5.48 = zero_zero_complex )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_0_iff
% 5.15/5.48 thf(fact_7208_of__nat__0__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( zero_zero_rat
% 5.15/5.48 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.15/5.48 = ( zero_zero_nat = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_eq_iff
% 5.15/5.48 thf(fact_7209_of__nat__0__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( zero_zero_int
% 5.15/5.48 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( zero_zero_nat = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_eq_iff
% 5.15/5.48 thf(fact_7210_of__nat__0__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( zero_zero_real
% 5.15/5.48 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 = ( zero_zero_nat = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_eq_iff
% 5.15/5.48 thf(fact_7211_of__nat__0__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( zero_zero_nat
% 5.15/5.48 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 = ( zero_zero_nat = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_eq_iff
% 5.15/5.48 thf(fact_7212_of__nat__0__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( zero_zero_complex
% 5.15/5.48 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.15/5.48 = ( zero_zero_nat = N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_eq_iff
% 5.15/5.48 thf(fact_7213_of__nat__0,axiom,
% 5.15/5.48 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.15/5.48 = zero_zero_rat ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0
% 5.15/5.48 thf(fact_7214_of__nat__0,axiom,
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.15/5.48 = zero_zero_int ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0
% 5.15/5.48 thf(fact_7215_of__nat__0,axiom,
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.15/5.48 = zero_zero_real ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0
% 5.15/5.48 thf(fact_7216_of__nat__0,axiom,
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.15/5.48 = zero_zero_nat ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0
% 5.15/5.48 thf(fact_7217_of__nat__0,axiom,
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.15/5.48 = zero_zero_complex ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0
% 5.15/5.48 thf(fact_7218_of__nat__less__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_iff
% 5.15/5.48 thf(fact_7219_of__nat__less__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_iff
% 5.15/5.48 thf(fact_7220_of__nat__less__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_iff
% 5.15/5.48 thf(fact_7221_of__nat__less__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_iff
% 5.15/5.48 thf(fact_7222_of__nat__numeral,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.48 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_numeral
% 5.15/5.48 thf(fact_7223_of__nat__numeral,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.48 = ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_numeral
% 5.15/5.48 thf(fact_7224_of__nat__numeral,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.48 = ( numeral_numeral_real @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_numeral
% 5.15/5.48 thf(fact_7225_of__nat__numeral,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.48 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_numeral
% 5.15/5.48 thf(fact_7226_of__nat__numeral,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.48 = ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_numeral
% 5.15/5.48 thf(fact_7227_of__nat__le__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_iff
% 5.15/5.48 thf(fact_7228_of__nat__le__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_iff
% 5.15/5.48 thf(fact_7229_of__nat__le__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_iff
% 5.15/5.48 thf(fact_7230_of__nat__le__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_iff
% 5.15/5.48 thf(fact_7231_of__nat__add,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.48 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_add
% 5.15/5.48 thf(fact_7232_of__nat__add,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_add
% 5.15/5.48 thf(fact_7233_of__nat__add,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.48 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_add
% 5.15/5.48 thf(fact_7234_of__nat__add,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.48 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_add
% 5.15/5.48 thf(fact_7235_of__nat__add,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.48 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_add
% 5.15/5.48 thf(fact_7236_of__nat__eq__1__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ( semiri681578069525770553at_rat @ N2 )
% 5.15/5.48 = one_one_rat )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_1_iff
% 5.15/5.48 thf(fact_7237_of__nat__eq__1__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ( semiri1314217659103216013at_int @ N2 )
% 5.15/5.48 = one_one_int )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_1_iff
% 5.15/5.48 thf(fact_7238_of__nat__eq__1__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ( semiri5074537144036343181t_real @ N2 )
% 5.15/5.48 = one_one_real )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_1_iff
% 5.15/5.48 thf(fact_7239_of__nat__eq__1__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 5.15/5.48 = one_one_nat )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_1_iff
% 5.15/5.48 thf(fact_7240_of__nat__eq__1__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ( semiri8010041392384452111omplex @ N2 )
% 5.15/5.48 = one_one_complex )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_1_iff
% 5.15/5.48 thf(fact_7241_of__nat__1__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( one_one_rat
% 5.15/5.48 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1_eq_iff
% 5.15/5.48 thf(fact_7242_of__nat__1__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( one_one_int
% 5.15/5.48 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1_eq_iff
% 5.15/5.48 thf(fact_7243_of__nat__1__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( one_one_real
% 5.15/5.48 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1_eq_iff
% 5.15/5.48 thf(fact_7244_of__nat__1__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( one_one_nat
% 5.15/5.48 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1_eq_iff
% 5.15/5.48 thf(fact_7245_of__nat__1__eq__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( one_one_complex
% 5.15/5.48 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.15/5.48 = ( N2 = one_one_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1_eq_iff
% 5.15/5.48 thf(fact_7246_of__nat__1,axiom,
% 5.15/5.48 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.15/5.48 = one_one_rat ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1
% 5.15/5.48 thf(fact_7247_of__nat__1,axiom,
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.15/5.48 = one_one_int ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1
% 5.15/5.48 thf(fact_7248_of__nat__1,axiom,
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.15/5.48 = one_one_real ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1
% 5.15/5.48 thf(fact_7249_of__nat__1,axiom,
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.15/5.48 = one_one_nat ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1
% 5.15/5.48 thf(fact_7250_of__nat__1,axiom,
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.15/5.48 = one_one_complex ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_1
% 5.15/5.48 thf(fact_7251_of__nat__mult,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.48 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mult
% 5.15/5.48 thf(fact_7252_of__nat__mult,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.48 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mult
% 5.15/5.48 thf(fact_7253_of__nat__mult,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mult
% 5.15/5.48 thf(fact_7254_of__nat__mult,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.48 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mult
% 5.15/5.48 thf(fact_7255_of__nat__mult,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N2 ) )
% 5.15/5.48 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mult
% 5.15/5.48 thf(fact_7256_of__nat__power,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N2 ) )
% 5.15/5.48 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power
% 5.15/5.48 thf(fact_7257_of__nat__power,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N2 ) )
% 5.15/5.48 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power
% 5.15/5.48 thf(fact_7258_of__nat__power,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
% 5.15/5.48 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power
% 5.15/5.48 thf(fact_7259_of__nat__power,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N2 ) )
% 5.15/5.48 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power
% 5.15/5.48 thf(fact_7260_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.15/5.48 = ( semiri1314217659103216013at_int @ X ) )
% 5.15/5.48 = ( ( power_power_nat @ B @ W )
% 5.15/5.48 = X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7261_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.15/5.48 = ( semiri5074537144036343181t_real @ X ) )
% 5.15/5.48 = ( ( power_power_nat @ B @ W )
% 5.15/5.48 = X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7262_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.15/5.48 = ( semiri1316708129612266289at_nat @ X ) )
% 5.15/5.48 = ( ( power_power_nat @ B @ W )
% 5.15/5.48 = X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7263_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.15/5.48 = ( semiri8010041392384452111omplex @ X ) )
% 5.15/5.48 = ( ( power_power_nat @ B @ W )
% 5.15/5.48 = X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_eq_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7264_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ( semiri1314217659103216013at_int @ X )
% 5.15/5.48 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.15/5.48 = ( X
% 5.15/5.48 = ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7265_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ( semiri5074537144036343181t_real @ X )
% 5.15/5.48 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.15/5.48 = ( X
% 5.15/5.48 = ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7266_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ( semiri1316708129612266289at_nat @ X )
% 5.15/5.48 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.15/5.48 = ( X
% 5.15/5.48 = ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7267_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ( semiri8010041392384452111omplex @ X )
% 5.15/5.48 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.15/5.48 = ( X
% 5.15/5.48 = ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7268_negative__zless,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.15/5.48
% 5.15/5.48 % negative_zless
% 5.15/5.48 thf(fact_7269_of__nat__of__bool,axiom,
% 5.15/5.48 ! [P: $o] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.15/5.48 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_of_bool
% 5.15/5.48 thf(fact_7270_of__nat__of__bool,axiom,
% 5.15/5.48 ! [P: $o] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.15/5.48 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_of_bool
% 5.15/5.48 thf(fact_7271_of__nat__of__bool,axiom,
% 5.15/5.48 ! [P: $o] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.15/5.48 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_of_bool
% 5.15/5.48 thf(fact_7272_of__nat__of__bool,axiom,
% 5.15/5.48 ! [P: $o] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.15/5.48 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_of_bool
% 5.15/5.48 thf(fact_7273_of__nat__of__bool,axiom,
% 5.15/5.48 ! [P: $o] :
% 5.15/5.48 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.15/5.48 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_of_bool
% 5.15/5.48 thf(fact_7274_of__nat__sum,axiom,
% 5.15/5.48 ! [F: int > nat,A2: set_int] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.15/5.48 = ( groups4538972089207619220nt_int
% 5.15/5.48 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_sum
% 5.15/5.48 thf(fact_7275_of__nat__sum,axiom,
% 5.15/5.48 ! [F: complex > nat,A2: set_complex] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A2 ) )
% 5.15/5.48 = ( groups7754918857620584856omplex
% 5.15/5.48 @ ^ [X2: complex] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_sum
% 5.15/5.48 thf(fact_7276_of__nat__sum,axiom,
% 5.15/5.48 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.48 = ( groups3539618377306564664at_int
% 5.15/5.48 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_sum
% 5.15/5.48 thf(fact_7277_of__nat__sum,axiom,
% 5.15/5.48 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.48 = ( groups2073611262835488442omplex
% 5.15/5.48 @ ^ [X2: nat] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_sum
% 5.15/5.48 thf(fact_7278_of__nat__sum,axiom,
% 5.15/5.48 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.48 = ( groups3542108847815614940at_nat
% 5.15/5.48 @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_sum
% 5.15/5.48 thf(fact_7279_of__nat__sum,axiom,
% 5.15/5.48 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.48 = ( groups6591440286371151544t_real
% 5.15/5.48 @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_sum
% 5.15/5.48 thf(fact_7280_of__nat__le__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_0_iff
% 5.15/5.48 thf(fact_7281_of__nat__le__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_0_iff
% 5.15/5.48 thf(fact_7282_of__nat__le__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_0_iff
% 5.15/5.48 thf(fact_7283_of__nat__le__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.15/5.48 = ( M = zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_0_iff
% 5.15/5.48 thf(fact_7284_of__nat__Suc,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.15/5.48 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_Suc
% 5.15/5.48 thf(fact_7285_of__nat__Suc,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.15/5.48 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_Suc
% 5.15/5.48 thf(fact_7286_of__nat__Suc,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.15/5.48 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_Suc
% 5.15/5.48 thf(fact_7287_of__nat__Suc,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.15/5.48 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_Suc
% 5.15/5.48 thf(fact_7288_of__nat__Suc,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.15/5.48 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_Suc
% 5.15/5.48 thf(fact_7289_real__of__nat__less__numeral__iff,axiom,
% 5.15/5.48 ! [N2: nat,W: num] :
% 5.15/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W ) )
% 5.15/5.48 = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_less_numeral_iff
% 5.15/5.48 thf(fact_7290_numeral__less__real__of__nat__iff,axiom,
% 5.15/5.48 ! [W: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_less_real_of_nat_iff
% 5.15/5.48 thf(fact_7291_numeral__le__real__of__nat__iff,axiom,
% 5.15/5.48 ! [N2: num,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_le_real_of_nat_iff
% 5.15/5.48 thf(fact_7292_of__nat__0__less__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_less_iff
% 5.15/5.48 thf(fact_7293_of__nat__0__less__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_less_iff
% 5.15/5.48 thf(fact_7294_of__nat__0__less__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_less_iff
% 5.15/5.48 thf(fact_7295_of__nat__0__less__iff,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_less_iff
% 5.15/5.48 thf(fact_7296_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.15/5.48 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_less_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7297_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.15/5.48 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_less_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7298_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.15/5.48 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_less_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7299_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.15/5.48 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_less_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7300_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.15/5.48 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7301_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.15/5.48 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7302_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.15/5.48 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7303_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.15/5.48 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7304_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [Y: nat,X: num,N2: nat] :
% 5.15/5.48 ( ( ( semiri681578069525770553at_rat @ Y )
% 5.15/5.48 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.15/5.48 = ( Y
% 5.15/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_eq_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7305_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [Y: nat,X: num,N2: nat] :
% 5.15/5.48 ( ( ( semiri1314217659103216013at_int @ Y )
% 5.15/5.48 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.15/5.48 = ( Y
% 5.15/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_eq_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7306_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [Y: nat,X: num,N2: nat] :
% 5.15/5.48 ( ( ( semiri5074537144036343181t_real @ Y )
% 5.15/5.48 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.15/5.48 = ( Y
% 5.15/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_eq_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7307_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [Y: nat,X: num,N2: nat] :
% 5.15/5.48 ( ( ( semiri1316708129612266289at_nat @ Y )
% 5.15/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.15/5.48 = ( Y
% 5.15/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_eq_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7308_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [Y: nat,X: num,N2: nat] :
% 5.15/5.48 ( ( ( semiri8010041392384452111omplex @ Y )
% 5.15/5.48 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 ) )
% 5.15/5.48 = ( Y
% 5.15/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_eq_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7309_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: num,N2: nat,Y: nat] :
% 5.15/5.48 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 )
% 5.15/5.48 = ( semiri681578069525770553at_rat @ Y ) )
% 5.15/5.48 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.15/5.48 = Y ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7310_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: num,N2: nat,Y: nat] :
% 5.15/5.48 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.15/5.48 = ( semiri1314217659103216013at_int @ Y ) )
% 5.15/5.48 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.15/5.48 = Y ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7311_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: num,N2: nat,Y: nat] :
% 5.15/5.48 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 )
% 5.15/5.48 = ( semiri5074537144036343181t_real @ Y ) )
% 5.15/5.48 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.15/5.48 = Y ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7312_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: num,N2: nat,Y: nat] :
% 5.15/5.48 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.15/5.48 = ( semiri1316708129612266289at_nat @ Y ) )
% 5.15/5.48 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.15/5.48 = Y ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7313_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: num,N2: nat,Y: nat] :
% 5.15/5.48 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 )
% 5.15/5.48 = ( semiri8010041392384452111omplex @ Y ) )
% 5.15/5.48 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.15/5.48 = Y ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_eq_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7314_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7315_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7316_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7317_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.15/5.48 ! [B: nat,W: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_of_nat_power_cancel_iff
% 5.15/5.48 thf(fact_7318_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.15/5.48 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_le_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7319_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.15/5.48 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_le_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7320_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.15/5.48 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_le_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7321_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,B: nat,W: nat] :
% 5.15/5.48 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.15/5.48 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_power_le_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7322_of__nat__zero__less__power__iff,axiom,
% 5.15/5.48 ! [X: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N2 ) )
% 5.15/5.48 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.15/5.48 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_zero_less_power_iff
% 5.15/5.48 thf(fact_7323_of__nat__zero__less__power__iff,axiom,
% 5.15/5.48 ! [X: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N2 ) )
% 5.15/5.48 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.15/5.48 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_zero_less_power_iff
% 5.15/5.48 thf(fact_7324_of__nat__zero__less__power__iff,axiom,
% 5.15/5.48 ! [X: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N2 ) )
% 5.15/5.48 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.15/5.48 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_zero_less_power_iff
% 5.15/5.48 thf(fact_7325_of__nat__zero__less__power__iff,axiom,
% 5.15/5.48 ! [X: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N2 ) )
% 5.15/5.48 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.15/5.48 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_zero_less_power_iff
% 5.15/5.48 thf(fact_7326_even__of__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.15/5.48 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % even_of_nat
% 5.15/5.48 thf(fact_7327_even__of__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % even_of_nat
% 5.15/5.48 thf(fact_7328_even__of__nat,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % even_of_nat
% 5.15/5.48 thf(fact_7329_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,I: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7330_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,I: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7331_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,I: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7332_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,I: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) )
% 5.15/5.48 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7333_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [I: num,N2: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.15/5.48 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_less_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7334_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [I: num,N2: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.15/5.48 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_less_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7335_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [I: num,N2: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.15/5.48 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_less_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7336_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [I: num,N2: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.15/5.48 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_less_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7337_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [I: num,N2: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_le_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7338_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [I: num,N2: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_le_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7339_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [I: num,N2: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_le_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7340_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.15/5.48 ! [I: num,N2: nat,X: nat] :
% 5.15/5.48 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.15/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % numeral_power_le_of_nat_cancel_iff
% 5.15/5.48 thf(fact_7341_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,I: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7342_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,I: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7343_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,I: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7344_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.15/5.48 ! [X: nat,I: num,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_le_numeral_power_cancel_iff
% 5.15/5.48 thf(fact_7345_set__encode__insert,axiom,
% 5.15/5.48 ! [A2: set_nat,N2: nat] :
% 5.15/5.48 ( ( finite_finite_nat @ A2 )
% 5.15/5.48 => ( ~ ( member_nat @ N2 @ A2 )
% 5.15/5.48 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 5.15/5.48 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_encode_insert
% 5.15/5.48 thf(fact_7346_real__arch__simple,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ? [N: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_arch_simple
% 5.15/5.48 thf(fact_7347_real__arch__simple,axiom,
% 5.15/5.48 ! [X: rat] :
% 5.15/5.48 ? [N: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_arch_simple
% 5.15/5.48 thf(fact_7348_reals__Archimedean2,axiom,
% 5.15/5.48 ! [X: rat] :
% 5.15/5.48 ? [N: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.15/5.48
% 5.15/5.48 % reals_Archimedean2
% 5.15/5.48 thf(fact_7349_reals__Archimedean2,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ? [N: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.15/5.48
% 5.15/5.48 % reals_Archimedean2
% 5.15/5.48 thf(fact_7350_mult__of__nat__commute,axiom,
% 5.15/5.48 ! [X: nat,Y: rat] :
% 5.15/5.48 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 5.15/5.48 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mult_of_nat_commute
% 5.15/5.48 thf(fact_7351_mult__of__nat__commute,axiom,
% 5.15/5.48 ! [X: nat,Y: int] :
% 5.15/5.48 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 5.15/5.48 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mult_of_nat_commute
% 5.15/5.48 thf(fact_7352_mult__of__nat__commute,axiom,
% 5.15/5.48 ! [X: nat,Y: real] :
% 5.15/5.48 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 5.15/5.48 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mult_of_nat_commute
% 5.15/5.48 thf(fact_7353_mult__of__nat__commute,axiom,
% 5.15/5.48 ! [X: nat,Y: nat] :
% 5.15/5.48 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 5.15/5.48 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mult_of_nat_commute
% 5.15/5.48 thf(fact_7354_mult__of__nat__commute,axiom,
% 5.15/5.48 ! [X: nat,Y: complex] :
% 5.15/5.48 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y )
% 5.15/5.48 = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mult_of_nat_commute
% 5.15/5.48 thf(fact_7355_of__nat__and__eq,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.15/5.48 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_and_eq
% 5.15/5.48 thf(fact_7356_of__nat__and__eq,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.15/5.48 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_and_eq
% 5.15/5.48 thf(fact_7357_of__nat__or__eq,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( bit_se1412395901928357646or_nat @ M @ N2 ) )
% 5.15/5.48 = ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_or_eq
% 5.15/5.48 thf(fact_7358_of__nat__or__eq,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( bit_se1412395901928357646or_nat @ M @ N2 ) )
% 5.15/5.48 = ( bit_se1412395901928357646or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_or_eq
% 5.15/5.48 thf(fact_7359_of__nat__less__of__int__iff,axiom,
% 5.15/5.48 ! [N2: nat,X: int] :
% 5.15/5.48 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X ) )
% 5.15/5.48 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_of_int_iff
% 5.15/5.48 thf(fact_7360_of__nat__less__of__int__iff,axiom,
% 5.15/5.48 ! [N2: nat,X: int] :
% 5.15/5.48 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X ) )
% 5.15/5.48 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_of_int_iff
% 5.15/5.48 thf(fact_7361_of__nat__less__of__int__iff,axiom,
% 5.15/5.48 ! [N2: nat,X: int] :
% 5.15/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X ) )
% 5.15/5.48 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_of_int_iff
% 5.15/5.48 thf(fact_7362_of__nat__0__le__iff,axiom,
% 5.15/5.48 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_le_iff
% 5.15/5.48 thf(fact_7363_of__nat__0__le__iff,axiom,
% 5.15/5.48 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_le_iff
% 5.15/5.48 thf(fact_7364_of__nat__0__le__iff,axiom,
% 5.15/5.48 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_le_iff
% 5.15/5.48 thf(fact_7365_of__nat__0__le__iff,axiom,
% 5.15/5.48 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_0_le_iff
% 5.15/5.48 thf(fact_7366_of__nat__less__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_0_iff
% 5.15/5.48 thf(fact_7367_of__nat__less__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_0_iff
% 5.15/5.48 thf(fact_7368_of__nat__less__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_0_iff
% 5.15/5.48 thf(fact_7369_of__nat__less__0__iff,axiom,
% 5.15/5.48 ! [M: nat] :
% 5.15/5.48 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_0_iff
% 5.15/5.48 thf(fact_7370_of__nat__neq__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 5.15/5.48 != zero_zero_rat ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_neq_0
% 5.15/5.48 thf(fact_7371_of__nat__neq__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.15/5.48 != zero_zero_int ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_neq_0
% 5.15/5.48 thf(fact_7372_of__nat__neq__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 5.15/5.48 != zero_zero_real ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_neq_0
% 5.15/5.48 thf(fact_7373_of__nat__neq__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 5.15/5.48 != zero_zero_nat ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_neq_0
% 5.15/5.48 thf(fact_7374_of__nat__neq__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 5.15/5.48 != zero_zero_complex ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_neq_0
% 5.15/5.48 thf(fact_7375_div__mult2__eq_H,axiom,
% 5.15/5.48 ! [A: int,M: nat,N2: nat] :
% 5.15/5.48 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.15/5.48 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % div_mult2_eq'
% 5.15/5.48 thf(fact_7376_div__mult2__eq_H,axiom,
% 5.15/5.48 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.48 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.15/5.48 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % div_mult2_eq'
% 5.15/5.48 thf(fact_7377_of__nat__less__imp__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.15/5.48 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_imp_less
% 5.15/5.48 thf(fact_7378_of__nat__less__imp__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_imp_less
% 5.15/5.48 thf(fact_7379_of__nat__less__imp__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_imp_less
% 5.15/5.48 thf(fact_7380_of__nat__less__imp__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_imp_less
% 5.15/5.48 thf(fact_7381_less__imp__of__nat__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.48 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % less_imp_of_nat_less
% 5.15/5.48 thf(fact_7382_less__imp__of__nat__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.48 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % less_imp_of_nat_less
% 5.15/5.48 thf(fact_7383_less__imp__of__nat__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.48 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % less_imp_of_nat_less
% 5.15/5.48 thf(fact_7384_less__imp__of__nat__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ M @ N2 )
% 5.15/5.48 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % less_imp_of_nat_less
% 5.15/5.48 thf(fact_7385_of__nat__mono,axiom,
% 5.15/5.48 ! [I: nat,J: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.48 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mono
% 5.15/5.48 thf(fact_7386_of__nat__mono,axiom,
% 5.15/5.48 ! [I: nat,J: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.48 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mono
% 5.15/5.48 thf(fact_7387_of__nat__mono,axiom,
% 5.15/5.48 ! [I: nat,J: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.48 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mono
% 5.15/5.48 thf(fact_7388_of__nat__mono,axiom,
% 5.15/5.48 ! [I: nat,J: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.48 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mono
% 5.15/5.48 thf(fact_7389_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) )
% 5.15/5.48 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.15/5.48 thf(fact_7390_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.15/5.48 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.15/5.48 thf(fact_7391_of__nat__dvd__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.15/5.48 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_dvd_iff
% 5.15/5.48 thf(fact_7392_of__nat__dvd__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_dvd_iff
% 5.15/5.48 thf(fact_7393_of__nat__dvd__iff,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.15/5.48 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_dvd_iff
% 5.15/5.48 thf(fact_7394_int__ops_I3_J,axiom,
% 5.15/5.48 ! [N2: num] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.48 = ( numeral_numeral_int @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_ops(3)
% 5.15/5.48 thf(fact_7395_int__cases,axiom,
% 5.15/5.48 ! [Z: int] :
% 5.15/5.48 ( ! [N: nat] :
% 5.15/5.48 ( Z
% 5.15/5.48 != ( semiri1314217659103216013at_int @ N ) )
% 5.15/5.48 => ~ ! [N: nat] :
% 5.15/5.48 ( Z
% 5.15/5.48 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_cases
% 5.15/5.48 thf(fact_7396_int__of__nat__induct,axiom,
% 5.15/5.48 ! [P: int > $o,Z: int] :
% 5.15/5.48 ( ! [N: nat] : ( P @ ( semiri1314217659103216013at_int @ N ) )
% 5.15/5.48 => ( ! [N: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) )
% 5.15/5.48 => ( P @ Z ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_of_nat_induct
% 5.15/5.48 thf(fact_7397_nat__int__comparison_I2_J,axiom,
% 5.15/5.48 ( ord_less_nat
% 5.15/5.48 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % nat_int_comparison(2)
% 5.15/5.48 thf(fact_7398_zle__int,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.48 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % zle_int
% 5.15/5.48 thf(fact_7399_nat__int__comparison_I3_J,axiom,
% 5.15/5.48 ( ord_less_eq_nat
% 5.15/5.48 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % nat_int_comparison(3)
% 5.15/5.48 thf(fact_7400_of__nat__mod,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.15/5.48 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mod
% 5.15/5.48 thf(fact_7401_of__nat__mod,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.15/5.48 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mod
% 5.15/5.48 thf(fact_7402_of__nat__mod,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.15/5.48 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mod
% 5.15/5.48 thf(fact_7403_int__ops_I2_J,axiom,
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.15/5.48 = one_one_int ) ).
% 5.15/5.48
% 5.15/5.48 % int_ops(2)
% 5.15/5.48 thf(fact_7404_zadd__int__left,axiom,
% 5.15/5.48 ! [M: nat,N2: nat,Z: int] :
% 5.15/5.48 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 5.15/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z ) ) ).
% 5.15/5.48
% 5.15/5.48 % zadd_int_left
% 5.15/5.48 thf(fact_7405_int__ops_I5_J,axiom,
% 5.15/5.48 ! [A: nat,B: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.15/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_ops(5)
% 5.15/5.48 thf(fact_7406_int__plus,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_plus
% 5.15/5.48 thf(fact_7407_int__ops_I7_J,axiom,
% 5.15/5.48 ! [A: nat,B: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.15/5.48 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_ops(7)
% 5.15/5.48 thf(fact_7408_zdiv__int,axiom,
% 5.15/5.48 ! [A: nat,B: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.15/5.48 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % zdiv_int
% 5.15/5.48 thf(fact_7409_of__nat__max,axiom,
% 5.15/5.48 ! [X: nat,Y: nat] :
% 5.15/5.48 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y ) )
% 5.15/5.48 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_max
% 5.15/5.48 thf(fact_7410_of__nat__max,axiom,
% 5.15/5.48 ! [X: nat,Y: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 5.15/5.48 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_max
% 5.15/5.48 thf(fact_7411_of__nat__max,axiom,
% 5.15/5.48 ! [X: nat,Y: nat] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 5.15/5.48 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_max
% 5.15/5.48 thf(fact_7412_of__nat__max,axiom,
% 5.15/5.48 ! [X: nat,Y: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 5.15/5.48 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_max
% 5.15/5.48 thf(fact_7413_zmod__int,axiom,
% 5.15/5.48 ! [A: nat,B: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.15/5.48 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % zmod_int
% 5.15/5.48 thf(fact_7414_take__bit__of__nat,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( bit_se2923211474154528505it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 5.15/5.48 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_of_nat
% 5.15/5.48 thf(fact_7415_take__bit__of__nat,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( bit_se2925701944663578781it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 5.15/5.48 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % take_bit_of_nat
% 5.15/5.48 thf(fact_7416_nat__less__as__int,axiom,
% 5.15/5.48 ( ord_less_nat
% 5.15/5.48 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % nat_less_as_int
% 5.15/5.48 thf(fact_7417_of__nat__mask__eq,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.15/5.48 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mask_eq
% 5.15/5.48 thf(fact_7418_of__nat__mask__eq,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.15/5.48 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_mask_eq
% 5.15/5.48 thf(fact_7419_nat__leq__as__int,axiom,
% 5.15/5.48 ( ord_less_eq_nat
% 5.15/5.48 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % nat_leq_as_int
% 5.15/5.48 thf(fact_7420_ex__less__of__nat__mult,axiom,
% 5.15/5.48 ! [X: rat,Y: rat] :
% 5.15/5.48 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.15/5.48 => ? [N: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % ex_less_of_nat_mult
% 5.15/5.48 thf(fact_7421_ex__less__of__nat__mult,axiom,
% 5.15/5.48 ! [X: real,Y: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ? [N: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % ex_less_of_nat_mult
% 5.15/5.48 thf(fact_7422_of__nat__diff,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.48 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.48 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_diff
% 5.15/5.48 thf(fact_7423_of__nat__diff,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.48 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.48 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_diff
% 5.15/5.48 thf(fact_7424_of__nat__diff,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.48 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.48 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_diff
% 5.15/5.48 thf(fact_7425_of__nat__diff,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.48 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.48 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_diff
% 5.15/5.48 thf(fact_7426_of__nat__diff,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.48 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N2 ) )
% 5.15/5.48 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_diff
% 5.15/5.48 thf(fact_7427_exp__of__nat2__mult,axiom,
% 5.15/5.48 ! [X: real,N2: nat] :
% 5.15/5.48 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.15/5.48 = ( power_power_real @ ( exp_real @ X ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_of_nat2_mult
% 5.15/5.48 thf(fact_7428_exp__of__nat2__mult,axiom,
% 5.15/5.48 ! [X: complex,N2: nat] :
% 5.15/5.48 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.15/5.48 = ( power_power_complex @ ( exp_complex @ X ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_of_nat2_mult
% 5.15/5.48 thf(fact_7429_exp__of__nat__mult,axiom,
% 5.15/5.48 ! [N2: nat,X: real] :
% 5.15/5.48 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) )
% 5.15/5.48 = ( power_power_real @ ( exp_real @ X ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_of_nat_mult
% 5.15/5.48 thf(fact_7430_exp__of__nat__mult,axiom,
% 5.15/5.48 ! [N2: nat,X: complex] :
% 5.15/5.48 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ X ) )
% 5.15/5.48 = ( power_power_complex @ ( exp_complex @ X ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_of_nat_mult
% 5.15/5.48 thf(fact_7431_reals__Archimedean3,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ! [Y4: real] :
% 5.15/5.48 ? [N: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % reals_Archimedean3
% 5.15/5.48 thf(fact_7432_int__cases4,axiom,
% 5.15/5.48 ! [M: int] :
% 5.15/5.48 ( ! [N: nat] :
% 5.15/5.48 ( M
% 5.15/5.48 != ( semiri1314217659103216013at_int @ N ) )
% 5.15/5.48 => ~ ! [N: nat] :
% 5.15/5.48 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.15/5.48 => ( M
% 5.15/5.48 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_cases4
% 5.15/5.48 thf(fact_7433_real__of__nat__div4,axiom,
% 5.15/5.48 ! [N2: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_div4
% 5.15/5.48 thf(fact_7434_atLeast0__atMost__Suc,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.15/5.48 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % atLeast0_atMost_Suc
% 5.15/5.48 thf(fact_7435_int__ops_I4_J,axiom,
% 5.15/5.48 ! [A: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.15/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_ops(4)
% 5.15/5.48 thf(fact_7436_int__Suc,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.15/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_Suc
% 5.15/5.48 thf(fact_7437_zless__iff__Suc__zadd,axiom,
% 5.15/5.48 ( ord_less_int
% 5.15/5.48 = ( ^ [W2: int,Z3: int] :
% 5.15/5.48 ? [N3: nat] :
% 5.15/5.48 ( Z3
% 5.15/5.48 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % zless_iff_Suc_zadd
% 5.15/5.48 thf(fact_7438_Icc__eq__insert__lb__nat,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.48 => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 5.15/5.48 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Icc_eq_insert_lb_nat
% 5.15/5.48 thf(fact_7439_atLeastAtMostSuc__conv,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.15/5.48 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 5.15/5.48 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % atLeastAtMostSuc_conv
% 5.15/5.48 thf(fact_7440_atLeastAtMost__insertL,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.48 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.15/5.48 = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % atLeastAtMost_insertL
% 5.15/5.48 thf(fact_7441_real__of__nat__div,axiom,
% 5.15/5.48 ! [D: nat,N2: nat] :
% 5.15/5.48 ( ( dvd_dvd_nat @ D @ N2 )
% 5.15/5.48 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ D ) )
% 5.15/5.48 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_div
% 5.15/5.48 thf(fact_7442_int__sum,axiom,
% 5.15/5.48 ! [F: int > nat,A2: set_int] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.15/5.48 = ( groups4538972089207619220nt_int
% 5.15/5.48 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_sum
% 5.15/5.48 thf(fact_7443_int__sum,axiom,
% 5.15/5.48 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.48 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.48 = ( groups3539618377306564664at_int
% 5.15/5.48 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_sum
% 5.15/5.48 thf(fact_7444_mod__mult2__eq_H,axiom,
% 5.15/5.48 ! [A: code_integer,M: nat,N2: nat] :
% 5.15/5.48 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.15/5.48 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mod_mult2_eq'
% 5.15/5.48 thf(fact_7445_mod__mult2__eq_H,axiom,
% 5.15/5.48 ! [A: int,M: nat,N2: nat] :
% 5.15/5.48 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mod_mult2_eq'
% 5.15/5.48 thf(fact_7446_mod__mult2__eq_H,axiom,
% 5.15/5.48 ! [A: nat,M: nat,N2: nat] :
% 5.15/5.48 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % mod_mult2_eq'
% 5.15/5.48 thf(fact_7447_field__char__0__class_Oof__nat__div,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N2 ) )
% 5.15/5.48 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % field_char_0_class.of_nat_div
% 5.15/5.48 thf(fact_7448_field__char__0__class_Oof__nat__div,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N2 ) )
% 5.15/5.48 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % field_char_0_class.of_nat_div
% 5.15/5.48 thf(fact_7449_field__char__0__class_Oof__nat__div,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N2 ) )
% 5.15/5.48 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % field_char_0_class.of_nat_div
% 5.15/5.48 thf(fact_7450_pos__int__cases,axiom,
% 5.15/5.48 ! [K: int] :
% 5.15/5.48 ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.48 => ~ ! [N: nat] :
% 5.15/5.48 ( ( K
% 5.15/5.48 = ( semiri1314217659103216013at_int @ N ) )
% 5.15/5.48 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % pos_int_cases
% 5.15/5.48 thf(fact_7451_zero__less__imp__eq__int,axiom,
% 5.15/5.48 ! [K: int] :
% 5.15/5.48 ( ( ord_less_int @ zero_zero_int @ K )
% 5.15/5.48 => ? [N: nat] :
% 5.15/5.48 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.15/5.48 & ( K
% 5.15/5.48 = ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % zero_less_imp_eq_int
% 5.15/5.48 thf(fact_7452_int__cases3,axiom,
% 5.15/5.48 ! [K: int] :
% 5.15/5.48 ( ( K != zero_zero_int )
% 5.15/5.48 => ( ! [N: nat] :
% 5.15/5.48 ( ( K
% 5.15/5.48 = ( semiri1314217659103216013at_int @ N ) )
% 5.15/5.48 => ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.15/5.48 => ~ ! [N: nat] :
% 5.15/5.48 ( ( K
% 5.15/5.48 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.15/5.48 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_cases3
% 5.15/5.48 thf(fact_7453_nat__less__real__le,axiom,
% 5.15/5.48 ( ord_less_nat
% 5.15/5.48 = ( ^ [N3: nat,M5: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M5 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % nat_less_real_le
% 5.15/5.48 thf(fact_7454_nat__le__real__less,axiom,
% 5.15/5.48 ( ord_less_eq_nat
% 5.15/5.48 = ( ^ [N3: nat,M5: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M5 ) @ one_one_real ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % nat_le_real_less
% 5.15/5.48 thf(fact_7455_zmult__zless__mono2__lemma,axiom,
% 5.15/5.48 ! [I: int,J: int,K: nat] :
% 5.15/5.48 ( ( ord_less_int @ I @ J )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.48 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % zmult_zless_mono2_lemma
% 5.15/5.48 thf(fact_7456_not__zle__0__negative,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % not_zle_0_negative
% 5.15/5.48 thf(fact_7457_negD,axiom,
% 5.15/5.48 ! [X: int] :
% 5.15/5.48 ( ( ord_less_int @ X @ zero_zero_int )
% 5.15/5.48 => ? [N: nat] :
% 5.15/5.48 ( X
% 5.15/5.48 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % negD
% 5.15/5.48 thf(fact_7458_negative__zless__0,axiom,
% 5.15/5.48 ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 5.15/5.48
% 5.15/5.48 % negative_zless_0
% 5.15/5.48 thf(fact_7459_int__ops_I6_J,axiom,
% 5.15/5.48 ! [A: nat,B: nat] :
% 5.15/5.48 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.15/5.48 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.15/5.48 = zero_zero_int ) )
% 5.15/5.48 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.15/5.48 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.15/5.48 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % int_ops(6)
% 5.15/5.48 thf(fact_7460_real__of__nat__div__aux,axiom,
% 5.15/5.48 ! [X: nat,D: nat] :
% 5.15/5.48 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.15/5.48 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_div_aux
% 5.15/5.48 thf(fact_7461_empty__def,axiom,
% 5.15/5.48 ( bot_bo1796632182523588997nt_int
% 5.15/5.48 = ( collec213857154873943460nt_int
% 5.15/5.48 @ ^ [X2: product_prod_int_int] : $false ) ) ).
% 5.15/5.48
% 5.15/5.48 % empty_def
% 5.15/5.48 thf(fact_7462_empty__def,axiom,
% 5.15/5.48 ( bot_bot_set_complex
% 5.15/5.48 = ( collect_complex
% 5.15/5.48 @ ^ [X2: complex] : $false ) ) ).
% 5.15/5.48
% 5.15/5.48 % empty_def
% 5.15/5.48 thf(fact_7463_empty__def,axiom,
% 5.15/5.48 ( bot_bot_set_set_nat
% 5.15/5.48 = ( collect_set_nat
% 5.15/5.48 @ ^ [X2: set_nat] : $false ) ) ).
% 5.15/5.48
% 5.15/5.48 % empty_def
% 5.15/5.48 thf(fact_7464_empty__def,axiom,
% 5.15/5.48 ( bot_bot_set_nat
% 5.15/5.48 = ( collect_nat
% 5.15/5.48 @ ^ [X2: nat] : $false ) ) ).
% 5.15/5.48
% 5.15/5.48 % empty_def
% 5.15/5.48 thf(fact_7465_empty__def,axiom,
% 5.15/5.48 ( bot_bot_set_int
% 5.15/5.48 = ( collect_int
% 5.15/5.48 @ ^ [X2: int] : $false ) ) ).
% 5.15/5.48
% 5.15/5.48 % empty_def
% 5.15/5.48 thf(fact_7466_empty__def,axiom,
% 5.15/5.48 ( bot_bot_set_real
% 5.15/5.48 = ( collect_real
% 5.15/5.48 @ ^ [X2: real] : $false ) ) ).
% 5.15/5.48
% 5.15/5.48 % empty_def
% 5.15/5.48 thf(fact_7467_insert__Collect,axiom,
% 5.15/5.48 ! [A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.15/5.48 ( ( insert_VEBT_VEBT @ A @ ( collect_VEBT_VEBT @ P ) )
% 5.15/5.48 = ( collect_VEBT_VEBT
% 5.15/5.48 @ ^ [U2: vEBT_VEBT] :
% 5.15/5.48 ( ( U2 != A )
% 5.15/5.48 => ( P @ U2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_Collect
% 5.15/5.48 thf(fact_7468_insert__Collect,axiom,
% 5.15/5.48 ! [A: real,P: real > $o] :
% 5.15/5.48 ( ( insert_real @ A @ ( collect_real @ P ) )
% 5.15/5.48 = ( collect_real
% 5.15/5.48 @ ^ [U2: real] :
% 5.15/5.48 ( ( U2 != A )
% 5.15/5.48 => ( P @ U2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_Collect
% 5.15/5.48 thf(fact_7469_insert__Collect,axiom,
% 5.15/5.48 ! [A: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.15/5.48 ( ( insert5033312907999012233nt_int @ A @ ( collec213857154873943460nt_int @ P ) )
% 5.15/5.48 = ( collec213857154873943460nt_int
% 5.15/5.48 @ ^ [U2: product_prod_int_int] :
% 5.15/5.48 ( ( U2 != A )
% 5.15/5.48 => ( P @ U2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_Collect
% 5.15/5.48 thf(fact_7470_insert__Collect,axiom,
% 5.15/5.48 ! [A: complex,P: complex > $o] :
% 5.15/5.48 ( ( insert_complex @ A @ ( collect_complex @ P ) )
% 5.15/5.48 = ( collect_complex
% 5.15/5.48 @ ^ [U2: complex] :
% 5.15/5.48 ( ( U2 != A )
% 5.15/5.48 => ( P @ U2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_Collect
% 5.15/5.48 thf(fact_7471_insert__Collect,axiom,
% 5.15/5.48 ! [A: set_nat,P: set_nat > $o] :
% 5.15/5.48 ( ( insert_set_nat @ A @ ( collect_set_nat @ P ) )
% 5.15/5.48 = ( collect_set_nat
% 5.15/5.48 @ ^ [U2: set_nat] :
% 5.15/5.48 ( ( U2 != A )
% 5.15/5.48 => ( P @ U2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_Collect
% 5.15/5.48 thf(fact_7472_insert__Collect,axiom,
% 5.15/5.48 ! [A: nat,P: nat > $o] :
% 5.15/5.48 ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 5.15/5.48 = ( collect_nat
% 5.15/5.48 @ ^ [U2: nat] :
% 5.15/5.48 ( ( U2 != A )
% 5.15/5.48 => ( P @ U2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_Collect
% 5.15/5.48 thf(fact_7473_insert__Collect,axiom,
% 5.15/5.48 ! [A: int,P: int > $o] :
% 5.15/5.48 ( ( insert_int @ A @ ( collect_int @ P ) )
% 5.15/5.48 = ( collect_int
% 5.15/5.48 @ ^ [U2: int] :
% 5.15/5.48 ( ( U2 != A )
% 5.15/5.48 => ( P @ U2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_Collect
% 5.15/5.48 thf(fact_7474_insert__compr,axiom,
% 5.15/5.48 ( insert_VEBT_VEBT
% 5.15/5.48 = ( ^ [A3: vEBT_VEBT,B5: set_VEBT_VEBT] :
% 5.15/5.48 ( collect_VEBT_VEBT
% 5.15/5.48 @ ^ [X2: vEBT_VEBT] :
% 5.15/5.48 ( ( X2 = A3 )
% 5.15/5.48 | ( member_VEBT_VEBT @ X2 @ B5 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_compr
% 5.15/5.48 thf(fact_7475_insert__compr,axiom,
% 5.15/5.48 ( insert_real
% 5.15/5.48 = ( ^ [A3: real,B5: set_real] :
% 5.15/5.48 ( collect_real
% 5.15/5.48 @ ^ [X2: real] :
% 5.15/5.48 ( ( X2 = A3 )
% 5.15/5.48 | ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_compr
% 5.15/5.48 thf(fact_7476_insert__compr,axiom,
% 5.15/5.48 ( insert5033312907999012233nt_int
% 5.15/5.48 = ( ^ [A3: product_prod_int_int,B5: set_Pr958786334691620121nt_int] :
% 5.15/5.48 ( collec213857154873943460nt_int
% 5.15/5.48 @ ^ [X2: product_prod_int_int] :
% 5.15/5.48 ( ( X2 = A3 )
% 5.15/5.48 | ( member5262025264175285858nt_int @ X2 @ B5 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_compr
% 5.15/5.48 thf(fact_7477_insert__compr,axiom,
% 5.15/5.48 ( insert_complex
% 5.15/5.48 = ( ^ [A3: complex,B5: set_complex] :
% 5.15/5.48 ( collect_complex
% 5.15/5.48 @ ^ [X2: complex] :
% 5.15/5.48 ( ( X2 = A3 )
% 5.15/5.48 | ( member_complex @ X2 @ B5 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_compr
% 5.15/5.48 thf(fact_7478_insert__compr,axiom,
% 5.15/5.48 ( insert_set_nat
% 5.15/5.48 = ( ^ [A3: set_nat,B5: set_set_nat] :
% 5.15/5.48 ( collect_set_nat
% 5.15/5.48 @ ^ [X2: set_nat] :
% 5.15/5.48 ( ( X2 = A3 )
% 5.15/5.48 | ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_compr
% 5.15/5.48 thf(fact_7479_insert__compr,axiom,
% 5.15/5.48 ( insert_nat
% 5.15/5.48 = ( ^ [A3: nat,B5: set_nat] :
% 5.15/5.48 ( collect_nat
% 5.15/5.48 @ ^ [X2: nat] :
% 5.15/5.48 ( ( X2 = A3 )
% 5.15/5.48 | ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_compr
% 5.15/5.48 thf(fact_7480_insert__compr,axiom,
% 5.15/5.48 ( insert_int
% 5.15/5.48 = ( ^ [A3: int,B5: set_int] :
% 5.15/5.48 ( collect_int
% 5.15/5.48 @ ^ [X2: int] :
% 5.15/5.48 ( ( X2 = A3 )
% 5.15/5.48 | ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % insert_compr
% 5.15/5.48 thf(fact_7481_nat__approx__posE,axiom,
% 5.15/5.48 ! [E: rat] :
% 5.15/5.48 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.15/5.48 => ~ ! [N: nat] :
% 5.15/5.48 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) ) @ E ) ) ).
% 5.15/5.48
% 5.15/5.48 % nat_approx_posE
% 5.15/5.48 thf(fact_7482_nat__approx__posE,axiom,
% 5.15/5.48 ! [E: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ E )
% 5.15/5.48 => ~ ! [N: nat] :
% 5.15/5.48 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ E ) ) ).
% 5.15/5.48
% 5.15/5.48 % nat_approx_posE
% 5.15/5.48 thf(fact_7483_of__nat__less__two__power,axiom,
% 5.15/5.48 ! [N2: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_two_power
% 5.15/5.48 thf(fact_7484_of__nat__less__two__power,axiom,
% 5.15/5.48 ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_two_power
% 5.15/5.48 thf(fact_7485_of__nat__less__two__power,axiom,
% 5.15/5.48 ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_less_two_power
% 5.15/5.48 thf(fact_7486_inverse__of__nat__le,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.48 => ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % inverse_of_nat_le
% 5.15/5.48 thf(fact_7487_inverse__of__nat__le,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.48 => ( ( N2 != zero_zero_nat )
% 5.15/5.48 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % inverse_of_nat_le
% 5.15/5.48 thf(fact_7488_exp__divide__power__eq,axiom,
% 5.15/5.48 ! [N2: nat,X: real] :
% 5.15/5.48 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.48 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.15/5.48 = ( exp_real @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_divide_power_eq
% 5.15/5.48 thf(fact_7489_exp__divide__power__eq,axiom,
% 5.15/5.48 ! [N2: nat,X: complex] :
% 5.15/5.48 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.48 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N2 ) ) ) @ N2 )
% 5.15/5.48 = ( exp_complex @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_divide_power_eq
% 5.15/5.48 thf(fact_7490_real__archimedian__rdiv__eq__0,axiom,
% 5.15/5.48 ! [X: real,C: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.15/5.48 => ( ! [M3: nat] :
% 5.15/5.48 ( ( ord_less_nat @ zero_zero_nat @ M3 )
% 5.15/5.48 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ X ) @ C ) )
% 5.15/5.48 => ( X = zero_zero_real ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_archimedian_rdiv_eq_0
% 5.15/5.48 thf(fact_7491_neg__int__cases,axiom,
% 5.15/5.48 ! [K: int] :
% 5.15/5.48 ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.48 => ~ ! [N: nat] :
% 5.15/5.48 ( ( K
% 5.15/5.48 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.15/5.48 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % neg_int_cases
% 5.15/5.48 thf(fact_7492_zdiff__int__split,axiom,
% 5.15/5.48 ! [P: int > $o,X: nat,Y: nat] :
% 5.15/5.48 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 5.15/5.48 = ( ( ( ord_less_eq_nat @ Y @ X )
% 5.15/5.48 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.15/5.48 & ( ( ord_less_nat @ X @ Y )
% 5.15/5.48 => ( P @ zero_zero_int ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % zdiff_int_split
% 5.15/5.48 thf(fact_7493_real__of__nat__div2,axiom,
% 5.15/5.48 ! [N2: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_div2
% 5.15/5.48 thf(fact_7494_real__of__nat__div3,axiom,
% 5.15/5.48 ! [N2: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) ) @ one_one_real ) ).
% 5.15/5.48
% 5.15/5.48 % real_of_nat_div3
% 5.15/5.48 thf(fact_7495_ln__realpow,axiom,
% 5.15/5.48 ! [X: real,N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ln_ln_real @ ( power_power_real @ X @ N2 ) )
% 5.15/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % ln_realpow
% 5.15/5.48 thf(fact_7496_linear__plus__1__le__power,axiom,
% 5.15/5.48 ! [X: real,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % linear_plus_1_le_power
% 5.15/5.48 thf(fact_7497_Bernoulli__inequality,axiom,
% 5.15/5.48 ! [X: real,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Bernoulli_inequality
% 5.15/5.48 thf(fact_7498_set__decode__plus__power__2,axiom,
% 5.15/5.48 ! [N2: nat,Z: nat] :
% 5.15/5.48 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 5.15/5.48 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 5.15/5.48 = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % set_decode_plus_power_2
% 5.15/5.48 thf(fact_7499_and__int_Opinduct,axiom,
% 5.15/5.48 ! [A0: int,A1: int,P: int > int > $o] :
% 5.15/5.48 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.15/5.48 => ( ! [K3: int,L4: int] :
% 5.15/5.48 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 5.15/5.48 => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.15/5.48 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.15/5.48 => ( P @ K3 @ L4 ) ) )
% 5.15/5.48 => ( P @ A0 @ A1 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % and_int.pinduct
% 5.15/5.48 thf(fact_7500_Collect__conv__if,axiom,
% 5.15/5.48 ! [P: vEBT_VEBT > $o,A: vEBT_VEBT] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_VEBT_VEBT
% 5.15/5.48 @ ^ [X2: vEBT_VEBT] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_VEBT_VEBT
% 5.15/5.48 @ ^ [X2: vEBT_VEBT] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if
% 5.15/5.48 thf(fact_7501_Collect__conv__if,axiom,
% 5.15/5.48 ! [P: product_prod_int_int > $o,A: product_prod_int_int] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collec213857154873943460nt_int
% 5.15/5.48 @ ^ [X2: product_prod_int_int] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collec213857154873943460nt_int
% 5.15/5.48 @ ^ [X2: product_prod_int_int] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bo1796632182523588997nt_int ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if
% 5.15/5.48 thf(fact_7502_Collect__conv__if,axiom,
% 5.15/5.48 ! [P: complex > $o,A: complex] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_complex
% 5.15/5.48 @ ^ [X2: complex] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_complex
% 5.15/5.48 @ ^ [X2: complex] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_complex ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if
% 5.15/5.48 thf(fact_7503_Collect__conv__if,axiom,
% 5.15/5.48 ! [P: set_nat > $o,A: set_nat] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_set_nat
% 5.15/5.48 @ ^ [X2: set_nat] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_set_nat
% 5.15/5.48 @ ^ [X2: set_nat] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_set_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if
% 5.15/5.48 thf(fact_7504_Collect__conv__if,axiom,
% 5.15/5.48 ! [P: nat > $o,A: nat] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_nat
% 5.15/5.48 @ ^ [X2: nat] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_nat
% 5.15/5.48 @ ^ [X2: nat] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if
% 5.15/5.48 thf(fact_7505_Collect__conv__if,axiom,
% 5.15/5.48 ! [P: int > $o,A: int] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_int
% 5.15/5.48 @ ^ [X2: int] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_int
% 5.15/5.48 @ ^ [X2: int] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_int ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if
% 5.15/5.48 thf(fact_7506_Collect__conv__if,axiom,
% 5.15/5.48 ! [P: real > $o,A: real] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_real
% 5.15/5.48 @ ^ [X2: real] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_real
% 5.15/5.48 @ ^ [X2: real] :
% 5.15/5.48 ( ( X2 = A )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_real ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if
% 5.15/5.48 thf(fact_7507_Collect__conv__if2,axiom,
% 5.15/5.48 ! [P: vEBT_VEBT > $o,A: vEBT_VEBT] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_VEBT_VEBT
% 5.15/5.48 @ ^ [X2: vEBT_VEBT] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_VEBT_VEBT
% 5.15/5.48 @ ^ [X2: vEBT_VEBT] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if2
% 5.15/5.48 thf(fact_7508_Collect__conv__if2,axiom,
% 5.15/5.48 ! [P: product_prod_int_int > $o,A: product_prod_int_int] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collec213857154873943460nt_int
% 5.15/5.48 @ ^ [X2: product_prod_int_int] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collec213857154873943460nt_int
% 5.15/5.48 @ ^ [X2: product_prod_int_int] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bo1796632182523588997nt_int ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if2
% 5.15/5.48 thf(fact_7509_Collect__conv__if2,axiom,
% 5.15/5.48 ! [P: complex > $o,A: complex] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_complex
% 5.15/5.48 @ ^ [X2: complex] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_complex
% 5.15/5.48 @ ^ [X2: complex] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_complex ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if2
% 5.15/5.48 thf(fact_7510_Collect__conv__if2,axiom,
% 5.15/5.48 ! [P: set_nat > $o,A: set_nat] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_set_nat
% 5.15/5.48 @ ^ [X2: set_nat] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_set_nat
% 5.15/5.48 @ ^ [X2: set_nat] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_set_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if2
% 5.15/5.48 thf(fact_7511_Collect__conv__if2,axiom,
% 5.15/5.48 ! [P: nat > $o,A: nat] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_nat
% 5.15/5.48 @ ^ [X2: nat] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_nat
% 5.15/5.48 @ ^ [X2: nat] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if2
% 5.15/5.48 thf(fact_7512_Collect__conv__if2,axiom,
% 5.15/5.48 ! [P: int > $o,A: int] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_int
% 5.15/5.48 @ ^ [X2: int] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_int
% 5.15/5.48 @ ^ [X2: int] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_int ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if2
% 5.15/5.48 thf(fact_7513_Collect__conv__if2,axiom,
% 5.15/5.48 ! [P: real > $o,A: real] :
% 5.15/5.48 ( ( ( P @ A )
% 5.15/5.48 => ( ( collect_real
% 5.15/5.48 @ ^ [X2: real] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.15/5.48 & ( ~ ( P @ A )
% 5.15/5.48 => ( ( collect_real
% 5.15/5.48 @ ^ [X2: real] :
% 5.15/5.48 ( ( A = X2 )
% 5.15/5.48 & ( P @ X2 ) ) )
% 5.15/5.48 = bot_bot_set_real ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Collect_conv_if2
% 5.15/5.48 thf(fact_7514_double__arith__series,axiom,
% 5.15/5.48 ! [A: rat,D: rat,N2: nat] :
% 5.15/5.48 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.15/5.48 @ ( groups2906978787729119204at_rat
% 5.15/5.48 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D ) )
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_arith_series
% 5.15/5.48 thf(fact_7515_double__arith__series,axiom,
% 5.15/5.48 ! [A: int,D: int,N2: nat] :
% 5.15/5.48 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.15/5.48 @ ( groups3539618377306564664at_int
% 5.15/5.48 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_arith_series
% 5.15/5.48 thf(fact_7516_double__arith__series,axiom,
% 5.15/5.48 ! [A: complex,D: complex,N2: nat] :
% 5.15/5.48 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.15/5.48 @ ( groups2073611262835488442omplex
% 5.15/5.48 @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D ) )
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_arith_series
% 5.15/5.48 thf(fact_7517_double__arith__series,axiom,
% 5.15/5.48 ! [A: nat,D: nat,N2: nat] :
% 5.15/5.48 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.15/5.48 @ ( groups3542108847815614940at_nat
% 5.15/5.48 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_arith_series
% 5.15/5.48 thf(fact_7518_double__arith__series,axiom,
% 5.15/5.48 ! [A: real,D: real,N2: nat] :
% 5.15/5.48 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.15/5.48 @ ( groups6591440286371151544t_real
% 5.15/5.48 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D ) )
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_arith_series
% 5.15/5.48 thf(fact_7519_double__gauss__sum,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum
% 5.15/5.48 thf(fact_7520_double__gauss__sum,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum
% 5.15/5.48 thf(fact_7521_double__gauss__sum,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum
% 5.15/5.48 thf(fact_7522_double__gauss__sum,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum
% 5.15/5.48 thf(fact_7523_double__gauss__sum,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum
% 5.15/5.48 thf(fact_7524_Bernoulli__inequality__even,axiom,
% 5.15/5.48 ! [N2: nat,X: real] :
% 5.15/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N2 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % Bernoulli_inequality_even
% 5.15/5.48 thf(fact_7525_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.15/5.48 ! [N2: nat,X: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.48 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_ge_one_plus_x_over_n_power_n
% 5.15/5.48 thf(fact_7526_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.15/5.48 ! [X: real,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.48 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_ge_one_minus_x_over_n_power_n
% 5.15/5.48 thf(fact_7527_arith__series,axiom,
% 5.15/5.48 ! [A: int,D: int,N2: nat] :
% 5.15/5.48 ( ( groups3539618377306564664at_int
% 5.15/5.48 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % arith_series
% 5.15/5.48 thf(fact_7528_arith__series,axiom,
% 5.15/5.48 ! [A: nat,D: nat,N2: nat] :
% 5.15/5.48 ( ( groups3542108847815614940at_nat
% 5.15/5.48 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 5.15/5.48 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.48 = ( 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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % arith_series
% 5.15/5.48 thf(fact_7529_gauss__sum,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.48 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % gauss_sum
% 5.15/5.48 thf(fact_7530_gauss__sum,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.48 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % gauss_sum
% 5.15/5.48 thf(fact_7531_double__gauss__sum__from__Suc__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.15/5.48 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum_from_Suc_0
% 5.15/5.48 thf(fact_7532_double__gauss__sum__from__Suc__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.15/5.48 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum_from_Suc_0
% 5.15/5.48 thf(fact_7533_double__gauss__sum__from__Suc__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.15/5.48 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum_from_Suc_0
% 5.15/5.48 thf(fact_7534_double__gauss__sum__from__Suc__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.15/5.48 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum_from_Suc_0
% 5.15/5.48 thf(fact_7535_double__gauss__sum__from__Suc__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.15/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % double_gauss_sum_from_Suc_0
% 5.15/5.48 thf(fact_7536_sum__gp__offset,axiom,
% 5.15/5.48 ! [X: rat,M: nat,N2: nat] :
% 5.15/5.48 ( ( ( X = one_one_rat )
% 5.15/5.48 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.15/5.48 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 5.15/5.48 & ( ( X != one_one_rat )
% 5.15/5.48 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.15/5.48 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_gp_offset
% 5.15/5.48 thf(fact_7537_sum__gp__offset,axiom,
% 5.15/5.48 ! [X: complex,M: nat,N2: nat] :
% 5.15/5.48 ( ( ( X = one_one_complex )
% 5.15/5.48 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.15/5.48 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 5.15/5.48 & ( ( X != one_one_complex )
% 5.15/5.48 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.15/5.48 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_gp_offset
% 5.15/5.48 thf(fact_7538_sum__gp__offset,axiom,
% 5.15/5.48 ! [X: real,M: nat,N2: nat] :
% 5.15/5.48 ( ( ( X = one_one_real )
% 5.15/5.48 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.15/5.48 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 5.15/5.48 & ( ( X != one_one_real )
% 5.15/5.48 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.15/5.48 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_gp_offset
% 5.15/5.48 thf(fact_7539_gauss__sum__from__Suc__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.15/5.48 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % gauss_sum_from_Suc_0
% 5.15/5.48 thf(fact_7540_gauss__sum__from__Suc__0,axiom,
% 5.15/5.48 ! [N2: nat] :
% 5.15/5.48 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.15/5.48 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % gauss_sum_from_Suc_0
% 5.15/5.48 thf(fact_7541_of__nat__code__if,axiom,
% 5.15/5.48 ( semiri681578069525770553at_rat
% 5.15/5.48 = ( ^ [N3: nat] :
% 5.15/5.48 ( if_rat @ ( N3 = zero_zero_nat ) @ zero_zero_rat
% 5.15/5.48 @ ( produc6207742614233964070at_rat
% 5.15/5.48 @ ^ [M5: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M5 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M5 ) ) @ one_one_rat ) )
% 5.15/5.48 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_code_if
% 5.15/5.48 thf(fact_7542_of__nat__code__if,axiom,
% 5.15/5.48 ( semiri1314217659103216013at_int
% 5.15/5.48 = ( ^ [N3: nat] :
% 5.15/5.48 ( if_int @ ( N3 = zero_zero_nat ) @ zero_zero_int
% 5.15/5.48 @ ( produc6840382203811409530at_int
% 5.15/5.48 @ ^ [M5: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M5 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M5 ) ) @ one_one_int ) )
% 5.15/5.48 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_code_if
% 5.15/5.48 thf(fact_7543_of__nat__code__if,axiom,
% 5.15/5.48 ( semiri5074537144036343181t_real
% 5.15/5.48 = ( ^ [N3: nat] :
% 5.15/5.48 ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 5.15/5.48 @ ( produc1703576794950452218t_real
% 5.15/5.48 @ ^ [M5: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M5 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M5 ) ) @ one_one_real ) )
% 5.15/5.48 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_code_if
% 5.15/5.48 thf(fact_7544_of__nat__code__if,axiom,
% 5.15/5.48 ( semiri1316708129612266289at_nat
% 5.15/5.48 = ( ^ [N3: nat] :
% 5.15/5.48 ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 5.15/5.48 @ ( produc6842872674320459806at_nat
% 5.15/5.48 @ ^ [M5: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M5 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M5 ) ) @ one_one_nat ) )
% 5.15/5.48 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_code_if
% 5.15/5.48 thf(fact_7545_of__nat__code__if,axiom,
% 5.15/5.48 ( semiri8010041392384452111omplex
% 5.15/5.48 = ( ^ [N3: nat] :
% 5.15/5.48 ( if_complex @ ( N3 = zero_zero_nat ) @ zero_zero_complex
% 5.15/5.48 @ ( produc1917071388513777916omplex
% 5.15/5.48 @ ^ [M5: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M5 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M5 ) ) @ one_one_complex ) )
% 5.15/5.48 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % of_nat_code_if
% 5.15/5.48 thf(fact_7546_height__double__log__univ__size,axiom,
% 5.15/5.48 ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 5.15/5.48 ( ( U
% 5.15/5.48 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 5.15/5.48 => ( ( vEBT_invar_vebt @ T @ Deg )
% 5.15/5.48 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % height_double_log_univ_size
% 5.15/5.48 thf(fact_7547_monoseq__arctan__series,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.48 => ( topolo6980174941875973593q_real
% 5.15/5.48 @ ^ [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 @ X @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % monoseq_arctan_series
% 5.15/5.48 thf(fact_7548_lemma__termdiff3,axiom,
% 5.15/5.48 ! [H2: real,Z: real,K5: real,N2: nat] :
% 5.15/5.48 ( ( H2 != zero_zero_real )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.15/5.48 => ( 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 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % lemma_termdiff3
% 5.15/5.48 thf(fact_7549_lemma__termdiff3,axiom,
% 5.15/5.48 ! [H2: complex,Z: complex,K5: real,N2: nat] :
% 5.15/5.48 ( ( H2 != zero_zero_complex )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.15/5.48 => ( 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 ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % lemma_termdiff3
% 5.15/5.48 thf(fact_7550_ln__series,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.48 => ( ( ln_ln_real @ X )
% 5.15/5.48 = ( suminf_real
% 5.15/5.48 @ ^ [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 @ X @ one_one_real ) @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % ln_series
% 5.15/5.48 thf(fact_7551_log__one,axiom,
% 5.15/5.48 ! [A: real] :
% 5.15/5.48 ( ( log @ A @ one_one_real )
% 5.15/5.48 = zero_zero_real ) ).
% 5.15/5.48
% 5.15/5.48 % log_one
% 5.15/5.48 thf(fact_7552_zero__less__log__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.15/5.48 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % zero_less_log_cancel_iff
% 5.15/5.48 thf(fact_7553_log__less__zero__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.15/5.48 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_less_zero_cancel_iff
% 5.15/5.48 thf(fact_7554_one__less__log__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 5.15/5.48 = ( ord_less_real @ A @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % one_less_log_cancel_iff
% 5.15/5.48 thf(fact_7555_log__less__one__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 5.15/5.48 = ( ord_less_real @ X @ A ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_less_one_cancel_iff
% 5.15/5.48 thf(fact_7556_log__less__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real,Y: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.48 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 5.15/5.48 = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_less_cancel_iff
% 5.15/5.48 thf(fact_7557_log__eq__one,axiom,
% 5.15/5.48 ! [A: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.48 => ( ( A != one_one_real )
% 5.15/5.48 => ( ( log @ A @ A )
% 5.15/5.48 = one_one_real ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_eq_one
% 5.15/5.48 thf(fact_7558_zero__le__log__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.15/5.48 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % zero_le_log_cancel_iff
% 5.15/5.48 thf(fact_7559_log__le__zero__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.15/5.48 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_le_zero_cancel_iff
% 5.15/5.48 thf(fact_7560_one__le__log__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 5.15/5.48 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % one_le_log_cancel_iff
% 5.15/5.48 thf(fact_7561_log__le__one__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 5.15/5.48 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_le_one_cancel_iff
% 5.15/5.48 thf(fact_7562_log__le__cancel__iff,axiom,
% 5.15/5.48 ! [A: real,X: real,Y: real] :
% 5.15/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 5.15/5.48 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_le_cancel_iff
% 5.15/5.48 thf(fact_7563_powser__zero,axiom,
% 5.15/5.48 ! [F: nat > complex] :
% 5.15/5.48 ( ( suminf_complex
% 5.15/5.48 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) )
% 5.15/5.48 = ( F @ zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % powser_zero
% 5.15/5.48 thf(fact_7564_powser__zero,axiom,
% 5.15/5.48 ! [F: nat > real] :
% 5.15/5.48 ( ( suminf_real
% 5.15/5.48 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) )
% 5.15/5.48 = ( F @ zero_zero_nat ) ) ).
% 5.15/5.48
% 5.15/5.48 % powser_zero
% 5.15/5.48 thf(fact_7565_log__pow__cancel,axiom,
% 5.15/5.48 ! [A: real,B: nat] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.48 => ( ( A != one_one_real )
% 5.15/5.48 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.15/5.48 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_pow_cancel
% 5.15/5.48 thf(fact_7566_log__def,axiom,
% 5.15/5.48 ( log
% 5.15/5.48 = ( ^ [A3: real,X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ A3 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_def
% 5.15/5.48 thf(fact_7567_complex__mod__minus__le__complex__mod,axiom,
% 5.15/5.48 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % complex_mod_minus_le_complex_mod
% 5.15/5.48 thf(fact_7568_complex__mod__triangle__ineq2,axiom,
% 5.15/5.48 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.15/5.48
% 5.15/5.48 % complex_mod_triangle_ineq2
% 5.15/5.48 thf(fact_7569_less__log__of__power,axiom,
% 5.15/5.48 ! [B: real,N2: nat,M: real] :
% 5.15/5.48 ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.15/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.48 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % less_log_of_power
% 5.15/5.48 thf(fact_7570_log__of__power__eq,axiom,
% 5.15/5.48 ! [M: nat,B: real,N2: nat] :
% 5.15/5.48 ( ( ( semiri5074537144036343181t_real @ M )
% 5.15/5.48 = ( power_power_real @ B @ N2 ) )
% 5.15/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.48 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.15/5.48 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_of_power_eq
% 5.15/5.48 thf(fact_7571_log__ln,axiom,
% 5.15/5.48 ( ln_ln_real
% 5.15/5.48 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_ln
% 5.15/5.48 thf(fact_7572_norm__exp,axiom,
% 5.15/5.48 ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_exp
% 5.15/5.48 thf(fact_7573_norm__exp,axiom,
% 5.15/5.48 ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_exp
% 5.15/5.48 thf(fact_7574_log__base__change,axiom,
% 5.15/5.48 ! [A: real,B: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.48 => ( ( A != one_one_real )
% 5.15/5.48 => ( ( log @ B @ X )
% 5.15/5.48 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_base_change
% 5.15/5.48 thf(fact_7575_le__log__of__power,axiom,
% 5.15/5.48 ! [B: real,N2: nat,M: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.15/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.48 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % le_log_of_power
% 5.15/5.48 thf(fact_7576_log__base__pow,axiom,
% 5.15/5.48 ! [A: real,N2: nat,X: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.48 => ( ( log @ ( power_power_real @ A @ N2 ) @ X )
% 5.15/5.48 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_base_pow
% 5.15/5.48 thf(fact_7577_log__nat__power,axiom,
% 5.15/5.48 ! [X: real,B: real,N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( log @ B @ ( power_power_real @ X @ N2 ) )
% 5.15/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_nat_power
% 5.15/5.48 thf(fact_7578_log2__of__power__eq,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( M
% 5.15/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.48 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.15/5.48 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log2_of_power_eq
% 5.15/5.48 thf(fact_7579_log__of__power__less,axiom,
% 5.15/5.48 ! [M: nat,B: real,N2: nat] :
% 5.15/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.15/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.48 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_of_power_less
% 5.15/5.48 thf(fact_7580_log__mult,axiom,
% 5.15/5.48 ! [A: real,X: real,Y: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.48 => ( ( A != one_one_real )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.48 => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 5.15/5.48 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_mult
% 5.15/5.48 thf(fact_7581_log__divide,axiom,
% 5.15/5.48 ! [A: real,X: real,Y: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.48 => ( ( A != one_one_real )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.48 => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.48 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_divide
% 5.15/5.48 thf(fact_7582_log__of__power__le,axiom,
% 5.15/5.48 ! [M: nat,B: real,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.15/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.48 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_of_power_le
% 5.15/5.48 thf(fact_7583_log__eq__div__ln__mult__log,axiom,
% 5.15/5.48 ! [A: real,B: real,X: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.48 => ( ( A != one_one_real )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.48 => ( ( B != one_one_real )
% 5.15/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( log @ A @ X )
% 5.15/5.48 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_eq_div_ln_mult_log
% 5.15/5.48 thf(fact_7584_monoseq__realpow,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.48 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % monoseq_realpow
% 5.15/5.48 thf(fact_7585_less__log2__of__power,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.15/5.48 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % less_log2_of_power
% 5.15/5.48 thf(fact_7586_le__log2__of__power,axiom,
% 5.15/5.48 ! [N2: nat,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.15/5.48 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % le_log2_of_power
% 5.15/5.48 thf(fact_7587_exp__bound__half,axiom,
% 5.15/5.48 ! [Z: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_bound_half
% 5.15/5.48 thf(fact_7588_exp__bound__half,axiom,
% 5.15/5.48 ! [Z: complex] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_bound_half
% 5.15/5.48 thf(fact_7589_log2__of__power__less,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.48 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log2_of_power_less
% 5.15/5.48 thf(fact_7590_log2__of__power__le,axiom,
% 5.15/5.48 ! [M: nat,N2: nat] :
% 5.15/5.48 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.48 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log2_of_power_le
% 5.15/5.48 thf(fact_7591_exp__bound__lemma,axiom,
% 5.15/5.48 ! [Z: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.48 => ( 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 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_bound_lemma
% 5.15/5.48 thf(fact_7592_exp__bound__lemma,axiom,
% 5.15/5.48 ! [Z: complex] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.48 => ( 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 ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % exp_bound_lemma
% 5.15/5.48 thf(fact_7593_log__base__10__eq2,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.48 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_base_10_eq2
% 5.15/5.48 thf(fact_7594_member__bound__size__univ,axiom,
% 5.15/5.48 ! [T: vEBT_VEBT,N2: nat,U: real,X: nat] :
% 5.15/5.48 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.48 => ( ( U
% 5.15/5.48 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % member_bound_size_univ
% 5.15/5.48 thf(fact_7595_log__base__10__eq1,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.48 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.48 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % log_base_10_eq1
% 5.15/5.48 thf(fact_7596_arctan__series,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.48 => ( ( arctan @ X )
% 5.15/5.48 = ( suminf_real
% 5.15/5.48 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % arctan_series
% 5.15/5.48 thf(fact_7597_norm__divide__numeral,axiom,
% 5.15/5.48 ! [A: real,W: num] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.48 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_divide_numeral
% 5.15/5.48 thf(fact_7598_norm__divide__numeral,axiom,
% 5.15/5.48 ! [A: complex,W: num] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.48 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_divide_numeral
% 5.15/5.48 thf(fact_7599_norm__mult__numeral1,axiom,
% 5.15/5.48 ! [W: num,A: real] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.15/5.48 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult_numeral1
% 5.15/5.48 thf(fact_7600_norm__mult__numeral1,axiom,
% 5.15/5.48 ! [W: num,A: complex] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.15/5.48 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult_numeral1
% 5.15/5.48 thf(fact_7601_norm__mult__numeral2,axiom,
% 5.15/5.48 ! [A: real,W: num] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.48 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult_numeral2
% 5.15/5.48 thf(fact_7602_norm__mult__numeral2,axiom,
% 5.15/5.48 ! [A: complex,W: num] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.48 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult_numeral2
% 5.15/5.48 thf(fact_7603_norm__neg__numeral,axiom,
% 5.15/5.48 ! [W: num] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.48 = ( numeral_numeral_real @ W ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_neg_numeral
% 5.15/5.48 thf(fact_7604_norm__neg__numeral,axiom,
% 5.15/5.48 ! [W: num] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.48 = ( numeral_numeral_real @ W ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_neg_numeral
% 5.15/5.48 thf(fact_7605_norm__le__zero__iff,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 5.15/5.48 = ( X = zero_zero_real ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_le_zero_iff
% 5.15/5.48 thf(fact_7606_norm__le__zero__iff,axiom,
% 5.15/5.48 ! [X: complex] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 5.15/5.48 = ( X = zero_zero_complex ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_le_zero_iff
% 5.15/5.48 thf(fact_7607_norm__one,axiom,
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.15/5.48 = one_one_real ) ).
% 5.15/5.48
% 5.15/5.48 % norm_one
% 5.15/5.48 thf(fact_7608_norm__one,axiom,
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.15/5.48 = one_one_real ) ).
% 5.15/5.48
% 5.15/5.48 % norm_one
% 5.15/5.48 thf(fact_7609_norm__numeral,axiom,
% 5.15/5.48 ! [W: num] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.48 = ( numeral_numeral_real @ W ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_numeral
% 5.15/5.48 thf(fact_7610_norm__numeral,axiom,
% 5.15/5.48 ! [W: num] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.15/5.48 = ( numeral_numeral_real @ W ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_numeral
% 5.15/5.48 thf(fact_7611_zero__less__norm__iff,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 5.15/5.48 = ( X != zero_zero_real ) ) ).
% 5.15/5.48
% 5.15/5.48 % zero_less_norm_iff
% 5.15/5.48 thf(fact_7612_zero__less__norm__iff,axiom,
% 5.15/5.48 ! [X: complex] :
% 5.15/5.48 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 5.15/5.48 = ( X != zero_zero_complex ) ) ).
% 5.15/5.48
% 5.15/5.48 % zero_less_norm_iff
% 5.15/5.48 thf(fact_7613_norm__minus__commute,axiom,
% 5.15/5.48 ! [A: real,B: real] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) )
% 5.15/5.48 = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_minus_commute
% 5.15/5.48 thf(fact_7614_norm__minus__commute,axiom,
% 5.15/5.48 ! [A: complex,B: complex] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 5.15/5.48 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_minus_commute
% 5.15/5.48 thf(fact_7615_norm__not__less__zero,axiom,
% 5.15/5.48 ! [X: complex] :
% 5.15/5.48 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 5.15/5.48
% 5.15/5.48 % norm_not_less_zero
% 5.15/5.48 thf(fact_7616_norm__ge__zero,axiom,
% 5.15/5.48 ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_ge_zero
% 5.15/5.48 thf(fact_7617_norm__mult,axiom,
% 5.15/5.48 ! [X: real,Y: real] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 5.15/5.48 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult
% 5.15/5.48 thf(fact_7618_norm__mult,axiom,
% 5.15/5.48 ! [X: complex,Y: complex] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 5.15/5.48 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult
% 5.15/5.48 thf(fact_7619_norm__divide,axiom,
% 5.15/5.48 ! [A: real,B: real] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.48 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_divide
% 5.15/5.48 thf(fact_7620_norm__divide,axiom,
% 5.15/5.48 ! [A: complex,B: complex] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.48 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_divide
% 5.15/5.48 thf(fact_7621_sum__norm__le,axiom,
% 5.15/5.48 ! [S3: set_real,F: real > complex,G: real > real] :
% 5.15/5.48 ( ! [X3: real] :
% 5.15/5.48 ( ( member_real @ X3 @ S3 )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S3 ) ) @ ( groups8097168146408367636l_real @ G @ S3 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_norm_le
% 5.15/5.48 thf(fact_7622_sum__norm__le,axiom,
% 5.15/5.48 ! [S3: set_set_nat,F: set_nat > complex,G: set_nat > real] :
% 5.15/5.48 ( ! [X3: set_nat] :
% 5.15/5.48 ( ( member_set_nat @ X3 @ S3 )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S3 ) ) @ ( groups5107569545109728110t_real @ G @ S3 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_norm_le
% 5.15/5.48 thf(fact_7623_sum__norm__le,axiom,
% 5.15/5.48 ! [S3: set_int,F: int > complex,G: int > real] :
% 5.15/5.48 ( ! [X3: int] :
% 5.15/5.48 ( ( member_int @ X3 @ S3 )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S3 ) ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_norm_le
% 5.15/5.48 thf(fact_7624_sum__norm__le,axiom,
% 5.15/5.48 ! [S3: set_nat,F: nat > complex,G: nat > real] :
% 5.15/5.48 ( ! [X3: nat] :
% 5.15/5.48 ( ( member_nat @ X3 @ S3 )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S3 ) ) @ ( groups6591440286371151544t_real @ G @ S3 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_norm_le
% 5.15/5.48 thf(fact_7625_sum__norm__le,axiom,
% 5.15/5.48 ! [S3: set_complex,F: complex > complex,G: complex > real] :
% 5.15/5.48 ( ! [X3: complex] :
% 5.15/5.48 ( ( member_complex @ X3 @ S3 )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S3 ) ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_norm_le
% 5.15/5.48 thf(fact_7626_sum__norm__le,axiom,
% 5.15/5.48 ! [S3: set_nat,F: nat > real,G: nat > real] :
% 5.15/5.48 ( ! [X3: nat] :
% 5.15/5.48 ( ( member_nat @ X3 @ S3 )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S3 ) ) @ ( groups6591440286371151544t_real @ G @ S3 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % sum_norm_le
% 5.15/5.48 thf(fact_7627_norm__power,axiom,
% 5.15/5.48 ! [X: real,N2: nat] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N2 ) )
% 5.15/5.48 = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_power
% 5.15/5.48 thf(fact_7628_norm__power,axiom,
% 5.15/5.48 ! [X: complex,N2: nat] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N2 ) )
% 5.15/5.48 = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_power
% 5.15/5.48 thf(fact_7629_norm__sum,axiom,
% 5.15/5.48 ! [F: nat > complex,A2: set_nat] :
% 5.15/5.48 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 5.15/5.48 @ ( groups6591440286371151544t_real
% 5.15/5.48 @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_sum
% 5.15/5.48 thf(fact_7630_norm__sum,axiom,
% 5.15/5.48 ! [F: complex > complex,A2: set_complex] :
% 5.15/5.48 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.15/5.48 @ ( groups5808333547571424918x_real
% 5.15/5.48 @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_sum
% 5.15/5.48 thf(fact_7631_norm__sum,axiom,
% 5.15/5.48 ! [F: nat > real,A2: set_nat] :
% 5.15/5.48 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.15/5.48 @ ( groups6591440286371151544t_real
% 5.15/5.48 @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( F @ I3 ) )
% 5.15/5.48 @ A2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_sum
% 5.15/5.48 thf(fact_7632_norm__uminus__minus,axiom,
% 5.15/5.48 ! [X: real,Y: real] :
% 5.15/5.48 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 5.15/5.48 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_uminus_minus
% 5.15/5.48 thf(fact_7633_norm__uminus__minus,axiom,
% 5.15/5.48 ! [X: complex,Y: complex] :
% 5.15/5.48 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 5.15/5.48 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_uminus_minus
% 5.15/5.48 thf(fact_7634_nonzero__norm__divide,axiom,
% 5.15/5.48 ! [B: real,A: real] :
% 5.15/5.48 ( ( B != zero_zero_real )
% 5.15/5.48 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.15/5.48 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % nonzero_norm_divide
% 5.15/5.48 thf(fact_7635_nonzero__norm__divide,axiom,
% 5.15/5.48 ! [B: complex,A: complex] :
% 5.15/5.48 ( ( B != zero_zero_complex )
% 5.15/5.48 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.48 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % nonzero_norm_divide
% 5.15/5.48 thf(fact_7636_power__eq__imp__eq__norm,axiom,
% 5.15/5.48 ! [W: real,N2: nat,Z: real] :
% 5.15/5.48 ( ( ( power_power_real @ W @ N2 )
% 5.15/5.48 = ( power_power_real @ Z @ N2 ) )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.48 => ( ( real_V7735802525324610683m_real @ W )
% 5.15/5.48 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % power_eq_imp_eq_norm
% 5.15/5.48 thf(fact_7637_power__eq__imp__eq__norm,axiom,
% 5.15/5.48 ! [W: complex,N2: nat,Z: complex] :
% 5.15/5.48 ( ( ( power_power_complex @ W @ N2 )
% 5.15/5.48 = ( power_power_complex @ Z @ N2 ) )
% 5.15/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.48 => ( ( real_V1022390504157884413omplex @ W )
% 5.15/5.48 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % power_eq_imp_eq_norm
% 5.15/5.48 thf(fact_7638_norm__mult__less,axiom,
% 5.15/5.48 ! [X: real,R2: real,Y: real,S: real] :
% 5.15/5.48 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.15/5.48 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 5.15/5.48 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult_less
% 5.15/5.48 thf(fact_7639_norm__mult__less,axiom,
% 5.15/5.48 ! [X: complex,R2: real,Y: complex,S: real] :
% 5.15/5.48 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.15/5.48 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 5.15/5.48 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult_less
% 5.15/5.48 thf(fact_7640_norm__mult__ineq,axiom,
% 5.15/5.48 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult_ineq
% 5.15/5.48 thf(fact_7641_norm__mult__ineq,axiom,
% 5.15/5.48 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_mult_ineq
% 5.15/5.48 thf(fact_7642_norm__triangle__lt,axiom,
% 5.15/5.48 ! [X: real,Y: real,E: real] :
% 5.15/5.48 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.15/5.48 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_lt
% 5.15/5.48 thf(fact_7643_norm__triangle__lt,axiom,
% 5.15/5.48 ! [X: complex,Y: complex,E: real] :
% 5.15/5.48 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.15/5.48 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_lt
% 5.15/5.48 thf(fact_7644_norm__add__less,axiom,
% 5.15/5.48 ! [X: real,R2: real,Y: real,S: real] :
% 5.15/5.48 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.15/5.48 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 5.15/5.48 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_add_less
% 5.15/5.48 thf(fact_7645_norm__add__less,axiom,
% 5.15/5.48 ! [X: complex,R2: real,Y: complex,S: real] :
% 5.15/5.48 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.15/5.48 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 5.15/5.48 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_add_less
% 5.15/5.48 thf(fact_7646_norm__triangle__mono,axiom,
% 5.15/5.48 ! [A: real,R2: real,B: real,S: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_mono
% 5.15/5.48 thf(fact_7647_norm__triangle__mono,axiom,
% 5.15/5.48 ! [A: complex,R2: real,B: complex,S: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_mono
% 5.15/5.48 thf(fact_7648_norm__triangle__ineq,axiom,
% 5.15/5.48 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_ineq
% 5.15/5.48 thf(fact_7649_norm__triangle__ineq,axiom,
% 5.15/5.48 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_ineq
% 5.15/5.48 thf(fact_7650_norm__triangle__le,axiom,
% 5.15/5.48 ! [X: real,Y: real,E: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_le
% 5.15/5.48 thf(fact_7651_norm__triangle__le,axiom,
% 5.15/5.48 ! [X: complex,Y: complex,E: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_le
% 5.15/5.48 thf(fact_7652_norm__add__leD,axiom,
% 5.15/5.48 ! [A: real,B: real,C: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_add_leD
% 5.15/5.48 thf(fact_7653_norm__add__leD,axiom,
% 5.15/5.48 ! [A: complex,B: complex,C: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_add_leD
% 5.15/5.48 thf(fact_7654_norm__power__ineq,axiom,
% 5.15/5.48 ! [X: real,N2: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_power_ineq
% 5.15/5.48 thf(fact_7655_norm__power__ineq,axiom,
% 5.15/5.48 ! [X: complex,N2: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N2 ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_power_ineq
% 5.15/5.48 thf(fact_7656_norm__diff__triangle__less,axiom,
% 5.15/5.48 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 5.15/5.48 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 5.15/5.48 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.15/5.48 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_diff_triangle_less
% 5.15/5.48 thf(fact_7657_norm__diff__triangle__less,axiom,
% 5.15/5.48 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.15/5.48 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.15/5.48 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.15/5.48 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_diff_triangle_less
% 5.15/5.48 thf(fact_7658_norm__triangle__le__diff,axiom,
% 5.15/5.48 ! [X: real,Y: real,E: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_le_diff
% 5.15/5.48 thf(fact_7659_norm__triangle__le__diff,axiom,
% 5.15/5.48 ! [X: complex,Y: complex,E: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_le_diff
% 5.15/5.48 thf(fact_7660_norm__diff__triangle__le,axiom,
% 5.15/5.48 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_diff_triangle_le
% 5.15/5.48 thf(fact_7661_norm__diff__triangle__le,axiom,
% 5.15/5.48 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.15/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_diff_triangle_le
% 5.15/5.48 thf(fact_7662_norm__triangle__ineq4,axiom,
% 5.15/5.48 ! [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 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_ineq4
% 5.15/5.48 thf(fact_7663_norm__triangle__ineq4,axiom,
% 5.15/5.48 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_ineq4
% 5.15/5.48 thf(fact_7664_norm__triangle__sub,axiom,
% 5.15/5.48 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_sub
% 5.15/5.48 thf(fact_7665_norm__triangle__sub,axiom,
% 5.15/5.48 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_sub
% 5.15/5.48 thf(fact_7666_norm__diff__ineq,axiom,
% 5.15/5.48 ! [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 ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_diff_ineq
% 5.15/5.48 thf(fact_7667_norm__diff__ineq,axiom,
% 5.15/5.48 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_diff_ineq
% 5.15/5.48 thf(fact_7668_norm__triangle__ineq2,axiom,
% 5.15/5.48 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_ineq2
% 5.15/5.48 thf(fact_7669_norm__triangle__ineq2,axiom,
% 5.15/5.48 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_ineq2
% 5.15/5.48 thf(fact_7670_power__eq__1__iff,axiom,
% 5.15/5.48 ! [W: real,N2: nat] :
% 5.15/5.48 ( ( ( power_power_real @ W @ N2 )
% 5.15/5.48 = one_one_real )
% 5.15/5.48 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.15/5.48 = one_one_real )
% 5.15/5.48 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % power_eq_1_iff
% 5.15/5.48 thf(fact_7671_power__eq__1__iff,axiom,
% 5.15/5.48 ! [W: complex,N2: nat] :
% 5.15/5.48 ( ( ( power_power_complex @ W @ N2 )
% 5.15/5.48 = one_one_complex )
% 5.15/5.48 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.15/5.48 = one_one_real )
% 5.15/5.48 | ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % power_eq_1_iff
% 5.15/5.48 thf(fact_7672_norm__diff__triangle__ineq,axiom,
% 5.15/5.48 ! [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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_diff_triangle_ineq
% 5.15/5.48 thf(fact_7673_norm__diff__triangle__ineq,axiom,
% 5.15/5.48 ! [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 ) ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_diff_triangle_ineq
% 5.15/5.48 thf(fact_7674_norm__triangle__ineq3,axiom,
% 5.15/5.48 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_ineq3
% 5.15/5.48 thf(fact_7675_norm__triangle__ineq3,axiom,
% 5.15/5.48 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.15/5.48
% 5.15/5.48 % norm_triangle_ineq3
% 5.15/5.48 thf(fact_7676_square__norm__one,axiom,
% 5.15/5.48 ! [X: real] :
% 5.15/5.48 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.48 = one_one_real )
% 5.15/5.48 => ( ( real_V7735802525324610683m_real @ X )
% 5.15/5.48 = one_one_real ) ) ).
% 5.15/5.48
% 5.15/5.48 % square_norm_one
% 5.15/5.48 thf(fact_7677_square__norm__one,axiom,
% 5.15/5.48 ! [X: complex] :
% 5.15/5.48 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.48 = one_one_complex )
% 5.15/5.48 => ( ( real_V1022390504157884413omplex @ X )
% 5.15/5.48 = one_one_real ) ) ).
% 5.15/5.48
% 5.15/5.48 % square_norm_one
% 5.15/5.48 thf(fact_7678_norm__power__diff,axiom,
% 5.15/5.48 ! [Z: real,W: real,M: nat] :
% 5.15/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.15/5.48 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.15/5.48 => ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_power_diff
% 5.15/5.49 thf(fact_7679_norm__power__diff,axiom,
% 5.15/5.49 ! [Z: complex,W: complex,M: nat] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.15/5.49 => ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_power_diff
% 5.15/5.49 thf(fact_7680_suminf__geometric,axiom,
% 5.15/5.49 ! [C: real] :
% 5.15/5.49 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.15/5.49 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.15/5.49 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_geometric
% 5.15/5.49 thf(fact_7681_suminf__geometric,axiom,
% 5.15/5.49 ! [C: complex] :
% 5.15/5.49 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.15/5.49 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_geometric
% 5.15/5.49 thf(fact_7682_suminf__zero,axiom,
% 5.15/5.49 ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : zero_zero_complex )
% 5.15/5.49 = zero_zero_complex ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_zero
% 5.15/5.49 thf(fact_7683_suminf__zero,axiom,
% 5.15/5.49 ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : zero_zero_real )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_zero
% 5.15/5.49 thf(fact_7684_suminf__zero,axiom,
% 5.15/5.49 ( ( suminf_nat
% 5.15/5.49 @ ^ [N3: nat] : zero_zero_nat )
% 5.15/5.49 = zero_zero_nat ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_zero
% 5.15/5.49 thf(fact_7685_suminf__zero,axiom,
% 5.15/5.49 ( ( suminf_int
% 5.15/5.49 @ ^ [N3: nat] : zero_zero_int )
% 5.15/5.49 = zero_zero_int ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_zero
% 5.15/5.49 thf(fact_7686_heigt__uplog__rel,axiom,
% 5.15/5.49 ! [T: vEBT_VEBT,N2: nat] :
% 5.15/5.49 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.15/5.49 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 5.15/5.49 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % heigt_uplog_rel
% 5.15/5.49 thf(fact_7687_suminf__finite,axiom,
% 5.15/5.49 ! [N5: set_nat,F: nat > complex] :
% 5.15/5.49 ( ( finite_finite_nat @ N5 )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ~ ( member_nat @ N @ N5 )
% 5.15/5.49 => ( ( F @ N )
% 5.15/5.49 = zero_zero_complex ) )
% 5.15/5.49 => ( ( suminf_complex @ F )
% 5.15/5.49 = ( groups2073611262835488442omplex @ F @ N5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_finite
% 5.15/5.49 thf(fact_7688_suminf__finite,axiom,
% 5.15/5.49 ! [N5: set_nat,F: nat > int] :
% 5.15/5.49 ( ( finite_finite_nat @ N5 )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ~ ( member_nat @ N @ N5 )
% 5.15/5.49 => ( ( F @ N )
% 5.15/5.49 = zero_zero_int ) )
% 5.15/5.49 => ( ( suminf_int @ F )
% 5.15/5.49 = ( groups3539618377306564664at_int @ F @ N5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_finite
% 5.15/5.49 thf(fact_7689_suminf__finite,axiom,
% 5.15/5.49 ! [N5: set_nat,F: nat > nat] :
% 5.15/5.49 ( ( finite_finite_nat @ N5 )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ~ ( member_nat @ N @ N5 )
% 5.15/5.49 => ( ( F @ N )
% 5.15/5.49 = zero_zero_nat ) )
% 5.15/5.49 => ( ( suminf_nat @ F )
% 5.15/5.49 = ( groups3542108847815614940at_nat @ F @ N5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_finite
% 5.15/5.49 thf(fact_7690_suminf__finite,axiom,
% 5.15/5.49 ! [N5: set_nat,F: nat > real] :
% 5.15/5.49 ( ( finite_finite_nat @ N5 )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ~ ( member_nat @ N @ N5 )
% 5.15/5.49 => ( ( F @ N )
% 5.15/5.49 = zero_zero_real ) )
% 5.15/5.49 => ( ( suminf_real @ F )
% 5.15/5.49 = ( groups6591440286371151544t_real @ F @ N5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_finite
% 5.15/5.49 thf(fact_7691_log__ceil__idem,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.49 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % log_ceil_idem
% 5.15/5.49 thf(fact_7692_of__int__ceiling__cancel,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = X )
% 5.15/5.49 = ( ? [N3: int] :
% 5.15/5.49 ( X
% 5.15/5.49 = ( ring_1_of_int_rat @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_int_ceiling_cancel
% 5.15/5.49 thf(fact_7693_of__int__ceiling__cancel,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = X )
% 5.15/5.49 = ( ? [N3: int] :
% 5.15/5.49 ( X
% 5.15/5.49 = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_int_ceiling_cancel
% 5.15/5.49 thf(fact_7694_ceiling__numeral,axiom,
% 5.15/5.49 ! [V: num] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.15/5.49 = ( numeral_numeral_int @ V ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_numeral
% 5.15/5.49 thf(fact_7695_ceiling__numeral,axiom,
% 5.15/5.49 ! [V: num] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.15/5.49 = ( numeral_numeral_int @ V ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_numeral
% 5.15/5.49 thf(fact_7696_ceiling__one,axiom,
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.15/5.49 = one_one_int ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_one
% 5.15/5.49 thf(fact_7697_ceiling__one,axiom,
% 5.15/5.49 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.15/5.49 = one_one_int ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_one
% 5.15/5.49 thf(fact_7698_ceiling__add__of__int,axiom,
% 5.15/5.49 ! [X: rat,Z: int] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 5.15/5.49 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_add_of_int
% 5.15/5.49 thf(fact_7699_ceiling__add__of__int,axiom,
% 5.15/5.49 ! [X: real,Z: int] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 5.15/5.49 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_add_of_int
% 5.15/5.49 thf(fact_7700_ceiling__diff__of__int,axiom,
% 5.15/5.49 ! [X: rat,Z: int] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 5.15/5.49 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_diff_of_int
% 5.15/5.49 thf(fact_7701_ceiling__diff__of__int,axiom,
% 5.15/5.49 ! [X: real,Z: int] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 5.15/5.49 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_diff_of_int
% 5.15/5.49 thf(fact_7702_ceiling__le__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.15/5.49 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_zero
% 5.15/5.49 thf(fact_7703_ceiling__le__zero,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_zero
% 5.15/5.49 thf(fact_7704_zero__less__ceiling,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % zero_less_ceiling
% 5.15/5.49 thf(fact_7705_zero__less__ceiling,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % zero_less_ceiling
% 5.15/5.49 thf(fact_7706_ceiling__le__numeral,axiom,
% 5.15/5.49 ! [X: real,V: num] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.49 = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_numeral
% 5.15/5.49 thf(fact_7707_ceiling__le__numeral,axiom,
% 5.15/5.49 ! [X: rat,V: num] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_numeral
% 5.15/5.49 thf(fact_7708_ceiling__less__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.15/5.49 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_one
% 5.15/5.49 thf(fact_7709_ceiling__less__one,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_one
% 5.15/5.49 thf(fact_7710_one__le__ceiling,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_le_ceiling
% 5.15/5.49 thf(fact_7711_one__le__ceiling,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_le_ceiling
% 5.15/5.49 thf(fact_7712_numeral__less__ceiling,axiom,
% 5.15/5.49 ! [V: num,X: real] :
% 5.15/5.49 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % numeral_less_ceiling
% 5.15/5.49 thf(fact_7713_numeral__less__ceiling,axiom,
% 5.15/5.49 ! [V: num,X: rat] :
% 5.15/5.49 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % numeral_less_ceiling
% 5.15/5.49 thf(fact_7714_ceiling__le__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.15/5.49 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_one
% 5.15/5.49 thf(fact_7715_ceiling__le__one,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_one
% 5.15/5.49 thf(fact_7716_one__less__ceiling,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_less_ceiling
% 5.15/5.49 thf(fact_7717_one__less__ceiling,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ one_one_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_less_ceiling
% 5.15/5.49 thf(fact_7718_ceiling__add__numeral,axiom,
% 5.15/5.49 ! [X: real,V: num] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.49 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_add_numeral
% 5.15/5.49 thf(fact_7719_ceiling__add__numeral,axiom,
% 5.15/5.49 ! [X: rat,V: num] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.49 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_add_numeral
% 5.15/5.49 thf(fact_7720_ceiling__neg__numeral,axiom,
% 5.15/5.49 ! [V: num] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.49 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_neg_numeral
% 5.15/5.49 thf(fact_7721_ceiling__neg__numeral,axiom,
% 5.15/5.49 ! [V: num] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.49 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_neg_numeral
% 5.15/5.49 thf(fact_7722_ceiling__add__one,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 5.15/5.49 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_add_one
% 5.15/5.49 thf(fact_7723_ceiling__add__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 5.15/5.49 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_add_one
% 5.15/5.49 thf(fact_7724_ceiling__diff__numeral,axiom,
% 5.15/5.49 ! [X: real,V: num] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.49 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_diff_numeral
% 5.15/5.49 thf(fact_7725_ceiling__diff__numeral,axiom,
% 5.15/5.49 ! [X: rat,V: num] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.49 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_diff_numeral
% 5.15/5.49 thf(fact_7726_ceiling__diff__one,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 5.15/5.49 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_diff_one
% 5.15/5.49 thf(fact_7727_ceiling__diff__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.15/5.49 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_diff_one
% 5.15/5.49 thf(fact_7728_ceiling__numeral__power,axiom,
% 5.15/5.49 ! [X: num,N2: nat] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.15/5.49 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_numeral_power
% 5.15/5.49 thf(fact_7729_ceiling__numeral__power,axiom,
% 5.15/5.49 ! [X: num,N2: nat] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.15/5.49 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_numeral_power
% 5.15/5.49 thf(fact_7730_ceiling__less__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.15/5.49 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_zero
% 5.15/5.49 thf(fact_7731_ceiling__less__zero,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_zero
% 5.15/5.49 thf(fact_7732_zero__le__ceiling,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % zero_le_ceiling
% 5.15/5.49 thf(fact_7733_zero__le__ceiling,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % zero_le_ceiling
% 5.15/5.49 thf(fact_7734_ceiling__divide__eq__div__numeral,axiom,
% 5.15/5.49 ! [A: num,B: num] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.15/5.49 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_divide_eq_div_numeral
% 5.15/5.49 thf(fact_7735_ceiling__less__numeral,axiom,
% 5.15/5.49 ! [X: real,V: num] :
% 5.15/5.49 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.49 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_numeral
% 5.15/5.49 thf(fact_7736_ceiling__less__numeral,axiom,
% 5.15/5.49 ! [X: rat,V: num] :
% 5.15/5.49 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_numeral
% 5.15/5.49 thf(fact_7737_numeral__le__ceiling,axiom,
% 5.15/5.49 ! [V: num,X: real] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % numeral_le_ceiling
% 5.15/5.49 thf(fact_7738_numeral__le__ceiling,axiom,
% 5.15/5.49 ! [V: num,X: rat] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % numeral_le_ceiling
% 5.15/5.49 thf(fact_7739_ceiling__le__neg__numeral,axiom,
% 5.15/5.49 ! [X: real,V: num] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.49 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_neg_numeral
% 5.15/5.49 thf(fact_7740_ceiling__le__neg__numeral,axiom,
% 5.15/5.49 ! [X: rat,V: num] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_neg_numeral
% 5.15/5.49 thf(fact_7741_neg__numeral__less__ceiling,axiom,
% 5.15/5.49 ! [V: num,X: real] :
% 5.15/5.49 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % neg_numeral_less_ceiling
% 5.15/5.49 thf(fact_7742_neg__numeral__less__ceiling,axiom,
% 5.15/5.49 ! [V: num,X: rat] :
% 5.15/5.49 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % neg_numeral_less_ceiling
% 5.15/5.49 thf(fact_7743_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.15/5.49 ! [A: num,B: num] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.15/5.49 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_minus_divide_eq_div_numeral
% 5.15/5.49 thf(fact_7744_ceiling__less__neg__numeral,axiom,
% 5.15/5.49 ! [X: real,V: num] :
% 5.15/5.49 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.49 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_neg_numeral
% 5.15/5.49 thf(fact_7745_ceiling__less__neg__numeral,axiom,
% 5.15/5.49 ! [X: rat,V: num] :
% 5.15/5.49 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_neg_numeral
% 5.15/5.49 thf(fact_7746_neg__numeral__le__ceiling,axiom,
% 5.15/5.49 ! [V: num,X: real] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % neg_numeral_le_ceiling
% 5.15/5.49 thf(fact_7747_neg__numeral__le__ceiling,axiom,
% 5.15/5.49 ! [V: num,X: rat] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % neg_numeral_le_ceiling
% 5.15/5.49 thf(fact_7748_ceiling__mono,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ Y @ X )
% 5.15/5.49 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_mono
% 5.15/5.49 thf(fact_7749_ceiling__mono,axiom,
% 5.15/5.49 ! [Y: rat,X: rat] :
% 5.15/5.49 ( ( ord_less_eq_rat @ Y @ X )
% 5.15/5.49 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_mono
% 5.15/5.49 thf(fact_7750_le__of__int__ceiling,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % le_of_int_ceiling
% 5.15/5.49 thf(fact_7751_le__of__int__ceiling,axiom,
% 5.15/5.49 ! [X: rat] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % le_of_int_ceiling
% 5.15/5.49 thf(fact_7752_ceiling__less__cancel,axiom,
% 5.15/5.49 ! [X: rat,Y: rat] :
% 5.15/5.49 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 5.15/5.49 => ( ord_less_rat @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_cancel
% 5.15/5.49 thf(fact_7753_ceiling__less__cancel,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) )
% 5.15/5.49 => ( ord_less_real @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_cancel
% 5.15/5.49 thf(fact_7754_ceiling__le__iff,axiom,
% 5.15/5.49 ! [X: real,Z: int] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 5.15/5.49 = ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_iff
% 5.15/5.49 thf(fact_7755_ceiling__le__iff,axiom,
% 5.15/5.49 ! [X: rat,Z: int] :
% 5.15/5.49 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le_iff
% 5.15/5.49 thf(fact_7756_ceiling__le,axiom,
% 5.15/5.49 ! [X: real,A: int] :
% 5.15/5.49 ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 5.15/5.49 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le
% 5.15/5.49 thf(fact_7757_ceiling__le,axiom,
% 5.15/5.49 ! [X: rat,A: int] :
% 5.15/5.49 ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) )
% 5.15/5.49 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ A ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_le
% 5.15/5.49 thf(fact_7758_less__ceiling__iff,axiom,
% 5.15/5.49 ! [Z: int,X: rat] :
% 5.15/5.49 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % less_ceiling_iff
% 5.15/5.49 thf(fact_7759_less__ceiling__iff,axiom,
% 5.15/5.49 ! [Z: int,X: real] :
% 5.15/5.49 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % less_ceiling_iff
% 5.15/5.49 thf(fact_7760_ceiling__add__le,axiom,
% 5.15/5.49 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_add_le
% 5.15/5.49 thf(fact_7761_ceiling__add__le,axiom,
% 5.15/5.49 ! [X: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_add_le
% 5.15/5.49 thf(fact_7762_of__int__ceiling__le__add__one,axiom,
% 5.15/5.49 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_int_ceiling_le_add_one
% 5.15/5.49 thf(fact_7763_of__int__ceiling__le__add__one,axiom,
% 5.15/5.49 ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_int_ceiling_le_add_one
% 5.15/5.49 thf(fact_7764_of__int__ceiling__diff__one__le,axiom,
% 5.15/5.49 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 5.15/5.49
% 5.15/5.49 % of_int_ceiling_diff_one_le
% 5.15/5.49 thf(fact_7765_of__int__ceiling__diff__one__le,axiom,
% 5.15/5.49 ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 5.15/5.49
% 5.15/5.49 % of_int_ceiling_diff_one_le
% 5.15/5.49 thf(fact_7766_ceiling__divide__eq__div,axiom,
% 5.15/5.49 ! [A: int,B: int] :
% 5.15/5.49 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.15/5.49 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_divide_eq_div
% 5.15/5.49 thf(fact_7767_ceiling__divide__eq__div,axiom,
% 5.15/5.49 ! [A: int,B: int] :
% 5.15/5.49 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 5.15/5.49 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_divide_eq_div
% 5.15/5.49 thf(fact_7768_ceiling__correct,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 5.15/5.49 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_correct
% 5.15/5.49 thf(fact_7769_ceiling__correct,axiom,
% 5.15/5.49 ! [X: rat] :
% 5.15/5.49 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 5.15/5.49 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_correct
% 5.15/5.49 thf(fact_7770_ceiling__unique,axiom,
% 5.15/5.49 ! [Z: int,X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) )
% 5.15/5.49 => ( ( archim7802044766580827645g_real @ X )
% 5.15/5.49 = Z ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_unique
% 5.15/5.49 thf(fact_7771_ceiling__unique,axiom,
% 5.15/5.49 ! [Z: int,X: rat] :
% 5.15/5.49 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 5.15/5.49 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 5.15/5.49 => ( ( archim2889992004027027881ng_rat @ X )
% 5.15/5.49 = Z ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_unique
% 5.15/5.49 thf(fact_7772_ceiling__eq__iff,axiom,
% 5.15/5.49 ! [X: real,A: int] :
% 5.15/5.49 ( ( ( archim7802044766580827645g_real @ X )
% 5.15/5.49 = A )
% 5.15/5.49 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 5.15/5.49 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_eq_iff
% 5.15/5.49 thf(fact_7773_ceiling__eq__iff,axiom,
% 5.15/5.49 ! [X: rat,A: int] :
% 5.15/5.49 ( ( ( archim2889992004027027881ng_rat @ X )
% 5.15/5.49 = A )
% 5.15/5.49 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 5.15/5.49 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_eq_iff
% 5.15/5.49 thf(fact_7774_ceiling__split,axiom,
% 5.15/5.49 ! [P: int > $o,T: real] :
% 5.15/5.49 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.15/5.49 = ( ! [I3: int] :
% 5.15/5.49 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) @ T )
% 5.15/5.49 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I3 ) ) )
% 5.15/5.49 => ( P @ I3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_split
% 5.15/5.49 thf(fact_7775_ceiling__split,axiom,
% 5.15/5.49 ! [P: int > $o,T: rat] :
% 5.15/5.49 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.15/5.49 = ( ! [I3: int] :
% 5.15/5.49 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T )
% 5.15/5.49 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I3 ) ) )
% 5.15/5.49 => ( P @ I3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_split
% 5.15/5.49 thf(fact_7776_mult__ceiling__le,axiom,
% 5.15/5.49 ! [A: real,B: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.49 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % mult_ceiling_le
% 5.15/5.49 thf(fact_7777_mult__ceiling__le,axiom,
% 5.15/5.49 ! [A: rat,B: rat] :
% 5.15/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.49 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % mult_ceiling_le
% 5.15/5.49 thf(fact_7778_ceiling__less__iff,axiom,
% 5.15/5.49 ! [X: real,Z: int] :
% 5.15/5.49 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 5.15/5.49 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_iff
% 5.15/5.49 thf(fact_7779_ceiling__less__iff,axiom,
% 5.15/5.49 ! [X: rat,Z: int] :
% 5.15/5.49 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_less_iff
% 5.15/5.49 thf(fact_7780_le__ceiling__iff,axiom,
% 5.15/5.49 ! [Z: int,X: rat] :
% 5.15/5.49 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 5.15/5.49 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % le_ceiling_iff
% 5.15/5.49 thf(fact_7781_le__ceiling__iff,axiom,
% 5.15/5.49 ! [Z: int,X: real] :
% 5.15/5.49 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 5.15/5.49 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % le_ceiling_iff
% 5.15/5.49 thf(fact_7782_ceiling__divide__upper,axiom,
% 5.15/5.49 ! [Q3: real,P2: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.15/5.49 => ( ord_less_eq_real @ P2 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_divide_upper
% 5.15/5.49 thf(fact_7783_ceiling__divide__upper,axiom,
% 5.15/5.49 ! [Q3: rat,P2: rat] :
% 5.15/5.49 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.15/5.49 => ( ord_less_eq_rat @ P2 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_divide_upper
% 5.15/5.49 thf(fact_7784_ceiling__divide__lower,axiom,
% 5.15/5.49 ! [Q3: real,P2: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.15/5.49 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_divide_lower
% 5.15/5.49 thf(fact_7785_ceiling__divide__lower,axiom,
% 5.15/5.49 ! [Q3: rat,P2: rat] :
% 5.15/5.49 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.15/5.49 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_divide_lower
% 5.15/5.49 thf(fact_7786_ceiling__eq,axiom,
% 5.15/5.49 ! [N2: int,X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.15/5.49 => ( ( archim7802044766580827645g_real @ X )
% 5.15/5.49 = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_eq
% 5.15/5.49 thf(fact_7787_ceiling__eq,axiom,
% 5.15/5.49 ! [N2: int,X: rat] :
% 5.15/5.49 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N2 ) @ X )
% 5.15/5.49 => ( ( ord_less_eq_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N2 ) @ one_one_rat ) )
% 5.15/5.49 => ( ( archim2889992004027027881ng_rat @ X )
% 5.15/5.49 = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_eq
% 5.15/5.49 thf(fact_7788_ceiling__log2__div2,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.49 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.15/5.49 = ( 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 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_log2_div2
% 5.15/5.49 thf(fact_7789_ceiling__log__nat__eq__if,axiom,
% 5.15/5.49 ! [B: nat,N2: nat,K: nat] :
% 5.15/5.49 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.15/5.49 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.15/5.49 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.15/5.49 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.15/5.49 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_log_nat_eq_if
% 5.15/5.49 thf(fact_7790_ceiling__log__nat__eq__powr__iff,axiom,
% 5.15/5.49 ! [B: nat,K: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.15/5.49 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.49 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.15/5.49 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 5.15/5.49 = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.15/5.49 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_log_nat_eq_powr_iff
% 5.15/5.49 thf(fact_7791_pi__series,axiom,
% 5.15/5.49 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = ( suminf_real
% 5.15/5.49 @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % pi_series
% 5.15/5.49 thf(fact_7792_upto_Opinduct,axiom,
% 5.15/5.49 ! [A0: int,A1: int,P: int > int > $o] :
% 5.15/5.49 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.15/5.49 => ( ! [I2: int,J2: int] :
% 5.15/5.49 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 5.15/5.49 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.15/5.49 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 5.15/5.49 => ( P @ I2 @ J2 ) ) )
% 5.15/5.49 => ( P @ A0 @ A1 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % upto.pinduct
% 5.15/5.49 thf(fact_7793_lemma__termdiff2,axiom,
% 5.15/5.49 ! [H2: rat,Z: rat,N2: nat] :
% 5.15/5.49 ( ( H2 != zero_zero_rat )
% 5.15/5.49 => ( ( 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 ) ) ) ) )
% 5.15/5.49 = ( times_times_rat @ H2
% 5.15/5.49 @ ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [P5: nat] :
% 5.15/5.49 ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [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 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lemma_termdiff2
% 5.15/5.49 thf(fact_7794_lemma__termdiff2,axiom,
% 5.15/5.49 ! [H2: complex,Z: complex,N2: nat] :
% 5.15/5.49 ( ( H2 != zero_zero_complex )
% 5.15/5.49 => ( ( 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 ) ) ) ) )
% 5.15/5.49 = ( times_times_complex @ H2
% 5.15/5.49 @ ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [P5: nat] :
% 5.15/5.49 ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [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 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lemma_termdiff2
% 5.15/5.49 thf(fact_7795_lemma__termdiff2,axiom,
% 5.15/5.49 ! [H2: real,Z: real,N2: nat] :
% 5.15/5.49 ( ( H2 != zero_zero_real )
% 5.15/5.49 => ( ( 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 ) ) ) ) )
% 5.15/5.49 = ( times_times_real @ H2
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [P5: nat] :
% 5.15/5.49 ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [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 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lemma_termdiff2
% 5.15/5.49 thf(fact_7796_summable__arctan__series,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_arctan_series
% 5.15/5.49 thf(fact_7797_ceiling__log__eq__powr__iff,axiom,
% 5.15/5.49 ! [X: real,B: real,K: nat] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 5.15/5.49 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.15/5.49 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 5.15/5.49 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ceiling_log_eq_powr_iff
% 5.15/5.49 thf(fact_7798_lessThan__iff,axiom,
% 5.15/5.49 ! [I: set_nat,K: set_nat] :
% 5.15/5.49 ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 5.15/5.49 = ( ord_less_set_nat @ I @ K ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_iff
% 5.15/5.49 thf(fact_7799_lessThan__iff,axiom,
% 5.15/5.49 ! [I: rat,K: rat] :
% 5.15/5.49 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 5.15/5.49 = ( ord_less_rat @ I @ K ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_iff
% 5.15/5.49 thf(fact_7800_lessThan__iff,axiom,
% 5.15/5.49 ! [I: num,K: num] :
% 5.15/5.49 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 5.15/5.49 = ( ord_less_num @ I @ K ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_iff
% 5.15/5.49 thf(fact_7801_lessThan__iff,axiom,
% 5.15/5.49 ! [I: int,K: int] :
% 5.15/5.49 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 5.15/5.49 = ( ord_less_int @ I @ K ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_iff
% 5.15/5.49 thf(fact_7802_lessThan__iff,axiom,
% 5.15/5.49 ! [I: nat,K: nat] :
% 5.15/5.49 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 5.15/5.49 = ( ord_less_nat @ I @ K ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_iff
% 5.15/5.49 thf(fact_7803_lessThan__iff,axiom,
% 5.15/5.49 ! [I: real,K: real] :
% 5.15/5.49 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 5.15/5.49 = ( ord_less_real @ I @ K ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_iff
% 5.15/5.49 thf(fact_7804_lessThan__iff,axiom,
% 5.15/5.49 ! [I: $o,K: $o] :
% 5.15/5.49 ( ( member_o @ I @ ( set_ord_lessThan_o @ K ) )
% 5.15/5.49 = ( ord_less_o @ I @ K ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_iff
% 5.15/5.49 thf(fact_7805_powr__one__eq__one,axiom,
% 5.15/5.49 ! [A: real] :
% 5.15/5.49 ( ( powr_real @ one_one_real @ A )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % powr_one_eq_one
% 5.15/5.49 thf(fact_7806_summable__single,axiom,
% 5.15/5.49 ! [I: nat,F: nat > complex] :
% 5.15/5.49 ( summable_complex
% 5.15/5.49 @ ^ [R5: nat] : ( if_complex @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_complex ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_single
% 5.15/5.49 thf(fact_7807_summable__single,axiom,
% 5.15/5.49 ! [I: nat,F: nat > real] :
% 5.15/5.49 ( summable_real
% 5.15/5.49 @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_single
% 5.15/5.49 thf(fact_7808_summable__single,axiom,
% 5.15/5.49 ! [I: nat,F: nat > nat] :
% 5.15/5.49 ( summable_nat
% 5.15/5.49 @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_single
% 5.15/5.49 thf(fact_7809_summable__single,axiom,
% 5.15/5.49 ! [I: nat,F: nat > int] :
% 5.15/5.49 ( summable_int
% 5.15/5.49 @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_single
% 5.15/5.49 thf(fact_7810_summable__zero,axiom,
% 5.15/5.49 ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : zero_zero_complex ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero
% 5.15/5.49 thf(fact_7811_summable__zero,axiom,
% 5.15/5.49 ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero
% 5.15/5.49 thf(fact_7812_summable__zero,axiom,
% 5.15/5.49 ( summable_nat
% 5.15/5.49 @ ^ [N3: nat] : zero_zero_nat ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero
% 5.15/5.49 thf(fact_7813_summable__zero,axiom,
% 5.15/5.49 ( summable_int
% 5.15/5.49 @ ^ [N3: nat] : zero_zero_int ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero
% 5.15/5.49 thf(fact_7814_summable__iff__shift,axiom,
% 5.15/5.49 ! [F: nat > real,K: nat] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.15/5.49 = ( summable_real @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_iff_shift
% 5.15/5.49 thf(fact_7815_summable__iff__shift,axiom,
% 5.15/5.49 ! [F: nat > complex,K: nat] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.15/5.49 = ( summable_complex @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_iff_shift
% 5.15/5.49 thf(fact_7816_lessThan__subset__iff,axiom,
% 5.15/5.49 ! [X: rat,Y: rat] :
% 5.15/5.49 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 5.15/5.49 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_subset_iff
% 5.15/5.49 thf(fact_7817_lessThan__subset__iff,axiom,
% 5.15/5.49 ! [X: num,Y: num] :
% 5.15/5.49 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 5.15/5.49 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_subset_iff
% 5.15/5.49 thf(fact_7818_lessThan__subset__iff,axiom,
% 5.15/5.49 ! [X: int,Y: int] :
% 5.15/5.49 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 5.15/5.49 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_subset_iff
% 5.15/5.49 thf(fact_7819_lessThan__subset__iff,axiom,
% 5.15/5.49 ! [X: nat,Y: nat] :
% 5.15/5.49 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.15/5.49 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_subset_iff
% 5.15/5.49 thf(fact_7820_lessThan__subset__iff,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 5.15/5.49 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_subset_iff
% 5.15/5.49 thf(fact_7821_lessThan__subset__iff,axiom,
% 5.15/5.49 ! [X: $o,Y: $o] :
% 5.15/5.49 ( ( ord_less_eq_set_o @ ( set_ord_lessThan_o @ X ) @ ( set_ord_lessThan_o @ Y ) )
% 5.15/5.49 = ( ord_less_eq_o @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_subset_iff
% 5.15/5.49 thf(fact_7822_powr__zero__eq__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( X = zero_zero_real )
% 5.15/5.49 => ( ( powr_real @ X @ zero_zero_real )
% 5.15/5.49 = zero_zero_real ) )
% 5.15/5.49 & ( ( X != zero_zero_real )
% 5.15/5.49 => ( ( powr_real @ X @ zero_zero_real )
% 5.15/5.49 = one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_zero_eq_one
% 5.15/5.49 thf(fact_7823_powr__gt__zero,axiom,
% 5.15/5.49 ! [X: real,A: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 5.15/5.49 = ( X != zero_zero_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_gt_zero
% 5.15/5.49 thf(fact_7824_powr__nonneg__iff,axiom,
% 5.15/5.49 ! [A: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 5.15/5.49 = ( A = zero_zero_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_nonneg_iff
% 5.15/5.49 thf(fact_7825_powr__less__cancel__iff,axiom,
% 5.15/5.49 ! [X: real,A: real,B: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.15/5.49 = ( ord_less_real @ A @ B ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_less_cancel_iff
% 5.15/5.49 thf(fact_7826_summable__cmult__iff,axiom,
% 5.15/5.49 ! [C: complex,F: nat > complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) ) )
% 5.15/5.49 = ( ( C = zero_zero_complex )
% 5.15/5.49 | ( summable_complex @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_cmult_iff
% 5.15/5.49 thf(fact_7827_summable__cmult__iff,axiom,
% 5.15/5.49 ! [C: real,F: nat > real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.15/5.49 = ( ( C = zero_zero_real )
% 5.15/5.49 | ( summable_real @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_cmult_iff
% 5.15/5.49 thf(fact_7828_summable__divide__iff,axiom,
% 5.15/5.49 ! [F: nat > complex,C: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) )
% 5.15/5.49 = ( ( C = zero_zero_complex )
% 5.15/5.49 | ( summable_complex @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_divide_iff
% 5.15/5.49 thf(fact_7829_summable__divide__iff,axiom,
% 5.15/5.49 ! [F: nat > real,C: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) )
% 5.15/5.49 = ( ( C = zero_zero_real )
% 5.15/5.49 | ( summable_real @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_divide_iff
% 5.15/5.49 thf(fact_7830_summable__If__finite,axiom,
% 5.15/5.49 ! [P: nat > $o,F: nat > complex] :
% 5.15/5.49 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_If_finite
% 5.15/5.49 thf(fact_7831_summable__If__finite,axiom,
% 5.15/5.49 ! [P: nat > $o,F: nat > real] :
% 5.15/5.49 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_If_finite
% 5.15/5.49 thf(fact_7832_summable__If__finite,axiom,
% 5.15/5.49 ! [P: nat > $o,F: nat > nat] :
% 5.15/5.49 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.49 => ( summable_nat
% 5.15/5.49 @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_If_finite
% 5.15/5.49 thf(fact_7833_summable__If__finite,axiom,
% 5.15/5.49 ! [P: nat > $o,F: nat > int] :
% 5.15/5.49 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.49 => ( summable_int
% 5.15/5.49 @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_If_finite
% 5.15/5.49 thf(fact_7834_summable__If__finite__set,axiom,
% 5.15/5.49 ! [A2: set_nat,F: nat > complex] :
% 5.15/5.49 ( ( finite_finite_nat @ A2 )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_If_finite_set
% 5.15/5.49 thf(fact_7835_summable__If__finite__set,axiom,
% 5.15/5.49 ! [A2: set_nat,F: nat > real] :
% 5.15/5.49 ( ( finite_finite_nat @ A2 )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_If_finite_set
% 5.15/5.49 thf(fact_7836_summable__If__finite__set,axiom,
% 5.15/5.49 ! [A2: set_nat,F: nat > nat] :
% 5.15/5.49 ( ( finite_finite_nat @ A2 )
% 5.15/5.49 => ( summable_nat
% 5.15/5.49 @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_If_finite_set
% 5.15/5.49 thf(fact_7837_summable__If__finite__set,axiom,
% 5.15/5.49 ! [A2: set_nat,F: nat > int] :
% 5.15/5.49 ( ( finite_finite_nat @ A2 )
% 5.15/5.49 => ( summable_int
% 5.15/5.49 @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_If_finite_set
% 5.15/5.49 thf(fact_7838_sum_OlessThan__Suc,axiom,
% 5.15/5.49 ! [G: nat > rat,N2: nat] :
% 5.15/5.49 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc
% 5.15/5.49 thf(fact_7839_sum_OlessThan__Suc,axiom,
% 5.15/5.49 ! [G: nat > int,N2: nat] :
% 5.15/5.49 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc
% 5.15/5.49 thf(fact_7840_sum_OlessThan__Suc,axiom,
% 5.15/5.49 ! [G: nat > complex,N2: nat] :
% 5.15/5.49 ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc
% 5.15/5.49 thf(fact_7841_sum_OlessThan__Suc,axiom,
% 5.15/5.49 ! [G: nat > nat,N2: nat] :
% 5.15/5.49 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc
% 5.15/5.49 thf(fact_7842_sum_OlessThan__Suc,axiom,
% 5.15/5.49 ! [G: nat > real,N2: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc
% 5.15/5.49 thf(fact_7843_powr__eq__one__iff,axiom,
% 5.15/5.49 ! [A: real,X: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ A )
% 5.15/5.49 => ( ( ( powr_real @ A @ X )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 = ( X = zero_zero_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_eq_one_iff
% 5.15/5.49 thf(fact_7844_powr__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( powr_real @ X @ one_one_real )
% 5.15/5.49 = X ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_one
% 5.15/5.49 thf(fact_7845_powr__one__gt__zero__iff,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( powr_real @ X @ one_one_real )
% 5.15/5.49 = X )
% 5.15/5.49 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_one_gt_zero_iff
% 5.15/5.49 thf(fact_7846_powr__le__cancel__iff,axiom,
% 5.15/5.49 ! [X: real,A: real,B: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.15/5.49 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_le_cancel_iff
% 5.15/5.49 thf(fact_7847_numeral__powr__numeral__real,axiom,
% 5.15/5.49 ! [M: num,N2: num] :
% 5.15/5.49 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.49 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % numeral_powr_numeral_real
% 5.15/5.49 thf(fact_7848_powr__log__cancel,axiom,
% 5.15/5.49 ! [A: real,X: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ( A != one_one_real )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 5.15/5.49 = X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_log_cancel
% 5.15/5.49 thf(fact_7849_log__powr__cancel,axiom,
% 5.15/5.49 ! [A: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ( A != one_one_real )
% 5.15/5.49 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 5.15/5.49 = Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % log_powr_cancel
% 5.15/5.49 thf(fact_7850_summable__geometric__iff,axiom,
% 5.15/5.49 ! [C: real] :
% 5.15/5.49 ( ( summable_real @ ( power_power_real @ C ) )
% 5.15/5.49 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_geometric_iff
% 5.15/5.49 thf(fact_7851_summable__geometric__iff,axiom,
% 5.15/5.49 ! [C: complex] :
% 5.15/5.49 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.15/5.49 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_geometric_iff
% 5.15/5.49 thf(fact_7852_powr__numeral,axiom,
% 5.15/5.49 ! [X: real,N2: num] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( powr_real @ X @ ( numeral_numeral_real @ N2 ) )
% 5.15/5.49 = ( power_power_real @ X @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_numeral
% 5.15/5.49 thf(fact_7853_square__powr__half,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = ( abs_abs_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % square_powr_half
% 5.15/5.49 thf(fact_7854_summable__norm__cancel,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( F @ N3 ) ) )
% 5.15/5.49 => ( summable_real @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_norm_cancel
% 5.15/5.49 thf(fact_7855_summable__norm__cancel,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) )
% 5.15/5.49 => ( summable_complex @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_norm_cancel
% 5.15/5.49 thf(fact_7856_powr__powr,axiom,
% 5.15/5.49 ! [X: real,A: real,B: real] :
% 5.15/5.49 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.15/5.49 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_powr
% 5.15/5.49 thf(fact_7857_summable__comparison__test,axiom,
% 5.15/5.49 ! [F: nat > real,G: nat > real] :
% 5.15/5.49 ( ? [N7: nat] :
% 5.15/5.49 ! [N: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N7 @ N )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( summable_real @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_comparison_test
% 5.15/5.49 thf(fact_7858_summable__comparison__test,axiom,
% 5.15/5.49 ! [F: nat > complex,G: nat > real] :
% 5.15/5.49 ( ? [N7: nat] :
% 5.15/5.49 ! [N: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N7 @ N )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( summable_complex @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_comparison_test
% 5.15/5.49 thf(fact_7859_summable__comparison__test_H,axiom,
% 5.15/5.49 ! [G: nat > real,N5: nat,F: nat > real] :
% 5.15/5.49 ( ( summable_real @ G )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N5 @ N )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.15/5.49 => ( summable_real @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_comparison_test'
% 5.15/5.49 thf(fact_7860_summable__comparison__test_H,axiom,
% 5.15/5.49 ! [G: nat > real,N5: nat,F: nat > complex] :
% 5.15/5.49 ( ( summable_real @ G )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N5 @ N )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.15/5.49 => ( summable_complex @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_comparison_test'
% 5.15/5.49 thf(fact_7861_summable__const__iff,axiom,
% 5.15/5.49 ! [C: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [Uu3: nat] : C )
% 5.15/5.49 = ( C = zero_zero_complex ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_const_iff
% 5.15/5.49 thf(fact_7862_summable__const__iff,axiom,
% 5.15/5.49 ! [C: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [Uu3: nat] : C )
% 5.15/5.49 = ( C = zero_zero_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_const_iff
% 5.15/5.49 thf(fact_7863_summable__mult,axiom,
% 5.15/5.49 ! [F: nat > complex,C: complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_mult
% 5.15/5.49 thf(fact_7864_summable__mult,axiom,
% 5.15/5.49 ! [F: nat > real,C: real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_mult
% 5.15/5.49 thf(fact_7865_summable__mult2,axiom,
% 5.15/5.49 ! [F: nat > complex,C: complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ C ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_mult2
% 5.15/5.49 thf(fact_7866_summable__mult2,axiom,
% 5.15/5.49 ! [F: nat > real,C: real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_mult2
% 5.15/5.49 thf(fact_7867_summable__add,axiom,
% 5.15/5.49 ! [F: nat > real,G: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_add
% 5.15/5.49 thf(fact_7868_summable__add,axiom,
% 5.15/5.49 ! [F: nat > nat,G: nat > nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ( summable_nat @ G )
% 5.15/5.49 => ( summable_nat
% 5.15/5.49 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_add
% 5.15/5.49 thf(fact_7869_summable__add,axiom,
% 5.15/5.49 ! [F: nat > int,G: nat > int] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ( summable_int @ G )
% 5.15/5.49 => ( summable_int
% 5.15/5.49 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_add
% 5.15/5.49 thf(fact_7870_summable__add,axiom,
% 5.15/5.49 ! [F: nat > complex,G: nat > complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( summable_complex @ G )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( plus_plus_complex @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_add
% 5.15/5.49 thf(fact_7871_summable__diff,axiom,
% 5.15/5.49 ! [F: nat > complex,G: nat > complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( summable_complex @ G )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_complex @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_diff
% 5.15/5.49 thf(fact_7872_summable__diff,axiom,
% 5.15/5.49 ! [F: nat > real,G: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_diff
% 5.15/5.49 thf(fact_7873_summable__divide,axiom,
% 5.15/5.49 ! [F: nat > complex,C: complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_divide
% 5.15/5.49 thf(fact_7874_summable__divide,axiom,
% 5.15/5.49 ! [F: nat > real,C: real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_divide
% 5.15/5.49 thf(fact_7875_summable__Suc__iff,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 5.15/5.49 = ( summable_real @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_Suc_iff
% 5.15/5.49 thf(fact_7876_summable__Suc__iff,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 5.15/5.49 = ( summable_complex @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_Suc_iff
% 5.15/5.49 thf(fact_7877_summable__minus__iff,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( uminus_uminus_real @ ( F @ N3 ) ) )
% 5.15/5.49 = ( summable_real @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_minus_iff
% 5.15/5.49 thf(fact_7878_summable__minus__iff,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( uminus1482373934393186551omplex @ ( F @ N3 ) ) )
% 5.15/5.49 = ( summable_complex @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_minus_iff
% 5.15/5.49 thf(fact_7879_summable__minus,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( uminus_uminus_real @ ( F @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_minus
% 5.15/5.49 thf(fact_7880_summable__minus,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( uminus1482373934393186551omplex @ ( F @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_minus
% 5.15/5.49 thf(fact_7881_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_complex,F: complex > nat > real] :
% 5.15/5.49 ( ! [I2: complex] :
% 5.15/5.49 ( ( member_complex @ I2 @ I5 )
% 5.15/5.49 => ( summable_real @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups5808333547571424918x_real
% 5.15/5.49 @ ^ [I3: complex] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7882_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_real,F: real > nat > real] :
% 5.15/5.49 ( ! [I2: real] :
% 5.15/5.49 ( ( member_real @ I2 @ I5 )
% 5.15/5.49 => ( summable_real @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups8097168146408367636l_real
% 5.15/5.49 @ ^ [I3: real] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7883_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_int,F: int > nat > real] :
% 5.15/5.49 ( ! [I2: int] :
% 5.15/5.49 ( ( member_int @ I2 @ I5 )
% 5.15/5.49 => ( summable_real @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups8778361861064173332t_real
% 5.15/5.49 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7884_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_real,F: real > nat > complex] :
% 5.15/5.49 ( ! [I2: real] :
% 5.15/5.49 ( ( member_real @ I2 @ I5 )
% 5.15/5.49 => ( summable_complex @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups5754745047067104278omplex
% 5.15/5.49 @ ^ [I3: real] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7885_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_nat,F: nat > nat > complex] :
% 5.15/5.49 ( ! [I2: nat] :
% 5.15/5.49 ( ( member_nat @ I2 @ I5 )
% 5.15/5.49 => ( summable_complex @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7886_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_int,F: int > nat > complex] :
% 5.15/5.49 ( ! [I2: int] :
% 5.15/5.49 ( ( member_int @ I2 @ I5 )
% 5.15/5.49 => ( summable_complex @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups3049146728041665814omplex
% 5.15/5.49 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7887_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_int,F: int > nat > int] :
% 5.15/5.49 ( ! [I2: int] :
% 5.15/5.49 ( ( member_int @ I2 @ I5 )
% 5.15/5.49 => ( summable_int @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_int
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups4538972089207619220nt_int
% 5.15/5.49 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7888_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_complex,F: complex > nat > complex] :
% 5.15/5.49 ( ! [I2: complex] :
% 5.15/5.49 ( ( member_complex @ I2 @ I5 )
% 5.15/5.49 => ( summable_complex @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups7754918857620584856omplex
% 5.15/5.49 @ ^ [I3: complex] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7889_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_nat,F: nat > nat > nat] :
% 5.15/5.49 ( ! [I2: nat] :
% 5.15/5.49 ( ( member_nat @ I2 @ I5 )
% 5.15/5.49 => ( summable_nat @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_nat
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups3542108847815614940at_nat
% 5.15/5.49 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7890_summable__sum,axiom,
% 5.15/5.49 ! [I5: set_nat,F: nat > nat > real] :
% 5.15/5.49 ( ! [I2: nat] :
% 5.15/5.49 ( ( member_nat @ I2 @ I5 )
% 5.15/5.49 => ( summable_real @ ( F @ I2 ) ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_sum
% 5.15/5.49 thf(fact_7891_summable__ignore__initial__segment,axiom,
% 5.15/5.49 ! [F: nat > real,K: nat] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_ignore_initial_segment
% 5.15/5.49 thf(fact_7892_summable__ignore__initial__segment,axiom,
% 5.15/5.49 ! [F: nat > complex,K: nat] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_ignore_initial_segment
% 5.15/5.49 thf(fact_7893_suminf__le__const,axiom,
% 5.15/5.49 ! [F: nat > int,X: int] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ X )
% 5.15/5.49 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_le_const
% 5.15/5.49 thf(fact_7894_suminf__le__const,axiom,
% 5.15/5.49 ! [F: nat > nat,X: nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ X )
% 5.15/5.49 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_le_const
% 5.15/5.49 thf(fact_7895_suminf__le__const,axiom,
% 5.15/5.49 ! [F: nat > real,X: real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ X )
% 5.15/5.49 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_le_const
% 5.15/5.49 thf(fact_7896_summable__rabs__cancel,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) )
% 5.15/5.49 => ( summable_real @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_rabs_cancel
% 5.15/5.49 thf(fact_7897_lessThan__def,axiom,
% 5.15/5.49 ( set_or890127255671739683et_nat
% 5.15/5.49 = ( ^ [U2: set_nat] :
% 5.15/5.49 ( collect_set_nat
% 5.15/5.49 @ ^ [X2: set_nat] : ( ord_less_set_nat @ X2 @ U2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_def
% 5.15/5.49 thf(fact_7898_lessThan__def,axiom,
% 5.15/5.49 ( set_ord_lessThan_rat
% 5.15/5.49 = ( ^ [U2: rat] :
% 5.15/5.49 ( collect_rat
% 5.15/5.49 @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_def
% 5.15/5.49 thf(fact_7899_lessThan__def,axiom,
% 5.15/5.49 ( set_ord_lessThan_num
% 5.15/5.49 = ( ^ [U2: num] :
% 5.15/5.49 ( collect_num
% 5.15/5.49 @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_def
% 5.15/5.49 thf(fact_7900_lessThan__def,axiom,
% 5.15/5.49 ( set_ord_lessThan_int
% 5.15/5.49 = ( ^ [U2: int] :
% 5.15/5.49 ( collect_int
% 5.15/5.49 @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_def
% 5.15/5.49 thf(fact_7901_lessThan__def,axiom,
% 5.15/5.49 ( set_ord_lessThan_nat
% 5.15/5.49 = ( ^ [U2: nat] :
% 5.15/5.49 ( collect_nat
% 5.15/5.49 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_def
% 5.15/5.49 thf(fact_7902_lessThan__def,axiom,
% 5.15/5.49 ( set_or5984915006950818249n_real
% 5.15/5.49 = ( ^ [U2: real] :
% 5.15/5.49 ( collect_real
% 5.15/5.49 @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_def
% 5.15/5.49 thf(fact_7903_lessThan__def,axiom,
% 5.15/5.49 ( set_ord_lessThan_o
% 5.15/5.49 = ( ^ [U2: $o] :
% 5.15/5.49 ( collect_o
% 5.15/5.49 @ ^ [X2: $o] : ( ord_less_o @ X2 @ U2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_def
% 5.15/5.49 thf(fact_7904_summableI__nonneg__bounded,axiom,
% 5.15/5.49 ! [F: nat > int,X: int] :
% 5.15/5.49 ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ X )
% 5.15/5.49 => ( summable_int @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summableI_nonneg_bounded
% 5.15/5.49 thf(fact_7905_summableI__nonneg__bounded,axiom,
% 5.15/5.49 ! [F: nat > nat,X: nat] :
% 5.15/5.49 ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ X )
% 5.15/5.49 => ( summable_nat @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summableI_nonneg_bounded
% 5.15/5.49 thf(fact_7906_summableI__nonneg__bounded,axiom,
% 5.15/5.49 ! [F: nat > real,X: real] :
% 5.15/5.49 ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ X )
% 5.15/5.49 => ( summable_real @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summableI_nonneg_bounded
% 5.15/5.49 thf(fact_7907_powser__insidea,axiom,
% 5.15/5.49 ! [F: nat > real,X: real,Z: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X @ N3 ) ) )
% 5.15/5.49 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_insidea
% 5.15/5.49 thf(fact_7908_powser__insidea,axiom,
% 5.15/5.49 ! [F: nat > complex,X: complex,Z: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X @ N3 ) ) )
% 5.15/5.49 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_insidea
% 5.15/5.49 thf(fact_7909_suminf__le,axiom,
% 5.15/5.49 ! [F: nat > real,G: nat > real] :
% 5.15/5.49 ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( G @ N ) )
% 5.15/5.49 => ( ( summable_real @ F )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_le
% 5.15/5.49 thf(fact_7910_suminf__le,axiom,
% 5.15/5.49 ! [F: nat > nat,G: nat > nat] :
% 5.15/5.49 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ ( G @ N ) )
% 5.15/5.49 => ( ( summable_nat @ F )
% 5.15/5.49 => ( ( summable_nat @ G )
% 5.15/5.49 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_le
% 5.15/5.49 thf(fact_7911_suminf__le,axiom,
% 5.15/5.49 ! [F: nat > int,G: nat > int] :
% 5.15/5.49 ( ! [N: nat] : ( ord_less_eq_int @ ( F @ N ) @ ( G @ N ) )
% 5.15/5.49 => ( ( summable_int @ F )
% 5.15/5.49 => ( ( summable_int @ G )
% 5.15/5.49 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_le
% 5.15/5.49 thf(fact_7912_powr__non__neg,axiom,
% 5.15/5.49 ! [A: real,X: real] :
% 5.15/5.49 ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % powr_non_neg
% 5.15/5.49 thf(fact_7913_powr__less__mono2__neg,axiom,
% 5.15/5.49 ! [A: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ Y )
% 5.15/5.49 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_less_mono2_neg
% 5.15/5.49 thf(fact_7914_powr__mono2,axiom,
% 5.15/5.49 ! [A: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.49 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_mono2
% 5.15/5.49 thf(fact_7915_powr__ge__pzero,axiom,
% 5.15/5.49 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_ge_pzero
% 5.15/5.49 thf(fact_7916_powr__less__cancel,axiom,
% 5.15/5.49 ! [X: real,A: real,B: real] :
% 5.15/5.49 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.15/5.49 => ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.49 => ( ord_less_real @ A @ B ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_less_cancel
% 5.15/5.49 thf(fact_7917_powr__less__mono,axiom,
% 5.15/5.49 ! [A: real,B: real,X: real] :
% 5.15/5.49 ( ( ord_less_real @ A @ B )
% 5.15/5.49 => ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.49 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_less_mono
% 5.15/5.49 thf(fact_7918_powr__mono,axiom,
% 5.15/5.49 ! [A: real,B: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.49 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.49 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_mono
% 5.15/5.49 thf(fact_7919_suminf__split__initial__segment,axiom,
% 5.15/5.49 ! [F: nat > complex,K: nat] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( suminf_complex @ F )
% 5.15/5.49 = ( plus_plus_complex
% 5.15/5.49 @ ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.15/5.49 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_split_initial_segment
% 5.15/5.49 thf(fact_7920_suminf__split__initial__segment,axiom,
% 5.15/5.49 ! [F: nat > real,K: nat] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( suminf_real @ F )
% 5.15/5.49 = ( plus_plus_real
% 5.15/5.49 @ ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.15/5.49 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_split_initial_segment
% 5.15/5.49 thf(fact_7921_suminf__minus__initial__segment,axiom,
% 5.15/5.49 ! [F: nat > complex,K: nat] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.15/5.49 = ( minus_minus_complex @ ( suminf_complex @ F ) @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_minus_initial_segment
% 5.15/5.49 thf(fact_7922_suminf__minus__initial__segment,axiom,
% 5.15/5.49 ! [F: nat > real,K: nat] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.15/5.49 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_minus_initial_segment
% 5.15/5.49 thf(fact_7923_lessThan__strict__subset__iff,axiom,
% 5.15/5.49 ! [M: rat,N2: rat] :
% 5.15/5.49 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 5.15/5.49 = ( ord_less_rat @ M @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_strict_subset_iff
% 5.15/5.49 thf(fact_7924_lessThan__strict__subset__iff,axiom,
% 5.15/5.49 ! [M: num,N2: num] :
% 5.15/5.49 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 5.15/5.49 = ( ord_less_num @ M @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_strict_subset_iff
% 5.15/5.49 thf(fact_7925_lessThan__strict__subset__iff,axiom,
% 5.15/5.49 ! [M: int,N2: int] :
% 5.15/5.49 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 5.15/5.49 = ( ord_less_int @ M @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_strict_subset_iff
% 5.15/5.49 thf(fact_7926_lessThan__strict__subset__iff,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_strict_subset_iff
% 5.15/5.49 thf(fact_7927_lessThan__strict__subset__iff,axiom,
% 5.15/5.49 ! [M: real,N2: real] :
% 5.15/5.49 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 5.15/5.49 = ( ord_less_real @ M @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_strict_subset_iff
% 5.15/5.49 thf(fact_7928_lessThan__strict__subset__iff,axiom,
% 5.15/5.49 ! [M: $o,N2: $o] :
% 5.15/5.49 ( ( ord_less_set_o @ ( set_ord_lessThan_o @ M ) @ ( set_ord_lessThan_o @ N2 ) )
% 5.15/5.49 = ( ord_less_o @ M @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_strict_subset_iff
% 5.15/5.49 thf(fact_7929_summable__mult__D,axiom,
% 5.15/5.49 ! [C: complex,F: nat > complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) ) )
% 5.15/5.49 => ( ( C != zero_zero_complex )
% 5.15/5.49 => ( summable_complex @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_mult_D
% 5.15/5.49 thf(fact_7930_summable__mult__D,axiom,
% 5.15/5.49 ! [C: real,F: nat > real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.15/5.49 => ( ( C != zero_zero_real )
% 5.15/5.49 => ( summable_real @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_mult_D
% 5.15/5.49 thf(fact_7931_summable__zero__power,axiom,
% 5.15/5.49 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero_power
% 5.15/5.49 thf(fact_7932_summable__zero__power,axiom,
% 5.15/5.49 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero_power
% 5.15/5.49 thf(fact_7933_summable__zero__power,axiom,
% 5.15/5.49 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero_power
% 5.15/5.49 thf(fact_7934_pi__not__less__zero,axiom,
% 5.15/5.49 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % pi_not_less_zero
% 5.15/5.49 thf(fact_7935_pi__gt__zero,axiom,
% 5.15/5.49 ord_less_real @ zero_zero_real @ pi ).
% 5.15/5.49
% 5.15/5.49 % pi_gt_zero
% 5.15/5.49 thf(fact_7936_pi__ge__zero,axiom,
% 5.15/5.49 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.15/5.49
% 5.15/5.49 % pi_ge_zero
% 5.15/5.49 thf(fact_7937_lessThan__Suc,axiom,
% 5.15/5.49 ! [K: nat] :
% 5.15/5.49 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.15/5.49 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_Suc
% 5.15/5.49 thf(fact_7938_sum__less__suminf,axiom,
% 5.15/5.49 ! [F: nat > int,N2: nat] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ! [M3: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.15/5.49 => ( ord_less_int @ zero_zero_int @ ( F @ M3 ) ) )
% 5.15/5.49 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_less_suminf
% 5.15/5.49 thf(fact_7939_sum__less__suminf,axiom,
% 5.15/5.49 ! [F: nat > nat,N2: nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ! [M3: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.15/5.49 => ( ord_less_nat @ zero_zero_nat @ ( F @ M3 ) ) )
% 5.15/5.49 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_less_suminf
% 5.15/5.49 thf(fact_7940_sum__less__suminf,axiom,
% 5.15/5.49 ! [F: nat > real,N2: nat] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [M3: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( F @ M3 ) ) )
% 5.15/5.49 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_less_suminf
% 5.15/5.49 thf(fact_7941_suminf__mult,axiom,
% 5.15/5.49 ! [F: nat > complex,C: complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) ) )
% 5.15/5.49 = ( times_times_complex @ C @ ( suminf_complex @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_mult
% 5.15/5.49 thf(fact_7942_suminf__mult,axiom,
% 5.15/5.49 ! [F: nat > real,C: real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.15/5.49 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_mult
% 5.15/5.49 thf(fact_7943_suminf__mult2,axiom,
% 5.15/5.49 ! [F: nat > complex,C: complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( times_times_complex @ ( suminf_complex @ F ) @ C )
% 5.15/5.49 = ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ C ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_mult2
% 5.15/5.49 thf(fact_7944_suminf__mult2,axiom,
% 5.15/5.49 ! [F: nat > real,C: real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.15/5.49 = ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_mult2
% 5.15/5.49 thf(fact_7945_suminf__add,axiom,
% 5.15/5.49 ! [F: nat > real,G: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.15/5.49 = ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_add
% 5.15/5.49 thf(fact_7946_suminf__add,axiom,
% 5.15/5.49 ! [F: nat > nat,G: nat > nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ( summable_nat @ G )
% 5.15/5.49 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.15/5.49 = ( suminf_nat
% 5.15/5.49 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_add
% 5.15/5.49 thf(fact_7947_suminf__add,axiom,
% 5.15/5.49 ! [F: nat > int,G: nat > int] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ( summable_int @ G )
% 5.15/5.49 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.15/5.49 = ( suminf_int
% 5.15/5.49 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_add
% 5.15/5.49 thf(fact_7948_suminf__add,axiom,
% 5.15/5.49 ! [F: nat > complex,G: nat > complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( summable_complex @ G )
% 5.15/5.49 => ( ( plus_plus_complex @ ( suminf_complex @ F ) @ ( suminf_complex @ G ) )
% 5.15/5.49 = ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( plus_plus_complex @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_add
% 5.15/5.49 thf(fact_7949_suminf__diff,axiom,
% 5.15/5.49 ! [F: nat > complex,G: nat > complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( summable_complex @ G )
% 5.15/5.49 => ( ( minus_minus_complex @ ( suminf_complex @ F ) @ ( suminf_complex @ G ) )
% 5.15/5.49 = ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_complex @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_diff
% 5.15/5.49 thf(fact_7950_suminf__diff,axiom,
% 5.15/5.49 ! [F: nat > real,G: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( ( minus_minus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.15/5.49 = ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_diff
% 5.15/5.49 thf(fact_7951_suminf__divide,axiom,
% 5.15/5.49 ! [F: nat > complex,C: complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_divide
% 5.15/5.49 thf(fact_7952_suminf__divide,axiom,
% 5.15/5.49 ! [F: nat > real,C: real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) )
% 5.15/5.49 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_divide
% 5.15/5.49 thf(fact_7953_suminf__minus,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( uminus_uminus_real @ ( F @ N3 ) ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( suminf_real @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_minus
% 5.15/5.49 thf(fact_7954_suminf__minus,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( uminus1482373934393186551omplex @ ( F @ N3 ) ) )
% 5.15/5.49 = ( uminus1482373934393186551omplex @ ( suminf_complex @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_minus
% 5.15/5.49 thf(fact_7955_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_complex,F: complex > nat > real] :
% 5.15/5.49 ( ! [I2: complex] :
% 5.15/5.49 ( ( member_complex @ I2 @ I5 )
% 5.15/5.49 => ( summable_real @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups5808333547571424918x_real
% 5.15/5.49 @ ^ [I3: complex] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups5808333547571424918x_real
% 5.15/5.49 @ ^ [I3: complex] : ( suminf_real @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7956_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_real,F: real > nat > real] :
% 5.15/5.49 ( ! [I2: real] :
% 5.15/5.49 ( ( member_real @ I2 @ I5 )
% 5.15/5.49 => ( summable_real @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups8097168146408367636l_real
% 5.15/5.49 @ ^ [I3: real] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups8097168146408367636l_real
% 5.15/5.49 @ ^ [I3: real] : ( suminf_real @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7957_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_int,F: int > nat > real] :
% 5.15/5.49 ( ! [I2: int] :
% 5.15/5.49 ( ( member_int @ I2 @ I5 )
% 5.15/5.49 => ( summable_real @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups8778361861064173332t_real
% 5.15/5.49 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups8778361861064173332t_real
% 5.15/5.49 @ ^ [I3: int] : ( suminf_real @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7958_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_real,F: real > nat > complex] :
% 5.15/5.49 ( ! [I2: real] :
% 5.15/5.49 ( ( member_real @ I2 @ I5 )
% 5.15/5.49 => ( summable_complex @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups5754745047067104278omplex
% 5.15/5.49 @ ^ [I3: real] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups5754745047067104278omplex
% 5.15/5.49 @ ^ [I3: real] : ( suminf_complex @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7959_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_nat,F: nat > nat > complex] :
% 5.15/5.49 ( ! [I2: nat] :
% 5.15/5.49 ( ( member_nat @ I2 @ I5 )
% 5.15/5.49 => ( summable_complex @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [I3: nat] : ( suminf_complex @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7960_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_int,F: int > nat > complex] :
% 5.15/5.49 ( ! [I2: int] :
% 5.15/5.49 ( ( member_int @ I2 @ I5 )
% 5.15/5.49 => ( summable_complex @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups3049146728041665814omplex
% 5.15/5.49 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups3049146728041665814omplex
% 5.15/5.49 @ ^ [I3: int] : ( suminf_complex @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7961_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_int,F: int > nat > int] :
% 5.15/5.49 ( ! [I2: int] :
% 5.15/5.49 ( ( member_int @ I2 @ I5 )
% 5.15/5.49 => ( summable_int @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_int
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups4538972089207619220nt_int
% 5.15/5.49 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups4538972089207619220nt_int
% 5.15/5.49 @ ^ [I3: int] : ( suminf_int @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7962_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_complex,F: complex > nat > complex] :
% 5.15/5.49 ( ! [I2: complex] :
% 5.15/5.49 ( ( member_complex @ I2 @ I5 )
% 5.15/5.49 => ( summable_complex @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups7754918857620584856omplex
% 5.15/5.49 @ ^ [I3: complex] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups7754918857620584856omplex
% 5.15/5.49 @ ^ [I3: complex] : ( suminf_complex @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7963_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_nat,F: nat > nat > nat] :
% 5.15/5.49 ( ! [I2: nat] :
% 5.15/5.49 ( ( member_nat @ I2 @ I5 )
% 5.15/5.49 => ( summable_nat @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_nat
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups3542108847815614940at_nat
% 5.15/5.49 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups3542108847815614940at_nat
% 5.15/5.49 @ ^ [I3: nat] : ( suminf_nat @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7964_suminf__sum,axiom,
% 5.15/5.49 ! [I5: set_nat,F: nat > nat > real] :
% 5.15/5.49 ( ! [I2: nat] :
% 5.15/5.49 ( ( member_nat @ I2 @ I5 )
% 5.15/5.49 => ( summable_real @ ( F @ I2 ) ) )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] :
% 5.15/5.49 ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.49 @ I5 ) )
% 5.15/5.49 = ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( suminf_real @ ( F @ I3 ) )
% 5.15/5.49 @ I5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_sum
% 5.15/5.49 thf(fact_7965_sum__less__suminf2,axiom,
% 5.15/5.49 ! [F: nat > int,N2: nat,I: nat] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ! [M3: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.15/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M3 ) ) )
% 5.15/5.49 => ( ( ord_less_eq_nat @ N2 @ I )
% 5.15/5.49 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.15/5.49 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_less_suminf2
% 5.15/5.49 thf(fact_7966_sum__less__suminf2,axiom,
% 5.15/5.49 ! [F: nat > nat,N2: nat,I: nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ! [M3: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.15/5.49 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M3 ) ) )
% 5.15/5.49 => ( ( ord_less_eq_nat @ N2 @ I )
% 5.15/5.49 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.15/5.49 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_less_suminf2
% 5.15/5.49 thf(fact_7967_sum__less__suminf2,axiom,
% 5.15/5.49 ! [F: nat > real,N2: nat,I: nat] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [M3: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.15/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M3 ) ) )
% 5.15/5.49 => ( ( ord_less_eq_nat @ N2 @ I )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.15/5.49 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_less_suminf2
% 5.15/5.49 thf(fact_7968_suminf__eq__zero__iff,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.15/5.49 => ( ( ( suminf_real @ F )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 = ( ! [N3: nat] :
% 5.15/5.49 ( ( F @ N3 )
% 5.15/5.49 = zero_zero_real ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_eq_zero_iff
% 5.15/5.49 thf(fact_7969_suminf__eq__zero__iff,axiom,
% 5.15/5.49 ! [F: nat > nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.15/5.49 => ( ( ( suminf_nat @ F )
% 5.15/5.49 = zero_zero_nat )
% 5.15/5.49 = ( ! [N3: nat] :
% 5.15/5.49 ( ( F @ N3 )
% 5.15/5.49 = zero_zero_nat ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_eq_zero_iff
% 5.15/5.49 thf(fact_7970_suminf__eq__zero__iff,axiom,
% 5.15/5.49 ! [F: nat > int] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.15/5.49 => ( ( ( suminf_int @ F )
% 5.15/5.49 = zero_zero_int )
% 5.15/5.49 = ( ! [N3: nat] :
% 5.15/5.49 ( ( F @ N3 )
% 5.15/5.49 = zero_zero_int ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_eq_zero_iff
% 5.15/5.49 thf(fact_7971_suminf__nonneg,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.15/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_nonneg
% 5.15/5.49 thf(fact_7972_suminf__nonneg,axiom,
% 5.15/5.49 ! [F: nat > nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.15/5.49 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_nonneg
% 5.15/5.49 thf(fact_7973_suminf__nonneg,axiom,
% 5.15/5.49 ! [F: nat > int] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.15/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_nonneg
% 5.15/5.49 thf(fact_7974_suminf__pos,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N ) )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos
% 5.15/5.49 thf(fact_7975_suminf__pos,axiom,
% 5.15/5.49 ! [F: nat > nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N ) )
% 5.15/5.49 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos
% 5.15/5.49 thf(fact_7976_suminf__pos,axiom,
% 5.15/5.49 ! [F: nat > int] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N ) )
% 5.15/5.49 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos
% 5.15/5.49 thf(fact_7977_powr__less__mono2,axiom,
% 5.15/5.49 ! [A: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ Y )
% 5.15/5.49 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_less_mono2
% 5.15/5.49 thf(fact_7978_powr__mono2_H,axiom,
% 5.15/5.49 ! [A: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.49 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_mono2'
% 5.15/5.49 thf(fact_7979_powr__inj,axiom,
% 5.15/5.49 ! [A: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ( A != one_one_real )
% 5.15/5.49 => ( ( ( powr_real @ A @ X )
% 5.15/5.49 = ( powr_real @ A @ Y ) )
% 5.15/5.49 = ( X = Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_inj
% 5.15/5.49 thf(fact_7980_gr__one__powr,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % gr_one_powr
% 5.15/5.49 thf(fact_7981_powr__le1,axiom,
% 5.15/5.49 ! [A: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.49 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_le1
% 5.15/5.49 thf(fact_7982_powr__mono__both,axiom,
% 5.15/5.49 ! [A: real,B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ( ord_less_eq_real @ A @ B )
% 5.15/5.49 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.49 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_mono_both
% 5.15/5.49 thf(fact_7983_ge__one__powr__ge__zero,axiom,
% 5.15/5.49 ! [X: real,A: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ge_one_powr_ge_zero
% 5.15/5.49 thf(fact_7984_powr__divide,axiom,
% 5.15/5.49 ! [X: real,Y: real,A: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 5.15/5.49 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_divide
% 5.15/5.49 thf(fact_7985_powr__mult,axiom,
% 5.15/5.49 ! [X: real,Y: real,A: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 5.15/5.49 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_mult
% 5.15/5.49 thf(fact_7986_divide__powr__uminus,axiom,
% 5.15/5.49 ! [A: real,B: real,C: real] :
% 5.15/5.49 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.15/5.49 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % divide_powr_uminus
% 5.15/5.49 thf(fact_7987_log__base__powr,axiom,
% 5.15/5.49 ! [A: real,B: real,X: real] :
% 5.15/5.49 ( ( A != zero_zero_real )
% 5.15/5.49 => ( ( log @ ( powr_real @ A @ B ) @ X )
% 5.15/5.49 = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % log_base_powr
% 5.15/5.49 thf(fact_7988_log__powr,axiom,
% 5.15/5.49 ! [X: real,B: real,Y: real] :
% 5.15/5.49 ( ( X != zero_zero_real )
% 5.15/5.49 => ( ( log @ B @ ( powr_real @ X @ Y ) )
% 5.15/5.49 = ( times_times_real @ Y @ ( log @ B @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % log_powr
% 5.15/5.49 thf(fact_7989_summable__0__powser,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_0_powser
% 5.15/5.49 thf(fact_7990_summable__0__powser,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_0_powser
% 5.15/5.49 thf(fact_7991_summable__zero__power_H,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero_power'
% 5.15/5.49 thf(fact_7992_summable__zero__power_H,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero_power'
% 5.15/5.49 thf(fact_7993_summable__zero__power_H,axiom,
% 5.15/5.49 ! [F: nat > int] :
% 5.15/5.49 ( summable_int
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_int @ ( F @ N3 ) @ ( power_power_int @ zero_zero_int @ N3 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_zero_power'
% 5.15/5.49 thf(fact_7994_ln__powr,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( X != zero_zero_real )
% 5.15/5.49 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 5.15/5.49 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ln_powr
% 5.15/5.49 thf(fact_7995_powser__split__head_I3_J,axiom,
% 5.15/5.49 ! [F: nat > complex,Z: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_split_head(3)
% 5.15/5.49 thf(fact_7996_powser__split__head_I3_J,axiom,
% 5.15/5.49 ! [F: nat > real,Z: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_split_head(3)
% 5.15/5.49 thf(fact_7997_summable__powser__split__head,axiom,
% 5.15/5.49 ! [F: nat > complex,Z: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 = ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_powser_split_head
% 5.15/5.49 thf(fact_7998_summable__powser__split__head,axiom,
% 5.15/5.49 ! [F: nat > real,Z: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 = ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_powser_split_head
% 5.15/5.49 thf(fact_7999_summable__powser__ignore__initial__segment,axiom,
% 5.15/5.49 ! [F: nat > complex,M: nat,Z: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 = ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_powser_ignore_initial_segment
% 5.15/5.49 thf(fact_8000_summable__powser__ignore__initial__segment,axiom,
% 5.15/5.49 ! [F: nat > real,M: nat,Z: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 = ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_powser_ignore_initial_segment
% 5.15/5.49 thf(fact_8001_powr__add,axiom,
% 5.15/5.49 ! [X: real,A: real,B: real] :
% 5.15/5.49 ( ( powr_real @ X @ ( plus_plus_real @ A @ B ) )
% 5.15/5.49 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_add
% 5.15/5.49 thf(fact_8002_powr__diff,axiom,
% 5.15/5.49 ! [W: real,Z1: real,Z22: real] :
% 5.15/5.49 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.15/5.49 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_diff
% 5.15/5.49 thf(fact_8003_summable__norm__comparison__test,axiom,
% 5.15/5.49 ! [F: nat > complex,G: nat > real] :
% 5.15/5.49 ( ? [N7: nat] :
% 5.15/5.49 ! [N: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N7 @ N )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_norm_comparison_test
% 5.15/5.49 thf(fact_8004_summable__rabs__comparison__test,axiom,
% 5.15/5.49 ! [F: nat > real,G: nat > real] :
% 5.15/5.49 ( ? [N7: nat] :
% 5.15/5.49 ! [N: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N7 @ N )
% 5.15/5.49 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.15/5.49 => ( ( summable_real @ G )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_rabs_comparison_test
% 5.15/5.49 thf(fact_8005_lessThan__nat__numeral,axiom,
% 5.15/5.49 ! [K: num] :
% 5.15/5.49 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.15/5.49 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lessThan_nat_numeral
% 5.15/5.49 thf(fact_8006_sum_Onat__diff__reindex,axiom,
% 5.15/5.49 ! [G: nat > nat,N2: nat] :
% 5.15/5.49 ( ( groups3542108847815614940at_nat
% 5.15/5.49 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.nat_diff_reindex
% 5.15/5.49 thf(fact_8007_sum_Onat__diff__reindex,axiom,
% 5.15/5.49 ! [G: nat > real,N2: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.nat_diff_reindex
% 5.15/5.49 thf(fact_8008_summable__rabs,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) )
% 5.15/5.49 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.15/5.49 @ ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_rabs
% 5.15/5.49 thf(fact_8009_sum__diff__distrib,axiom,
% 5.15/5.49 ! [Q: real > nat,P: real > nat,N2: real] :
% 5.15/5.49 ( ! [X3: real] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.15/5.49 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 5.15/5.49 = ( groups1935376822645274424al_nat
% 5.15/5.49 @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.15/5.49 @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_diff_distrib
% 5.15/5.49 thf(fact_8010_sum__diff__distrib,axiom,
% 5.15/5.49 ! [Q: $o > nat,P: $o > nat,N2: $o] :
% 5.15/5.49 ( ! [X3: $o] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.15/5.49 => ( ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ P @ ( set_ord_lessThan_o @ N2 ) ) @ ( groups8507830703676809646_o_nat @ Q @ ( set_ord_lessThan_o @ N2 ) ) )
% 5.15/5.49 = ( groups8507830703676809646_o_nat
% 5.15/5.49 @ ^ [X2: $o] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.15/5.49 @ ( set_ord_lessThan_o @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_diff_distrib
% 5.15/5.49 thf(fact_8011_sum__diff__distrib,axiom,
% 5.15/5.49 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 5.15/5.49 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.15/5.49 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.15/5.49 = ( groups3542108847815614940at_nat
% 5.15/5.49 @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_diff_distrib
% 5.15/5.49 thf(fact_8012_suminf__pos__iff,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.15/5.49 = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos_iff
% 5.15/5.49 thf(fact_8013_suminf__pos__iff,axiom,
% 5.15/5.49 ! [F: nat > nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.15/5.49 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.15/5.49 = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos_iff
% 5.15/5.49 thf(fact_8014_suminf__pos__iff,axiom,
% 5.15/5.49 ! [F: nat > int] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.15/5.49 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.15/5.49 = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos_iff
% 5.15/5.49 thf(fact_8015_suminf__pos2,axiom,
% 5.15/5.49 ! [F: nat > real,I: nat] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos2
% 5.15/5.49 thf(fact_8016_suminf__pos2,axiom,
% 5.15/5.49 ! [F: nat > nat,I: nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.15/5.49 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.15/5.49 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos2
% 5.15/5.49 thf(fact_8017_suminf__pos2,axiom,
% 5.15/5.49 ! [F: nat > int,I: nat] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.15/5.49 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.15/5.49 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_pos2
% 5.15/5.49 thf(fact_8018_powr__realpow,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.15/5.49 = ( power_power_real @ X @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_realpow
% 5.15/5.49 thf(fact_8019_powr__less__iff,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 5.15/5.49 = ( ord_less_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_less_iff
% 5.15/5.49 thf(fact_8020_less__powr__iff,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 5.15/5.49 = ( ord_less_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % less_powr_iff
% 5.15/5.49 thf(fact_8021_log__less__iff,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ ( log @ B @ X ) @ Y )
% 5.15/5.49 = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % log_less_iff
% 5.15/5.49 thf(fact_8022_less__log__iff,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ Y @ ( log @ B @ X ) )
% 5.15/5.49 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % less_log_iff
% 5.15/5.49 thf(fact_8023_powser__inside,axiom,
% 5.15/5.49 ! [F: nat > real,X: real,Z: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X @ N3 ) ) )
% 5.15/5.49 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_inside
% 5.15/5.49 thf(fact_8024_powser__inside,axiom,
% 5.15/5.49 ! [F: nat > complex,X: complex,Z: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X @ N3 ) ) )
% 5.15/5.49 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_inside
% 5.15/5.49 thf(fact_8025_summable__geometric,axiom,
% 5.15/5.49 ! [C: real] :
% 5.15/5.49 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.15/5.49 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_geometric
% 5.15/5.49 thf(fact_8026_summable__geometric,axiom,
% 5.15/5.49 ! [C: complex] :
% 5.15/5.49 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.15/5.49 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_geometric
% 5.15/5.49 thf(fact_8027_complete__algebra__summable__geometric,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ one_one_real )
% 5.15/5.49 => ( summable_real @ ( power_power_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % complete_algebra_summable_geometric
% 5.15/5.49 thf(fact_8028_complete__algebra__summable__geometric,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ one_one_real )
% 5.15/5.49 => ( summable_complex @ ( power_power_complex @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % complete_algebra_summable_geometric
% 5.15/5.49 thf(fact_8029_suminf__split__head,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 5.15/5.49 = ( minus_minus_complex @ ( suminf_complex @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_split_head
% 5.15/5.49 thf(fact_8030_suminf__split__head,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 5.15/5.49 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_split_head
% 5.15/5.49 thf(fact_8031_pi__less__4,axiom,
% 5.15/5.49 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % pi_less_4
% 5.15/5.49 thf(fact_8032_pi__ge__two,axiom,
% 5.15/5.49 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.15/5.49
% 5.15/5.49 % pi_ge_two
% 5.15/5.49 thf(fact_8033_pi__half__neq__two,axiom,
% 5.15/5.49 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.49 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % pi_half_neq_two
% 5.15/5.49 thf(fact_8034_sum__pos__lt__pair,axiom,
% 5.15/5.49 ! [F: nat > real,K: nat] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ! [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 ) ) ) ) )
% 5.15/5.49 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_pos_lt_pair
% 5.15/5.49 thf(fact_8035_sum_OlessThan__Suc__shift,axiom,
% 5.15/5.49 ! [G: nat > rat,N2: nat] :
% 5.15/5.49 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.15/5.49 @ ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc_shift
% 5.15/5.49 thf(fact_8036_sum_OlessThan__Suc__shift,axiom,
% 5.15/5.49 ! [G: nat > int,N2: nat] :
% 5.15/5.49 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.15/5.49 @ ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc_shift
% 5.15/5.49 thf(fact_8037_sum_OlessThan__Suc__shift,axiom,
% 5.15/5.49 ! [G: nat > complex,N2: nat] :
% 5.15/5.49 ( ( groups2073611262835488442omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_complex @ ( G @ zero_zero_nat )
% 5.15/5.49 @ ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc_shift
% 5.15/5.49 thf(fact_8038_sum_OlessThan__Suc__shift,axiom,
% 5.15/5.49 ! [G: nat > nat,N2: nat] :
% 5.15/5.49 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.15/5.49 @ ( groups3542108847815614940at_nat
% 5.15/5.49 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc_shift
% 5.15/5.49 thf(fact_8039_sum_OlessThan__Suc__shift,axiom,
% 5.15/5.49 ! [G: nat > real,N2: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.lessThan_Suc_shift
% 5.15/5.49 thf(fact_8040_sum__lessThan__telescope_H,axiom,
% 5.15/5.49 ! [F: nat > rat,M: nat] :
% 5.15/5.49 ( ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_lessThan_telescope'
% 5.15/5.49 thf(fact_8041_sum__lessThan__telescope_H,axiom,
% 5.15/5.49 ! [F: nat > int,M: nat] :
% 5.15/5.49 ( ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_lessThan_telescope'
% 5.15/5.49 thf(fact_8042_sum__lessThan__telescope_H,axiom,
% 5.15/5.49 ! [F: nat > real,M: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_lessThan_telescope'
% 5.15/5.49 thf(fact_8043_sum__lessThan__telescope,axiom,
% 5.15/5.49 ! [F: nat > rat,M: nat] :
% 5.15/5.49 ( ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_lessThan_telescope
% 5.15/5.49 thf(fact_8044_sum__lessThan__telescope,axiom,
% 5.15/5.49 ! [F: nat > int,M: nat] :
% 5.15/5.49 ( ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_lessThan_telescope
% 5.15/5.49 thf(fact_8045_sum__lessThan__telescope,axiom,
% 5.15/5.49 ! [F: nat > real,M: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_lessThan_telescope
% 5.15/5.49 thf(fact_8046_sumr__diff__mult__const2,axiom,
% 5.15/5.49 ! [F: nat > rat,N2: nat,R2: rat] :
% 5.15/5.49 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ R2 ) )
% 5.15/5.49 = ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ R2 )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sumr_diff_mult_const2
% 5.15/5.49 thf(fact_8047_sumr__diff__mult__const2,axiom,
% 5.15/5.49 ! [F: nat > int,N2: nat,R2: int] :
% 5.15/5.49 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ R2 ) )
% 5.15/5.49 = ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ R2 )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sumr_diff_mult_const2
% 5.15/5.49 thf(fact_8048_sumr__diff__mult__const2,axiom,
% 5.15/5.49 ! [F: nat > complex,N2: nat,R2: complex] :
% 5.15/5.49 ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ R2 ) )
% 5.15/5.49 = ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [I3: nat] : ( minus_minus_complex @ ( F @ I3 ) @ R2 )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sumr_diff_mult_const2
% 5.15/5.49 thf(fact_8049_sumr__diff__mult__const2,axiom,
% 5.15/5.49 ! [F: nat > real,N2: nat,R2: real] :
% 5.15/5.49 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ R2 ) )
% 5.15/5.49 = ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ R2 )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sumr_diff_mult_const2
% 5.15/5.49 thf(fact_8050_summable__norm,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( F @ N3 ) ) )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 5.15/5.49 @ ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_norm
% 5.15/5.49 thf(fact_8051_summable__norm,axiom,
% 5.15/5.49 ! [F: nat > complex] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 5.15/5.49 @ ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_norm
% 5.15/5.49 thf(fact_8052_sum_OatLeast1__atMost__eq,axiom,
% 5.15/5.49 ! [G: nat > nat,N2: nat] :
% 5.15/5.49 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.15/5.49 = ( groups3542108847815614940at_nat
% 5.15/5.49 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.atLeast1_atMost_eq
% 5.15/5.49 thf(fact_8053_sum_OatLeast1__atMost__eq,axiom,
% 5.15/5.49 ! [G: nat > real,N2: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.15/5.49 = ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum.atLeast1_atMost_eq
% 5.15/5.49 thf(fact_8054_powr__minus__divide,axiom,
% 5.15/5.49 ! [X: real,A: real] :
% 5.15/5.49 ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 5.15/5.49 = ( divide_divide_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_minus_divide
% 5.15/5.49 thf(fact_8055_sum__le__suminf,axiom,
% 5.15/5.49 ! [F: nat > int,I5: set_nat] :
% 5.15/5.49 ( ( summable_int @ F )
% 5.15/5.49 => ( ( finite_finite_nat @ I5 )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ( member_nat @ N @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.15/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) ) )
% 5.15/5.49 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_le_suminf
% 5.15/5.49 thf(fact_8056_sum__le__suminf,axiom,
% 5.15/5.49 ! [F: nat > nat,I5: set_nat] :
% 5.15/5.49 ( ( summable_nat @ F )
% 5.15/5.49 => ( ( finite_finite_nat @ I5 )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ( member_nat @ N @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.15/5.49 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) ) )
% 5.15/5.49 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_le_suminf
% 5.15/5.49 thf(fact_8057_sum__le__suminf,axiom,
% 5.15/5.49 ! [F: nat > real,I5: set_nat] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( finite_finite_nat @ I5 )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ( member_nat @ N @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.15/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) ) )
% 5.15/5.49 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_le_suminf
% 5.15/5.49 thf(fact_8058_powr__neg__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.49 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_neg_one
% 5.15/5.49 thf(fact_8059_powr__mult__base,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 5.15/5.49 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_mult_base
% 5.15/5.49 thf(fact_8060_powr__le__iff,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 5.15/5.49 = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_le_iff
% 5.15/5.49 thf(fact_8061_le__powr__iff,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 5.15/5.49 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % le_powr_iff
% 5.15/5.49 thf(fact_8062_log__le__iff,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 5.15/5.49 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % log_le_iff
% 5.15/5.49 thf(fact_8063_le__log__iff,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 5.15/5.49 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % le_log_iff
% 5.15/5.49 thf(fact_8064_pi__half__neq__zero,axiom,
% 5.15/5.49 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.49 != zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % pi_half_neq_zero
% 5.15/5.49 thf(fact_8065_pi__half__less__two,axiom,
% 5.15/5.49 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.15/5.49
% 5.15/5.49 % pi_half_less_two
% 5.15/5.49 thf(fact_8066_pi__half__le__two,axiom,
% 5.15/5.49 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.15/5.49
% 5.15/5.49 % pi_half_le_two
% 5.15/5.49 thf(fact_8067_power__diff__1__eq,axiom,
% 5.15/5.49 ! [X: complex,N2: nat] :
% 5.15/5.49 ( ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ one_one_complex )
% 5.15/5.49 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % power_diff_1_eq
% 5.15/5.49 thf(fact_8068_power__diff__1__eq,axiom,
% 5.15/5.49 ! [X: rat,N2: nat] :
% 5.15/5.49 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat )
% 5.15/5.49 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % power_diff_1_eq
% 5.15/5.49 thf(fact_8069_power__diff__1__eq,axiom,
% 5.15/5.49 ! [X: int,N2: nat] :
% 5.15/5.49 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ one_one_int )
% 5.15/5.49 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % power_diff_1_eq
% 5.15/5.49 thf(fact_8070_power__diff__1__eq,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ one_one_real )
% 5.15/5.49 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % power_diff_1_eq
% 5.15/5.49 thf(fact_8071_one__diff__power__eq,axiom,
% 5.15/5.49 ! [X: complex,N2: nat] :
% 5.15/5.49 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) )
% 5.15/5.49 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_diff_power_eq
% 5.15/5.49 thf(fact_8072_one__diff__power__eq,axiom,
% 5.15/5.49 ! [X: rat,N2: nat] :
% 5.15/5.49 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 5.15/5.49 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_diff_power_eq
% 5.15/5.49 thf(fact_8073_one__diff__power__eq,axiom,
% 5.15/5.49 ! [X: int,N2: nat] :
% 5.15/5.49 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 5.15/5.49 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_diff_power_eq
% 5.15/5.49 thf(fact_8074_one__diff__power__eq,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) )
% 5.15/5.49 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_diff_power_eq
% 5.15/5.49 thf(fact_8075_geometric__sum,axiom,
% 5.15/5.49 ! [X: complex,N2: nat] :
% 5.15/5.49 ( ( X != one_one_complex )
% 5.15/5.49 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % geometric_sum
% 5.15/5.49 thf(fact_8076_geometric__sum,axiom,
% 5.15/5.49 ! [X: rat,N2: nat] :
% 5.15/5.49 ( ( X != one_one_rat )
% 5.15/5.49 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % geometric_sum
% 5.15/5.49 thf(fact_8077_geometric__sum,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( X != one_one_real )
% 5.15/5.49 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % geometric_sum
% 5.15/5.49 thf(fact_8078_powser__split__head_I1_J,axiom,
% 5.15/5.49 ! [F: nat > complex,Z: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 => ( ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.15/5.49 @ ( times_times_complex
% 5.15/5.49 @ ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 @ Z ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_split_head(1)
% 5.15/5.49 thf(fact_8079_powser__split__head_I1_J,axiom,
% 5.15/5.49 ! [F: nat > real,Z: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 => ( ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.15/5.49 @ ( times_times_real
% 5.15/5.49 @ ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 @ Z ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_split_head(1)
% 5.15/5.49 thf(fact_8080_powser__split__head_I2_J,axiom,
% 5.15/5.49 ! [F: nat > complex,Z: complex] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 => ( ( times_times_complex
% 5.15/5.49 @ ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 @ Z )
% 5.15/5.49 = ( minus_minus_complex
% 5.15/5.49 @ ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.15/5.49 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_split_head(2)
% 5.15/5.49 thf(fact_8081_powser__split__head_I2_J,axiom,
% 5.15/5.49 ! [F: nat > real,Z: real] :
% 5.15/5.49 ( ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 => ( ( times_times_real
% 5.15/5.49 @ ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 @ Z )
% 5.15/5.49 = ( minus_minus_real
% 5.15/5.49 @ ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.15/5.49 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powser_split_head(2)
% 5.15/5.49 thf(fact_8082_ln__powr__bound,axiom,
% 5.15/5.49 ! [X: real,A: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ln_powr_bound
% 5.15/5.49 thf(fact_8083_ln__powr__bound2,axiom,
% 5.15/5.49 ! [X: real,A: real] :
% 5.15/5.49 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.49 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % ln_powr_bound2
% 5.15/5.49 thf(fact_8084_add__log__eq__powr,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.49 => ( ( B != one_one_real )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 5.15/5.49 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % add_log_eq_powr
% 5.15/5.49 thf(fact_8085_log__add__eq__powr,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.49 => ( ( B != one_one_real )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 5.15/5.49 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % log_add_eq_powr
% 5.15/5.49 thf(fact_8086_summable__partial__sum__bound,axiom,
% 5.15/5.49 ! [F: nat > complex,E: real] :
% 5.15/5.49 ( ( summable_complex @ F )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.15/5.49 => ~ ! [N8: nat] :
% 5.15/5.49 ~ ! [M4: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N8 @ M4 )
% 5.15/5.49 => ! [N9: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M4 @ N9 ) ) ) @ E ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_partial_sum_bound
% 5.15/5.49 thf(fact_8087_summable__partial__sum__bound,axiom,
% 5.15/5.49 ! [F: nat > real,E: real] :
% 5.15/5.49 ( ( summable_real @ F )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.15/5.49 => ~ ! [N8: nat] :
% 5.15/5.49 ~ ! [M4: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N8 @ M4 )
% 5.15/5.49 => ! [N9: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M4 @ N9 ) ) ) @ E ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_partial_sum_bound
% 5.15/5.49 thf(fact_8088_suminf__exist__split,axiom,
% 5.15/5.49 ! [R2: real,F: nat > real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.15/5.49 => ( ( summable_real @ F )
% 5.15/5.49 => ? [N8: nat] :
% 5.15/5.49 ! [N9: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N8 @ N9 )
% 5.15/5.49 => ( ord_less_real
% 5.15/5.49 @ ( real_V7735802525324610683m_real
% 5.15/5.49 @ ( suminf_real
% 5.15/5.49 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N9 ) ) ) )
% 5.15/5.49 @ R2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_exist_split
% 5.15/5.49 thf(fact_8089_suminf__exist__split,axiom,
% 5.15/5.49 ! [R2: real,F: nat > complex] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.15/5.49 => ( ( summable_complex @ F )
% 5.15/5.49 => ? [N8: nat] :
% 5.15/5.49 ! [N9: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N8 @ N9 )
% 5.15/5.49 => ( ord_less_real
% 5.15/5.49 @ ( real_V1022390504157884413omplex
% 5.15/5.49 @ ( suminf_complex
% 5.15/5.49 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N9 ) ) ) )
% 5.15/5.49 @ R2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_exist_split
% 5.15/5.49 thf(fact_8090_minus__log__eq__powr,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.49 => ( ( B != one_one_real )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 5.15/5.49 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % minus_log_eq_powr
% 5.15/5.49 thf(fact_8091_summable__power__series,axiom,
% 5.15/5.49 ! [F: nat > real,Z: real] :
% 5.15/5.49 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 5.15/5.49 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.15/5.49 => ( ( ord_less_real @ Z @ one_one_real )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_power_series
% 5.15/5.49 thf(fact_8092_Abel__lemma,axiom,
% 5.15/5.49 ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.15/5.49 => ( ( ord_less_real @ R2 @ R0 )
% 5.15/5.49 => ( ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R0 @ N ) ) @ M7 )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R2 @ N3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Abel_lemma
% 5.15/5.49 thf(fact_8093_sum__gp__strict,axiom,
% 5.15/5.49 ! [X: rat,N2: nat] :
% 5.15/5.49 ( ( ( X = one_one_rat )
% 5.15/5.49 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( semiri681578069525770553at_rat @ N2 ) ) )
% 5.15/5.49 & ( ( X != one_one_rat )
% 5.15/5.49 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_gp_strict
% 5.15/5.49 thf(fact_8094_sum__gp__strict,axiom,
% 5.15/5.49 ! [X: complex,N2: nat] :
% 5.15/5.49 ( ( ( X = one_one_complex )
% 5.15/5.49 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.15/5.49 & ( ( X != one_one_complex )
% 5.15/5.49 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_gp_strict
% 5.15/5.49 thf(fact_8095_sum__gp__strict,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( ( X = one_one_real )
% 5.15/5.49 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.15/5.49 & ( ( X != one_one_real )
% 5.15/5.49 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_gp_strict
% 5.15/5.49 thf(fact_8096_lemma__termdiff1,axiom,
% 5.15/5.49 ! [Z: complex,H2: complex,M: nat] :
% 5.15/5.49 ( ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lemma_termdiff1
% 5.15/5.49 thf(fact_8097_lemma__termdiff1,axiom,
% 5.15/5.49 ! [Z: rat,H2: rat,M: nat] :
% 5.15/5.49 ( ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lemma_termdiff1
% 5.15/5.49 thf(fact_8098_lemma__termdiff1,axiom,
% 5.15/5.49 ! [Z: int,H2: int,M: nat] :
% 5.15/5.49 ( ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lemma_termdiff1
% 5.15/5.49 thf(fact_8099_lemma__termdiff1,axiom,
% 5.15/5.49 ! [Z: real,H2: real,M: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) )
% 5.15/5.49 = ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % lemma_termdiff1
% 5.15/5.49 thf(fact_8100_pi__half__gt__zero,axiom,
% 5.15/5.49 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % pi_half_gt_zero
% 5.15/5.49 thf(fact_8101_power__diff__sumr2,axiom,
% 5.15/5.49 ! [X: complex,N2: nat,Y: complex] :
% 5.15/5.49 ( ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.15/5.49 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.15/5.49 @ ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % power_diff_sumr2
% 5.15/5.49 thf(fact_8102_power__diff__sumr2,axiom,
% 5.15/5.49 ! [X: rat,N2: nat,Y: rat] :
% 5.15/5.49 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.15/5.49 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.15/5.49 @ ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % power_diff_sumr2
% 5.15/5.49 thf(fact_8103_power__diff__sumr2,axiom,
% 5.15/5.49 ! [X: int,N2: nat,Y: int] :
% 5.15/5.49 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.15/5.49 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.15/5.49 @ ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % power_diff_sumr2
% 5.15/5.49 thf(fact_8104_power__diff__sumr2,axiom,
% 5.15/5.49 ! [X: real,N2: nat,Y: real] :
% 5.15/5.49 ( ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.15/5.49 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_real @ X @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % power_diff_sumr2
% 5.15/5.49 thf(fact_8105_diff__power__eq__sum,axiom,
% 5.15/5.49 ! [X: complex,N2: nat,Y: complex] :
% 5.15/5.49 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.15/5.49 @ ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X @ P5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % diff_power_eq_sum
% 5.15/5.49 thf(fact_8106_diff__power__eq__sum,axiom,
% 5.15/5.49 ! [X: rat,N2: nat,Y: rat] :
% 5.15/5.49 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.15/5.49 @ ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X @ P5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % diff_power_eq_sum
% 5.15/5.49 thf(fact_8107_diff__power__eq__sum,axiom,
% 5.15/5.49 ! [X: int,N2: nat,Y: int] :
% 5.15/5.49 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.15/5.49 @ ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X @ P5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % diff_power_eq_sum
% 5.15/5.49 thf(fact_8108_diff__power__eq__sum,axiom,
% 5.15/5.49 ! [X: real,N2: nat,Y: real] :
% 5.15/5.49 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 5.15/5.49 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X @ P5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % diff_power_eq_sum
% 5.15/5.49 thf(fact_8109_pi__half__ge__zero,axiom,
% 5.15/5.49 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % pi_half_ge_zero
% 5.15/5.49 thf(fact_8110_m2pi__less__pi,axiom,
% 5.15/5.49 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.15/5.49
% 5.15/5.49 % m2pi_less_pi
% 5.15/5.49 thf(fact_8111_powr__def,axiom,
% 5.15/5.49 ( powr_real
% 5.15/5.49 = ( ^ [X2: real,A3: real] : ( if_real @ ( X2 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A3 @ ( ln_ln_real @ X2 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_def
% 5.15/5.49 thf(fact_8112_summable__ratio__test,axiom,
% 5.15/5.49 ! [C: real,N5: nat,F: nat > real] :
% 5.15/5.49 ( ( ord_less_real @ C @ one_one_real )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N5 @ N )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N ) ) ) ) )
% 5.15/5.49 => ( summable_real @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_ratio_test
% 5.15/5.49 thf(fact_8113_summable__ratio__test,axiom,
% 5.15/5.49 ! [C: real,N5: nat,F: nat > complex] :
% 5.15/5.49 ( ( ord_less_real @ C @ one_one_real )
% 5.15/5.49 => ( ! [N: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N5 @ N )
% 5.15/5.49 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) )
% 5.15/5.49 => ( summable_complex @ F ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_ratio_test
% 5.15/5.49 thf(fact_8114_arctan__ubound,axiom,
% 5.15/5.49 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % arctan_ubound
% 5.15/5.49 thf(fact_8115_arctan__one,axiom,
% 5.15/5.49 ( ( arctan @ one_one_real )
% 5.15/5.49 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % arctan_one
% 5.15/5.49 thf(fact_8116_real__sum__nat__ivl__bounded2,axiom,
% 5.15/5.49 ! [N2: nat,F: nat > rat,K5: rat,K: nat] :
% 5.15/5.49 ( ! [P7: nat] :
% 5.15/5.49 ( ( ord_less_nat @ P7 @ N2 )
% 5.15/5.49 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.15/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.15/5.49 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % real_sum_nat_ivl_bounded2
% 5.15/5.49 thf(fact_8117_real__sum__nat__ivl__bounded2,axiom,
% 5.15/5.49 ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 5.15/5.49 ( ! [P7: nat] :
% 5.15/5.49 ( ( ord_less_nat @ P7 @ N2 )
% 5.15/5.49 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.15/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.15/5.49 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % real_sum_nat_ivl_bounded2
% 5.15/5.49 thf(fact_8118_real__sum__nat__ivl__bounded2,axiom,
% 5.15/5.49 ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 5.15/5.49 ( ! [P7: nat] :
% 5.15/5.49 ( ( ord_less_nat @ P7 @ N2 )
% 5.15/5.49 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.15/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.15/5.49 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % real_sum_nat_ivl_bounded2
% 5.15/5.49 thf(fact_8119_real__sum__nat__ivl__bounded2,axiom,
% 5.15/5.49 ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 5.15/5.49 ( ! [P7: nat] :
% 5.15/5.49 ( ( ord_less_nat @ P7 @ N2 )
% 5.15/5.49 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.15/5.49 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % real_sum_nat_ivl_bounded2
% 5.15/5.49 thf(fact_8120_log__minus__eq__powr,axiom,
% 5.15/5.49 ! [B: real,X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.49 => ( ( B != one_one_real )
% 5.15/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 5.15/5.49 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % log_minus_eq_powr
% 5.15/5.49 thf(fact_8121_one__diff__power__eq_H,axiom,
% 5.15/5.49 ! [X: complex,N2: nat] :
% 5.15/5.49 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) )
% 5.15/5.49 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 5.15/5.49 @ ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [I3: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_diff_power_eq'
% 5.15/5.49 thf(fact_8122_one__diff__power__eq_H,axiom,
% 5.15/5.49 ! [X: rat,N2: nat] :
% 5.15/5.49 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 5.15/5.49 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 5.15/5.49 @ ( groups2906978787729119204at_rat
% 5.15/5.49 @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_diff_power_eq'
% 5.15/5.49 thf(fact_8123_one__diff__power__eq_H,axiom,
% 5.15/5.49 ! [X: int,N2: nat] :
% 5.15/5.49 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 5.15/5.49 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 5.15/5.49 @ ( groups3539618377306564664at_int
% 5.15/5.49 @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_diff_power_eq'
% 5.15/5.49 thf(fact_8124_one__diff__power__eq_H,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) )
% 5.15/5.49 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % one_diff_power_eq'
% 5.15/5.49 thf(fact_8125_minus__pi__half__less__zero,axiom,
% 5.15/5.49 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.15/5.49
% 5.15/5.49 % minus_pi_half_less_zero
% 5.15/5.49 thf(fact_8126_arctan__bounded,axiom,
% 5.15/5.49 ! [Y: real] :
% 5.15/5.49 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.15/5.49 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % arctan_bounded
% 5.15/5.49 thf(fact_8127_arctan__lbound,axiom,
% 5.15/5.49 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.15/5.49
% 5.15/5.49 % arctan_lbound
% 5.15/5.49 thf(fact_8128_powr__half__sqrt,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = ( sqrt @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_half_sqrt
% 5.15/5.49 thf(fact_8129_powr__neg__numeral,axiom,
% 5.15/5.49 ! [X: real,N2: num] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.15/5.49 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % powr_neg_numeral
% 5.15/5.49 thf(fact_8130_sum__split__even__odd,axiom,
% 5.15/5.49 ! [F: nat > real,G: nat > real,N2: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.49 = ( plus_plus_real
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_split_even_odd
% 5.15/5.49 thf(fact_8131_machin__Euler,axiom,
% 5.15/5.49 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.15/5.49 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % machin_Euler
% 5.15/5.49 thf(fact_8132_machin,axiom,
% 5.15/5.49 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % machin
% 5.15/5.49 thf(fact_8133_sum__bounds__lt__plus1,axiom,
% 5.15/5.49 ! [F: nat > nat,Mm: nat] :
% 5.15/5.49 ( ( groups3542108847815614940at_nat
% 5.15/5.49 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.15/5.49 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_bounds_lt_plus1
% 5.15/5.49 thf(fact_8134_sum__bounds__lt__plus1,axiom,
% 5.15/5.49 ! [F: nat > real,Mm: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.15/5.49 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sum_bounds_lt_plus1
% 5.15/5.49 thf(fact_8135_sin__cos__npi,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( 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 ) ) ) )
% 5.15/5.49 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_npi
% 5.15/5.49 thf(fact_8136_sumr__cos__zero__one,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ zero_zero_real @ M5 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % sumr_cos_zero_one
% 5.15/5.49 thf(fact_8137_cos__pi__eq__zero,axiom,
% 5.15/5.49 ! [M: nat] :
% 5.15/5.49 ( ( 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 ) ) ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_pi_eq_zero
% 5.15/5.49 thf(fact_8138_arcosh__def,axiom,
% 5.15/5.49 ( arcosh_real
% 5.15/5.49 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % arcosh_def
% 5.15/5.49 thf(fact_8139_summable__complex__of__real,axiom,
% 5.15/5.49 ! [F: nat > real] :
% 5.15/5.49 ( ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( real_V4546457046886955230omplex @ ( F @ N3 ) ) )
% 5.15/5.49 = ( summable_real @ F ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_complex_of_real
% 5.15/5.49 thf(fact_8140_cos__zero,axiom,
% 5.15/5.49 ( ( cos_complex @ zero_zero_complex )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % cos_zero
% 5.15/5.49 thf(fact_8141_cos__zero,axiom,
% 5.15/5.49 ( ( cos_real @ zero_zero_real )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_zero
% 5.15/5.49 thf(fact_8142_of__real__1,axiom,
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_1
% 5.15/5.49 thf(fact_8143_of__real__1,axiom,
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_1
% 5.15/5.49 thf(fact_8144_of__real__eq__1__iff,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( real_V1803761363581548252l_real @ X )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 = ( X = one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_eq_1_iff
% 5.15/5.49 thf(fact_8145_of__real__eq__1__iff,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( real_V4546457046886955230omplex @ X )
% 5.15/5.49 = one_one_complex )
% 5.15/5.49 = ( X = one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_eq_1_iff
% 5.15/5.49 thf(fact_8146_of__real__numeral,axiom,
% 5.15/5.49 ! [W: num] :
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.15/5.49 = ( numeral_numeral_real @ W ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_numeral
% 5.15/5.49 thf(fact_8147_of__real__numeral,axiom,
% 5.15/5.49 ! [W: num] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.15/5.49 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_numeral
% 5.15/5.49 thf(fact_8148_of__real__mult,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X @ Y ) )
% 5.15/5.49 = ( times_times_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_mult
% 5.15/5.49 thf(fact_8149_of__real__mult,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X @ Y ) )
% 5.15/5.49 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_mult
% 5.15/5.49 thf(fact_8150_of__real__divide,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.49 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_divide
% 5.15/5.49 thf(fact_8151_of__real__divide,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_divide
% 5.15/5.49 thf(fact_8152_of__real__add,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.49 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_add
% 5.15/5.49 thf(fact_8153_of__real__add,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.49 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_add
% 5.15/5.49 thf(fact_8154_of__real__power,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X @ N2 ) )
% 5.15/5.49 = ( power_power_real @ ( real_V1803761363581548252l_real @ X ) @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_power
% 5.15/5.49 thf(fact_8155_of__real__power,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X @ N2 ) )
% 5.15/5.49 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X ) @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_power
% 5.15/5.49 thf(fact_8156_of__real__diff,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ ( minus_minus_real @ X @ Y ) )
% 5.15/5.49 = ( minus_minus_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_diff
% 5.15/5.49 thf(fact_8157_of__real__diff,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( minus_minus_real @ X @ Y ) )
% 5.15/5.49 = ( minus_minus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_diff
% 5.15/5.49 thf(fact_8158_sin__pi__minus,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 5.15/5.49 = ( sin_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_pi_minus
% 5.15/5.49 thf(fact_8159_cos__coeff__0,axiom,
% 5.15/5.49 ( ( cos_coeff @ zero_zero_nat )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_coeff_0
% 5.15/5.49 thf(fact_8160_of__real__sum,axiom,
% 5.15/5.49 ! [F: complex > real,S: set_complex] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( groups5808333547571424918x_real @ F @ S ) )
% 5.15/5.49 = ( groups7754918857620584856omplex
% 5.15/5.49 @ ^ [X2: complex] : ( real_V4546457046886955230omplex @ ( F @ X2 ) )
% 5.15/5.49 @ S ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_sum
% 5.15/5.49 thf(fact_8161_of__real__sum,axiom,
% 5.15/5.49 ! [F: nat > real,S: set_nat] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( groups6591440286371151544t_real @ F @ S ) )
% 5.15/5.49 = ( groups2073611262835488442omplex
% 5.15/5.49 @ ^ [X2: nat] : ( real_V4546457046886955230omplex @ ( F @ X2 ) )
% 5.15/5.49 @ S ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_sum
% 5.15/5.49 thf(fact_8162_of__real__sum,axiom,
% 5.15/5.49 ! [F: nat > real,S: set_nat] :
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ ( groups6591440286371151544t_real @ F @ S ) )
% 5.15/5.49 = ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [X2: nat] : ( real_V1803761363581548252l_real @ ( F @ X2 ) )
% 5.15/5.49 @ S ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_sum
% 5.15/5.49 thf(fact_8163_cos__pi,axiom,
% 5.15/5.49 ( ( cos_real @ pi )
% 5.15/5.49 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_pi
% 5.15/5.49 thf(fact_8164_cos__periodic__pi,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_periodic_pi
% 5.15/5.49 thf(fact_8165_cos__periodic__pi2,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_periodic_pi2
% 5.15/5.49 thf(fact_8166_sin__periodic__pi,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_periodic_pi
% 5.15/5.49 thf(fact_8167_sin__periodic__pi2,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_periodic_pi2
% 5.15/5.49 thf(fact_8168_cos__pi__minus,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_pi_minus
% 5.15/5.49 thf(fact_8169_cos__minus__pi,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_minus_pi
% 5.15/5.49 thf(fact_8170_sin__minus__pi,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_minus_pi
% 5.15/5.49 thf(fact_8171_sin__cos__squared__add3,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_squared_add3
% 5.15/5.49 thf(fact_8172_sin__cos__squared__add3,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_squared_add3
% 5.15/5.49 thf(fact_8173_of__real__neg__numeral,axiom,
% 5.15/5.49 ! [W: num] :
% 5.15/5.49 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_neg_numeral
% 5.15/5.49 thf(fact_8174_of__real__neg__numeral,axiom,
% 5.15/5.49 ! [W: num] :
% 5.15/5.49 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.49 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % of_real_neg_numeral
% 5.15/5.49 thf(fact_8175_cos__of__real__pi,axiom,
% 5.15/5.49 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.15/5.49 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_of_real_pi
% 5.15/5.49 thf(fact_8176_cos__of__real__pi,axiom,
% 5.15/5.49 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.15/5.49 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_of_real_pi
% 5.15/5.49 thf(fact_8177_sin__npi2,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_npi2
% 5.15/5.49 thf(fact_8178_sin__npi,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_npi
% 5.15/5.49 thf(fact_8179_sin__npi__int,axiom,
% 5.15/5.49 ! [N2: int] :
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_npi_int
% 5.15/5.49 thf(fact_8180_cos__pi__half,axiom,
% 5.15/5.49 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_pi_half
% 5.15/5.49 thf(fact_8181_sin__two__pi,axiom,
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_two_pi
% 5.15/5.49 thf(fact_8182_sin__pi__half,axiom,
% 5.15/5.49 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_pi_half
% 5.15/5.49 thf(fact_8183_cos__two__pi,axiom,
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_two_pi
% 5.15/5.49 thf(fact_8184_norm__of__real__add1,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ one_one_real ) )
% 5.15/5.49 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_of_real_add1
% 5.15/5.49 thf(fact_8185_norm__of__real__add1,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ one_one_complex ) )
% 5.15/5.49 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_of_real_add1
% 5.15/5.49 thf(fact_8186_norm__of__real__addn,axiom,
% 5.15/5.49 ! [X: real,B: num] :
% 5.15/5.49 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( numeral_numeral_real @ B ) ) )
% 5.15/5.49 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_of_real_addn
% 5.15/5.49 thf(fact_8187_norm__of__real__addn,axiom,
% 5.15/5.49 ! [X: real,B: num] :
% 5.15/5.49 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( numera6690914467698888265omplex @ B ) ) )
% 5.15/5.49 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_of_real_addn
% 5.15/5.49 thf(fact_8188_cos__periodic,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.15/5.49 = ( cos_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_periodic
% 5.15/5.49 thf(fact_8189_sin__periodic,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.15/5.49 = ( sin_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_periodic
% 5.15/5.49 thf(fact_8190_cos__2pi__minus,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.15/5.49 = ( cos_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_2pi_minus
% 5.15/5.49 thf(fact_8191_cos__npi2,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.15/5.49 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_npi2
% 5.15/5.49 thf(fact_8192_cos__npi,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.15/5.49 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_npi
% 5.15/5.49 thf(fact_8193_sin__cos__squared__add,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_squared_add
% 5.15/5.49 thf(fact_8194_sin__cos__squared__add,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_squared_add
% 5.15/5.49 thf(fact_8195_sin__cos__squared__add2,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_squared_add2
% 5.15/5.49 thf(fact_8196_sin__cos__squared__add2,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_squared_add2
% 5.15/5.49 thf(fact_8197_cos__of__real__pi__half,axiom,
% 5.15/5.49 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_of_real_pi_half
% 5.15/5.49 thf(fact_8198_cos__of__real__pi__half,axiom,
% 5.15/5.49 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = zero_zero_complex ) ).
% 5.15/5.49
% 5.15/5.49 % cos_of_real_pi_half
% 5.15/5.49 thf(fact_8199_sin__of__real__pi__half,axiom,
% 5.15/5.49 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_of_real_pi_half
% 5.15/5.49 thf(fact_8200_sin__of__real__pi__half,axiom,
% 5.15/5.49 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % sin_of_real_pi_half
% 5.15/5.49 thf(fact_8201_sin__2npi,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_2npi
% 5.15/5.49 thf(fact_8202_cos__2npi,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_2npi
% 5.15/5.49 thf(fact_8203_sin__2pi__minus,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_2pi_minus
% 5.15/5.49 thf(fact_8204_sin__int__2pin,axiom,
% 5.15/5.49 ! [N2: int] :
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_int_2pin
% 5.15/5.49 thf(fact_8205_cos__int__2pin,axiom,
% 5.15/5.49 ! [N2: int] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_int_2pin
% 5.15/5.49 thf(fact_8206_cos__3over2__pi,axiom,
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_3over2_pi
% 5.15/5.49 thf(fact_8207_sin__3over2__pi,axiom,
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.15/5.49 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_3over2_pi
% 5.15/5.49 thf(fact_8208_cos__npi__int,axiom,
% 5.15/5.49 ! [N2: int] :
% 5.15/5.49 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.49 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.15/5.49 = one_one_real ) )
% 5.15/5.49 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.49 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.15/5.49 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_npi_int
% 5.15/5.49 thf(fact_8209_sin__add,axiom,
% 5.15/5.49 ! [X: complex,Y: complex] :
% 5.15/5.49 ( ( sin_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.15/5.49 = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_add
% 5.15/5.49 thf(fact_8210_sin__add,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( sin_real @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.49 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_add
% 5.15/5.49 thf(fact_8211_uminus__set__def,axiom,
% 5.15/5.49 ( uminus612125837232591019t_real
% 5.15/5.49 = ( ^ [A7: set_real] :
% 5.15/5.49 ( collect_real
% 5.15/5.49 @ ( uminus_uminus_real_o
% 5.15/5.49 @ ^ [X2: real] : ( member_real @ X2 @ A7 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % uminus_set_def
% 5.15/5.49 thf(fact_8212_uminus__set__def,axiom,
% 5.15/5.49 ( uminus6221592323253981072nt_int
% 5.15/5.49 = ( ^ [A7: set_Pr958786334691620121nt_int] :
% 5.15/5.49 ( collec213857154873943460nt_int
% 5.15/5.49 @ ( uminus7117520113953359693_int_o
% 5.15/5.49 @ ^ [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ A7 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % uminus_set_def
% 5.15/5.49 thf(fact_8213_uminus__set__def,axiom,
% 5.15/5.49 ( uminus8566677241136511917omplex
% 5.15/5.49 = ( ^ [A7: set_complex] :
% 5.15/5.49 ( collect_complex
% 5.15/5.49 @ ( uminus1680532995456772888plex_o
% 5.15/5.49 @ ^ [X2: complex] : ( member_complex @ X2 @ A7 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % uminus_set_def
% 5.15/5.49 thf(fact_8214_uminus__set__def,axiom,
% 5.15/5.49 ( uminus613421341184616069et_nat
% 5.15/5.49 = ( ^ [A7: set_set_nat] :
% 5.15/5.49 ( collect_set_nat
% 5.15/5.49 @ ( uminus6401447641752708672_nat_o
% 5.15/5.49 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A7 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % uminus_set_def
% 5.15/5.49 thf(fact_8215_uminus__set__def,axiom,
% 5.15/5.49 ( uminus5710092332889474511et_nat
% 5.15/5.49 = ( ^ [A7: set_nat] :
% 5.15/5.49 ( collect_nat
% 5.15/5.49 @ ( uminus_uminus_nat_o
% 5.15/5.49 @ ^ [X2: nat] : ( member_nat @ X2 @ A7 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % uminus_set_def
% 5.15/5.49 thf(fact_8216_uminus__set__def,axiom,
% 5.15/5.49 ( uminus1532241313380277803et_int
% 5.15/5.49 = ( ^ [A7: set_int] :
% 5.15/5.49 ( collect_int
% 5.15/5.49 @ ( uminus_uminus_int_o
% 5.15/5.49 @ ^ [X2: int] : ( member_int @ X2 @ A7 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % uminus_set_def
% 5.15/5.49 thf(fact_8217_Collect__neg__eq,axiom,
% 5.15/5.49 ! [P: product_prod_int_int > $o] :
% 5.15/5.49 ( ( collec213857154873943460nt_int
% 5.15/5.49 @ ^ [X2: product_prod_int_int] :
% 5.15/5.49 ~ ( P @ X2 ) )
% 5.15/5.49 = ( uminus6221592323253981072nt_int @ ( collec213857154873943460nt_int @ P ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Collect_neg_eq
% 5.15/5.49 thf(fact_8218_Collect__neg__eq,axiom,
% 5.15/5.49 ! [P: complex > $o] :
% 5.15/5.49 ( ( collect_complex
% 5.15/5.49 @ ^ [X2: complex] :
% 5.15/5.49 ~ ( P @ X2 ) )
% 5.15/5.49 = ( uminus8566677241136511917omplex @ ( collect_complex @ P ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Collect_neg_eq
% 5.15/5.49 thf(fact_8219_Collect__neg__eq,axiom,
% 5.15/5.49 ! [P: set_nat > $o] :
% 5.15/5.49 ( ( collect_set_nat
% 5.15/5.49 @ ^ [X2: set_nat] :
% 5.15/5.49 ~ ( P @ X2 ) )
% 5.15/5.49 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Collect_neg_eq
% 5.15/5.49 thf(fact_8220_Collect__neg__eq,axiom,
% 5.15/5.49 ! [P: nat > $o] :
% 5.15/5.49 ( ( collect_nat
% 5.15/5.49 @ ^ [X2: nat] :
% 5.15/5.49 ~ ( P @ X2 ) )
% 5.15/5.49 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Collect_neg_eq
% 5.15/5.49 thf(fact_8221_Collect__neg__eq,axiom,
% 5.15/5.49 ! [P: int > $o] :
% 5.15/5.49 ( ( collect_int
% 5.15/5.49 @ ^ [X2: int] :
% 5.15/5.49 ~ ( P @ X2 ) )
% 5.15/5.49 = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Collect_neg_eq
% 5.15/5.49 thf(fact_8222_Compl__eq,axiom,
% 5.15/5.49 ( uminus612125837232591019t_real
% 5.15/5.49 = ( ^ [A7: set_real] :
% 5.15/5.49 ( collect_real
% 5.15/5.49 @ ^ [X2: real] :
% 5.15/5.49 ~ ( member_real @ X2 @ A7 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Compl_eq
% 5.15/5.49 thf(fact_8223_Compl__eq,axiom,
% 5.15/5.49 ( uminus6221592323253981072nt_int
% 5.15/5.49 = ( ^ [A7: set_Pr958786334691620121nt_int] :
% 5.15/5.49 ( collec213857154873943460nt_int
% 5.15/5.49 @ ^ [X2: product_prod_int_int] :
% 5.15/5.49 ~ ( member5262025264175285858nt_int @ X2 @ A7 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Compl_eq
% 5.15/5.49 thf(fact_8224_Compl__eq,axiom,
% 5.15/5.49 ( uminus8566677241136511917omplex
% 5.15/5.49 = ( ^ [A7: set_complex] :
% 5.15/5.49 ( collect_complex
% 5.15/5.49 @ ^ [X2: complex] :
% 5.15/5.49 ~ ( member_complex @ X2 @ A7 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Compl_eq
% 5.15/5.49 thf(fact_8225_Compl__eq,axiom,
% 5.15/5.49 ( uminus613421341184616069et_nat
% 5.15/5.49 = ( ^ [A7: set_set_nat] :
% 5.15/5.49 ( collect_set_nat
% 5.15/5.49 @ ^ [X2: set_nat] :
% 5.15/5.49 ~ ( member_set_nat @ X2 @ A7 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Compl_eq
% 5.15/5.49 thf(fact_8226_Compl__eq,axiom,
% 5.15/5.49 ( uminus5710092332889474511et_nat
% 5.15/5.49 = ( ^ [A7: set_nat] :
% 5.15/5.49 ( collect_nat
% 5.15/5.49 @ ^ [X2: nat] :
% 5.15/5.49 ~ ( member_nat @ X2 @ A7 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Compl_eq
% 5.15/5.49 thf(fact_8227_Compl__eq,axiom,
% 5.15/5.49 ( uminus1532241313380277803et_int
% 5.15/5.49 = ( ^ [A7: set_int] :
% 5.15/5.49 ( collect_int
% 5.15/5.49 @ ^ [X2: int] :
% 5.15/5.49 ~ ( member_int @ X2 @ A7 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Compl_eq
% 5.15/5.49 thf(fact_8228_sin__diff,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( sin_real @ ( minus_minus_real @ X @ Y ) )
% 5.15/5.49 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_diff
% 5.15/5.49 thf(fact_8229_polar__Ex,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ? [R3: real,A5: real] :
% 5.15/5.49 ( ( X
% 5.15/5.49 = ( times_times_real @ R3 @ ( cos_real @ A5 ) ) )
% 5.15/5.49 & ( Y
% 5.15/5.49 = ( times_times_real @ R3 @ ( sin_real @ A5 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % polar_Ex
% 5.15/5.49 thf(fact_8230_cos__one__sin__zero,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( ( cos_complex @ X )
% 5.15/5.49 = one_one_complex )
% 5.15/5.49 => ( ( sin_complex @ X )
% 5.15/5.49 = zero_zero_complex ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_one_sin_zero
% 5.15/5.49 thf(fact_8231_cos__one__sin__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( cos_real @ X )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 => ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_one_sin_zero
% 5.15/5.49 thf(fact_8232_cos__int__times__real,axiom,
% 5.15/5.49 ! [M: int,X: real] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 5.15/5.49 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_int_times_real
% 5.15/5.49 thf(fact_8233_cos__int__times__real,axiom,
% 5.15/5.49 ! [M: int,X: real] :
% 5.15/5.49 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 5.15/5.49 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_int_times_real
% 5.15/5.49 thf(fact_8234_sin__int__times__real,axiom,
% 5.15/5.49 ! [M: int,X: real] :
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 5.15/5.49 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_int_times_real
% 5.15/5.49 thf(fact_8235_sin__int__times__real,axiom,
% 5.15/5.49 ! [M: int,X: real] :
% 5.15/5.49 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 5.15/5.49 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_int_times_real
% 5.15/5.49 thf(fact_8236_cos__diff,axiom,
% 5.15/5.49 ! [X: complex,Y: complex] :
% 5.15/5.49 ( ( cos_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.15/5.49 = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_diff
% 5.15/5.49 thf(fact_8237_cos__diff,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.15/5.49 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_diff
% 5.15/5.49 thf(fact_8238_cos__add,axiom,
% 5.15/5.49 ! [X: complex,Y: complex] :
% 5.15/5.49 ( ( cos_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.15/5.49 = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_add
% 5.15/5.49 thf(fact_8239_cos__add,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.49 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_add
% 5.15/5.49 thf(fact_8240_sin__zero__norm__cos__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 5.15/5.49 = one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_zero_norm_cos_one
% 5.15/5.49 thf(fact_8241_sin__zero__norm__cos__one,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( ( sin_complex @ X )
% 5.15/5.49 = zero_zero_complex )
% 5.15/5.49 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 5.15/5.49 = one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_zero_norm_cos_one
% 5.15/5.49 thf(fact_8242_sin__zero__abs__cos__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 => ( ( abs_abs_real @ ( cos_real @ X ) )
% 5.15/5.49 = one_one_real ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_zero_abs_cos_one
% 5.15/5.49 thf(fact_8243_sin__cos__eq,axiom,
% 5.15/5.49 ( sin_real
% 5.15/5.49 = ( ^ [X2: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_eq
% 5.15/5.49 thf(fact_8244_sin__cos__eq,axiom,
% 5.15/5.49 ( sin_complex
% 5.15/5.49 = ( ^ [X2: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_eq
% 5.15/5.49 thf(fact_8245_cos__sin__eq,axiom,
% 5.15/5.49 ( cos_real
% 5.15/5.49 = ( ^ [X2: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_sin_eq
% 5.15/5.49 thf(fact_8246_cos__sin__eq,axiom,
% 5.15/5.49 ( cos_complex
% 5.15/5.49 = ( ^ [X2: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_sin_eq
% 5.15/5.49 thf(fact_8247_sin__double,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_double
% 5.15/5.49 thf(fact_8248_sin__double,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_double
% 5.15/5.49 thf(fact_8249_sincos__principal__value,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ? [Y3: real] :
% 5.15/5.49 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.15/5.49 & ( ord_less_eq_real @ Y3 @ pi )
% 5.15/5.49 & ( ( sin_real @ Y3 )
% 5.15/5.49 = ( sin_real @ X ) )
% 5.15/5.49 & ( ( cos_real @ Y3 )
% 5.15/5.49 = ( cos_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sincos_principal_value
% 5.15/5.49 thf(fact_8250_sin__x__le__x,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_x_le_x
% 5.15/5.49 thf(fact_8251_minus__sin__cos__eq,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( uminus_uminus_real @ ( sin_real @ X ) )
% 5.15/5.49 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % minus_sin_cos_eq
% 5.15/5.49 thf(fact_8252_minus__sin__cos__eq,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X ) )
% 5.15/5.49 = ( cos_complex @ ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % minus_sin_cos_eq
% 5.15/5.49 thf(fact_8253_sin__le__one,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_le_one
% 5.15/5.49 thf(fact_8254_cos__le__one,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_le_one
% 5.15/5.49 thf(fact_8255_abs__sin__x__le__abs__x,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % abs_sin_x_le_abs_x
% 5.15/5.49 thf(fact_8256_sin__cos__le1,axiom,
% 5.15/5.49 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_le1
% 5.15/5.49 thf(fact_8257_summable__of__real,axiom,
% 5.15/5.49 ! [X8: nat > real] :
% 5.15/5.49 ( ( summable_real @ X8 )
% 5.15/5.49 => ( summable_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V1803761363581548252l_real @ ( X8 @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_of_real
% 5.15/5.49 thf(fact_8258_summable__of__real,axiom,
% 5.15/5.49 ! [X8: nat > real] :
% 5.15/5.49 ( ( summable_real @ X8 )
% 5.15/5.49 => ( summable_complex
% 5.15/5.49 @ ^ [N3: nat] : ( real_V4546457046886955230omplex @ ( X8 @ N3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % summable_of_real
% 5.15/5.49 thf(fact_8259_cos__squared__eq,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_squared_eq
% 5.15/5.49 thf(fact_8260_cos__squared__eq,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_squared_eq
% 5.15/5.49 thf(fact_8261_sin__squared__eq,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_squared_eq
% 5.15/5.49 thf(fact_8262_sin__squared__eq,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_squared_eq
% 5.15/5.49 thf(fact_8263_nonzero__of__real__divide,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( Y != zero_zero_real )
% 5.15/5.49 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.49 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % nonzero_of_real_divide
% 5.15/5.49 thf(fact_8264_nonzero__of__real__divide,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( Y != zero_zero_real )
% 5.15/5.49 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % nonzero_of_real_divide
% 5.15/5.49 thf(fact_8265_sin__gt__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ pi )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_gt_zero
% 5.15/5.49 thf(fact_8266_sin__x__ge__neg__x,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_x_ge_neg_x
% 5.15/5.49 thf(fact_8267_sin__ge__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ pi )
% 5.15/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_ge_zero
% 5.15/5.49 thf(fact_8268_sin__ge__minus__one,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_ge_minus_one
% 5.15/5.49 thf(fact_8269_cos__inj__pi,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ pi )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ pi )
% 5.15/5.49 => ( ( ( cos_real @ X )
% 5.15/5.49 = ( cos_real @ Y ) )
% 5.15/5.49 => ( X = Y ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_inj_pi
% 5.15/5.49 thf(fact_8270_cos__mono__le__eq,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ pi )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ pi )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.15/5.49 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_mono_le_eq
% 5.15/5.49 thf(fact_8271_cos__monotone__0__pi__le,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ pi )
% 5.15/5.49 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_monotone_0_pi_le
% 5.15/5.49 thf(fact_8272_cos__ge__minus__one,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_ge_minus_one
% 5.15/5.49 thf(fact_8273_abs__sin__le__one,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % abs_sin_le_one
% 5.15/5.49 thf(fact_8274_abs__cos__le__one,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % abs_cos_le_one
% 5.15/5.49 thf(fact_8275_cos__diff__cos,axiom,
% 5.15/5.49 ! [W: complex,Z: complex] :
% 5.15/5.49 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_diff_cos
% 5.15/5.49 thf(fact_8276_cos__diff__cos,axiom,
% 5.15/5.49 ! [W: real,Z: real] :
% 5.15/5.49 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_diff_cos
% 5.15/5.49 thf(fact_8277_sin__diff__sin,axiom,
% 5.15/5.49 ! [W: complex,Z: complex] :
% 5.15/5.49 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_diff_sin
% 5.15/5.49 thf(fact_8278_sin__diff__sin,axiom,
% 5.15/5.49 ! [W: real,Z: real] :
% 5.15/5.49 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_diff_sin
% 5.15/5.49 thf(fact_8279_sin__plus__sin,axiom,
% 5.15/5.49 ! [W: complex,Z: complex] :
% 5.15/5.49 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_plus_sin
% 5.15/5.49 thf(fact_8280_sin__plus__sin,axiom,
% 5.15/5.49 ! [W: real,Z: real] :
% 5.15/5.49 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_plus_sin
% 5.15/5.49 thf(fact_8281_cos__times__sin,axiom,
% 5.15/5.49 ! [W: complex,Z: complex] :
% 5.15/5.49 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_times_sin
% 5.15/5.49 thf(fact_8282_cos__times__sin,axiom,
% 5.15/5.49 ! [W: real,Z: real] :
% 5.15/5.49 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_times_sin
% 5.15/5.49 thf(fact_8283_sin__times__cos,axiom,
% 5.15/5.49 ! [W: complex,Z: complex] :
% 5.15/5.49 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_times_cos
% 5.15/5.49 thf(fact_8284_sin__times__cos,axiom,
% 5.15/5.49 ! [W: real,Z: real] :
% 5.15/5.49 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_times_cos
% 5.15/5.49 thf(fact_8285_sin__times__sin,axiom,
% 5.15/5.49 ! [W: complex,Z: complex] :
% 5.15/5.49 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_times_sin
% 5.15/5.49 thf(fact_8286_sin__times__sin,axiom,
% 5.15/5.49 ! [W: real,Z: real] :
% 5.15/5.49 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_times_sin
% 5.15/5.49 thf(fact_8287_cos__double,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_double
% 5.15/5.49 thf(fact_8288_cos__double,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_double
% 5.15/5.49 thf(fact_8289_cos__double__sin,axiom,
% 5.15/5.49 ! [W: complex] :
% 5.15/5.49 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.15/5.49 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_double_sin
% 5.15/5.49 thf(fact_8290_cos__double__sin,axiom,
% 5.15/5.49 ! [W: real] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_double_sin
% 5.15/5.49 thf(fact_8291_suminf__of__real,axiom,
% 5.15/5.49 ! [X8: nat > real] :
% 5.15/5.49 ( ( summable_real @ X8 )
% 5.15/5.49 => ( ( real_V1803761363581548252l_real @ ( suminf_real @ X8 ) )
% 5.15/5.49 = ( suminf_real
% 5.15/5.49 @ ^ [N3: nat] : ( real_V1803761363581548252l_real @ ( X8 @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_of_real
% 5.15/5.49 thf(fact_8292_suminf__of__real,axiom,
% 5.15/5.49 ! [X8: nat > real] :
% 5.15/5.49 ( ( summable_real @ X8 )
% 5.15/5.49 => ( ( real_V4546457046886955230omplex @ ( suminf_real @ X8 ) )
% 5.15/5.49 = ( suminf_complex
% 5.15/5.49 @ ^ [N3: nat] : ( real_V4546457046886955230omplex @ ( X8 @ N3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % suminf_of_real
% 5.15/5.49 thf(fact_8293_norm__less__p1,axiom,
% 5.15/5.49 ! [X: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X ) ) @ one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_less_p1
% 5.15/5.49 thf(fact_8294_norm__less__p1,axiom,
% 5.15/5.49 ! [X: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X ) ) @ one_one_complex ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_less_p1
% 5.15/5.49 thf(fact_8295_cos__two__neq__zero,axiom,
% 5.15/5.49 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.49 != zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % cos_two_neq_zero
% 5.15/5.49 thf(fact_8296_cos__mono__less__eq,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ pi )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ pi )
% 5.15/5.49 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.15/5.49 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_mono_less_eq
% 5.15/5.49 thf(fact_8297_cos__monotone__0__pi,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( ord_less_real @ Y @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ pi )
% 5.15/5.49 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_monotone_0_pi
% 5.15/5.49 thf(fact_8298_sin__eq__0__pi,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ pi )
% 5.15/5.49 => ( ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 => ( X = zero_zero_real ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_eq_0_pi
% 5.15/5.49 thf(fact_8299_sin__zero__pi__iff,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 5.15/5.49 => ( ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 = ( X = zero_zero_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_zero_pi_iff
% 5.15/5.49 thf(fact_8300_cos__monotone__minus__pi__0_H,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.49 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_monotone_minus_pi_0'
% 5.15/5.49 thf(fact_8301_sin__zero__iff__int2,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 = ( ? [I3: int] :
% 5.15/5.49 ( X
% 5.15/5.49 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ pi ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_zero_iff_int2
% 5.15/5.49 thf(fact_8302_sincos__total__pi,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 => ? [T3: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.15/5.49 & ( ord_less_eq_real @ T3 @ pi )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( cos_real @ T3 ) )
% 5.15/5.49 & ( Y
% 5.15/5.49 = ( sin_real @ T3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sincos_total_pi
% 5.15/5.49 thf(fact_8303_sin__cos__sqrt,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 5.15/5.49 => ( ( sin_real @ X )
% 5.15/5.49 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_cos_sqrt
% 5.15/5.49 thf(fact_8304_sin__expansion__lemma,axiom,
% 5.15/5.49 ! [X: real,M: nat] :
% 5.15/5.49 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.15/5.49 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_expansion_lemma
% 5.15/5.49 thf(fact_8305_cos__expansion__lemma,axiom,
% 5.15/5.49 ! [X: real,M: nat] :
% 5.15/5.49 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.15/5.49 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_expansion_lemma
% 5.15/5.49 thf(fact_8306_sin__gt__zero__02,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_gt_zero_02
% 5.15/5.49 thf(fact_8307_cos__two__less__zero,axiom,
% 5.15/5.49 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.15/5.49
% 5.15/5.49 % cos_two_less_zero
% 5.15/5.49 thf(fact_8308_cos__two__le__zero,axiom,
% 5.15/5.49 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.15/5.49
% 5.15/5.49 % cos_two_le_zero
% 5.15/5.49 thf(fact_8309_cos__is__zero,axiom,
% 5.15/5.49 ? [X3: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.15/5.49 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.49 & ( ( cos_real @ X3 )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 & ! [Y4: real] :
% 5.15/5.49 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.15/5.49 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.49 & ( ( cos_real @ Y4 )
% 5.15/5.49 = zero_zero_real ) )
% 5.15/5.49 => ( Y4 = X3 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_is_zero
% 5.15/5.49 thf(fact_8310_norm__of__real__diff,axiom,
% 5.15/5.49 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_of_real_diff
% 5.15/5.49 thf(fact_8311_norm__of__real__diff,axiom,
% 5.15/5.49 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % norm_of_real_diff
% 5.15/5.49 thf(fact_8312_cos__monotone__minus__pi__0,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.15/5.49 => ( ( ord_less_real @ Y @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.49 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_monotone_minus_pi_0
% 5.15/5.49 thf(fact_8313_cos__total,axiom,
% 5.15/5.49 ! [Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.49 => ? [X3: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.15/5.49 & ( ord_less_eq_real @ X3 @ pi )
% 5.15/5.49 & ( ( cos_real @ X3 )
% 5.15/5.49 = Y )
% 5.15/5.49 & ! [Y4: real] :
% 5.15/5.49 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.15/5.49 & ( ord_less_eq_real @ Y4 @ pi )
% 5.15/5.49 & ( ( cos_real @ Y4 )
% 5.15/5.49 = Y ) )
% 5.15/5.49 => ( Y4 = X3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_total
% 5.15/5.49 thf(fact_8314_sincos__total__pi__half,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.49 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 => ? [T3: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.15/5.49 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( cos_real @ T3 ) )
% 5.15/5.49 & ( Y
% 5.15/5.49 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sincos_total_pi_half
% 5.15/5.49 thf(fact_8315_sincos__total__2pi__le,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 => ? [T3: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.15/5.49 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( cos_real @ T3 ) )
% 5.15/5.49 & ( Y
% 5.15/5.49 = ( sin_real @ T3 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sincos_total_2pi_le
% 5.15/5.49 thf(fact_8316_sincos__total__2pi,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 => ~ ! [T3: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.15/5.49 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.15/5.49 => ( ( X
% 5.15/5.49 = ( cos_real @ T3 ) )
% 5.15/5.49 => ( Y
% 5.15/5.49 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sincos_total_2pi
% 5.15/5.49 thf(fact_8317_sin__pi__divide__n__ge__0,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( N2 != zero_zero_nat )
% 5.15/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_pi_divide_n_ge_0
% 5.15/5.49 thf(fact_8318_sin__45,axiom,
% 5.15/5.49 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.49 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_45
% 5.15/5.49 thf(fact_8319_cos__45,axiom,
% 5.15/5.49 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.49 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_45
% 5.15/5.49 thf(fact_8320_cos__plus__cos,axiom,
% 5.15/5.49 ! [W: complex,Z: complex] :
% 5.15/5.49 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_plus_cos
% 5.15/5.49 thf(fact_8321_cos__plus__cos,axiom,
% 5.15/5.49 ! [W: real,Z: real] :
% 5.15/5.49 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_plus_cos
% 5.15/5.49 thf(fact_8322_cos__times__cos,axiom,
% 5.15/5.49 ! [W: complex,Z: complex] :
% 5.15/5.49 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_times_cos
% 5.15/5.49 thf(fact_8323_cos__times__cos,axiom,
% 5.15/5.49 ! [W: real,Z: real] :
% 5.15/5.49 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.15/5.49 = ( 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 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_times_cos
% 5.15/5.49 thf(fact_8324_sin__gt__zero2,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_gt_zero2
% 5.15/5.49 thf(fact_8325_sin__lt__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ pi @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.15/5.49 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_lt_zero
% 5.15/5.49 thf(fact_8326_cos__double__less__one,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.49 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_double_less_one
% 5.15/5.49 thf(fact_8327_sin__30,axiom,
% 5.15/5.49 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.15/5.49 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_30
% 5.15/5.49 thf(fact_8328_cos__gt__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_gt_zero
% 5.15/5.49 thf(fact_8329_sin__monotone__2pi__le,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_monotone_2pi_le
% 5.15/5.49 thf(fact_8330_sin__mono__le__eq,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.15/5.49 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_mono_le_eq
% 5.15/5.49 thf(fact_8331_sin__inj__pi,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ( ( sin_real @ X )
% 5.15/5.49 = ( sin_real @ Y ) )
% 5.15/5.49 => ( X = Y ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_inj_pi
% 5.15/5.49 thf(fact_8332_cos__60,axiom,
% 5.15/5.49 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.15/5.49 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_60
% 5.15/5.49 thf(fact_8333_sin__60,axiom,
% 5.15/5.49 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.15/5.49 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_60
% 5.15/5.49 thf(fact_8334_cos__30,axiom,
% 5.15/5.49 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.15/5.49 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_30
% 5.15/5.49 thf(fact_8335_cos__one__2pi__int,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( cos_real @ X )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 = ( ? [X2: int] :
% 5.15/5.49 ( X
% 5.15/5.49 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_one_2pi_int
% 5.15/5.49 thf(fact_8336_cos__double__cos,axiom,
% 5.15/5.49 ! [W: complex] :
% 5.15/5.49 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.15/5.49 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_double_cos
% 5.15/5.49 thf(fact_8337_cos__double__cos,axiom,
% 5.15/5.49 ! [W: real] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.15/5.49 = ( 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 ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_double_cos
% 5.15/5.49 thf(fact_8338_cos__treble__cos,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 5.15/5.49 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_treble_cos
% 5.15/5.49 thf(fact_8339_cos__treble__cos,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 5.15/5.49 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_treble_cos
% 5.15/5.49 thf(fact_8340_sin__le__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ pi @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.15/5.49 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_le_zero
% 5.15/5.49 thf(fact_8341_sin__less__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.49 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_less_zero
% 5.15/5.49 thf(fact_8342_sin__monotone__2pi,axiom,
% 5.15/5.49 ! [Y: real,X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.49 => ( ( ord_less_real @ Y @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_monotone_2pi
% 5.15/5.49 thf(fact_8343_sin__mono__less__eq,axiom,
% 5.15/5.49 ! [X: real,Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.15/5.49 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_mono_less_eq
% 5.15/5.49 thf(fact_8344_sin__total,axiom,
% 5.15/5.49 ! [Y: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.49 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.49 => ? [X3: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.15/5.49 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 & ( ( sin_real @ X3 )
% 5.15/5.49 = Y )
% 5.15/5.49 & ! [Y4: real] :
% 5.15/5.49 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.15/5.49 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 & ( ( sin_real @ Y4 )
% 5.15/5.49 = Y ) )
% 5.15/5.49 => ( Y4 = X3 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_total
% 5.15/5.49 thf(fact_8345_cos__gt__zero__pi,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.49 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_gt_zero_pi
% 5.15/5.49 thf(fact_8346_cos__ge__zero,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.49 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_ge_zero
% 5.15/5.49 thf(fact_8347_cos__one__2pi,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( cos_real @ X )
% 5.15/5.49 = one_one_real )
% 5.15/5.49 = ( ? [X2: nat] :
% 5.15/5.49 ( X
% 5.15/5.49 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.15/5.49 | ? [X2: nat] :
% 5.15/5.49 ( X
% 5.15/5.49 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_one_2pi
% 5.15/5.49 thf(fact_8348_sin__pi__divide__n__gt__0,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.49 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_pi_divide_n_gt_0
% 5.15/5.49 thf(fact_8349_sin__arctan,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( sin_real @ ( arctan @ X ) )
% 5.15/5.49 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_arctan
% 5.15/5.49 thf(fact_8350_cos__arctan,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( cos_real @ ( arctan @ X ) )
% 5.15/5.49 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_arctan
% 5.15/5.49 thf(fact_8351_sin__zero__iff__int,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 = ( ? [I3: int] :
% 5.15/5.49 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_zero_iff_int
% 5.15/5.49 thf(fact_8352_cos__zero__iff__int,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( cos_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 = ( ? [I3: int] :
% 5.15/5.49 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_zero_iff_int
% 5.15/5.49 thf(fact_8353_sin__zero__lemma,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 => ? [N: nat] :
% 5.15/5.49 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_zero_lemma
% 5.15/5.49 thf(fact_8354_sin__zero__iff,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( sin_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 = ( ? [N3: nat] :
% 5.15/5.49 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.49 | ? [N3: nat] :
% 5.15/5.49 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_zero_iff
% 5.15/5.49 thf(fact_8355_cos__zero__lemma,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ( cos_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 => ? [N: nat] :
% 5.15/5.49 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_zero_lemma
% 5.15/5.49 thf(fact_8356_cos__zero__iff,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( cos_real @ X )
% 5.15/5.49 = zero_zero_real )
% 5.15/5.49 = ( ? [N3: nat] :
% 5.15/5.49 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.49 | ? [N3: nat] :
% 5.15/5.49 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.15/5.49 & ( X
% 5.15/5.49 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % cos_zero_iff
% 5.15/5.49 thf(fact_8357_arsinh__def,axiom,
% 5.15/5.49 ( arsinh_real
% 5.15/5.49 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % arsinh_def
% 5.15/5.49 thf(fact_8358_Maclaurin__minus__cos__expansion,axiom,
% 5.15/5.49 ! [N2: nat,X: real] :
% 5.15/5.49 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.49 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.49 => ? [T3: real] :
% 5.15/5.49 ( ( ord_less_real @ X @ T3 )
% 5.15/5.49 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.15/5.49 & ( ( cos_real @ X )
% 5.15/5.49 = ( plus_plus_real
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 @ ( 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 @ X @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Maclaurin_minus_cos_expansion
% 5.15/5.49 thf(fact_8359_Maclaurin__cos__expansion2,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.49 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.49 => ? [T3: real] :
% 5.15/5.49 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.15/5.49 & ( ord_less_real @ T3 @ X )
% 5.15/5.49 & ( ( cos_real @ X )
% 5.15/5.49 = ( plus_plus_real
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 @ ( 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 @ X @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Maclaurin_cos_expansion2
% 5.15/5.49 thf(fact_8360_Maclaurin__cos__expansion,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ? [T3: real] :
% 5.15/5.49 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.15/5.49 & ( ( cos_real @ X )
% 5.15/5.49 = ( plus_plus_real
% 5.15/5.49 @ ( groups6591440286371151544t_real
% 5.15/5.49 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.49 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.49 @ ( 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 @ X @ N2 ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % Maclaurin_cos_expansion
% 5.15/5.49 thf(fact_8361_tan__double,axiom,
% 5.15/5.49 ! [X: complex] :
% 5.15/5.49 ( ( ( cos_complex @ X )
% 5.15/5.49 != zero_zero_complex )
% 5.15/5.49 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 != zero_zero_complex )
% 5.15/5.49 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % tan_double
% 5.15/5.49 thf(fact_8362_tan__double,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ( cos_real @ X )
% 5.15/5.49 != zero_zero_real )
% 5.15/5.49 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 != zero_zero_real )
% 5.15/5.49 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.15/5.49 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % tan_double
% 5.15/5.49 thf(fact_8363_sin__tan,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.49 => ( ( sin_real @ X )
% 5.15/5.49 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % sin_tan
% 5.15/5.49 thf(fact_8364_fact__0,axiom,
% 5.15/5.49 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % fact_0
% 5.15/5.49 thf(fact_8365_fact__0,axiom,
% 5.15/5.49 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.15/5.49 = one_one_rat ) ).
% 5.15/5.49
% 5.15/5.49 % fact_0
% 5.15/5.49 thf(fact_8366_fact__0,axiom,
% 5.15/5.49 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.15/5.49 = one_one_int ) ).
% 5.15/5.49
% 5.15/5.49 % fact_0
% 5.15/5.49 thf(fact_8367_fact__0,axiom,
% 5.15/5.49 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % fact_0
% 5.15/5.49 thf(fact_8368_fact__0,axiom,
% 5.15/5.49 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.15/5.49 = one_one_nat ) ).
% 5.15/5.49
% 5.15/5.49 % fact_0
% 5.15/5.49 thf(fact_8369_fact__1,axiom,
% 5.15/5.49 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % fact_1
% 5.15/5.49 thf(fact_8370_fact__1,axiom,
% 5.15/5.49 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.15/5.49 = one_one_rat ) ).
% 5.15/5.49
% 5.15/5.49 % fact_1
% 5.15/5.49 thf(fact_8371_fact__1,axiom,
% 5.15/5.49 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.15/5.49 = one_one_int ) ).
% 5.15/5.49
% 5.15/5.49 % fact_1
% 5.15/5.49 thf(fact_8372_fact__1,axiom,
% 5.15/5.49 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % fact_1
% 5.15/5.49 thf(fact_8373_fact__1,axiom,
% 5.15/5.49 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.15/5.49 = one_one_nat ) ).
% 5.15/5.49
% 5.15/5.49 % fact_1
% 5.15/5.49 thf(fact_8374_tan__periodic__pi,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 5.15/5.49 = ( tan_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % tan_periodic_pi
% 5.15/5.49 thf(fact_8375_fact__Suc__0,axiom,
% 5.15/5.49 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.15/5.49 = one_one_complex ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc_0
% 5.15/5.49 thf(fact_8376_fact__Suc__0,axiom,
% 5.15/5.49 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.15/5.49 = one_one_rat ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc_0
% 5.15/5.49 thf(fact_8377_fact__Suc__0,axiom,
% 5.15/5.49 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.15/5.49 = one_one_int ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc_0
% 5.15/5.49 thf(fact_8378_fact__Suc__0,axiom,
% 5.15/5.49 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.15/5.49 = one_one_real ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc_0
% 5.15/5.49 thf(fact_8379_fact__Suc__0,axiom,
% 5.15/5.49 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.15/5.49 = one_one_nat ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc_0
% 5.15/5.49 thf(fact_8380_fact__Suc,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( semiri773545260158071498ct_rat @ ( suc @ N2 ) )
% 5.15/5.49 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc
% 5.15/5.49 thf(fact_8381_fact__Suc,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 5.15/5.49 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc
% 5.15/5.49 thf(fact_8382_fact__Suc,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( semiri5044797733671781792omplex @ ( suc @ N2 ) )
% 5.15/5.49 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc
% 5.15/5.49 thf(fact_8383_fact__Suc,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( semiri2265585572941072030t_real @ ( suc @ N2 ) )
% 5.15/5.49 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc
% 5.15/5.49 thf(fact_8384_fact__Suc,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 5.15/5.49 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_Suc
% 5.15/5.49 thf(fact_8385_fact__2,axiom,
% 5.15/5.49 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_2
% 5.15/5.49 thf(fact_8386_fact__2,axiom,
% 5.15/5.49 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_2
% 5.15/5.49 thf(fact_8387_fact__2,axiom,
% 5.15/5.49 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_2
% 5.15/5.49 thf(fact_8388_fact__2,axiom,
% 5.15/5.49 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_2
% 5.15/5.49 thf(fact_8389_fact__2,axiom,
% 5.15/5.49 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.49 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_2
% 5.15/5.49 thf(fact_8390_tan__npi,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.15/5.49 = zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % tan_npi
% 5.15/5.49 thf(fact_8391_tan__periodic__n,axiom,
% 5.15/5.49 ! [X: real,N2: num] :
% 5.15/5.49 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N2 ) @ pi ) ) )
% 5.15/5.49 = ( tan_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % tan_periodic_n
% 5.15/5.49 thf(fact_8392_tan__periodic__nat,axiom,
% 5.15/5.49 ! [X: real,N2: nat] :
% 5.15/5.49 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) ) )
% 5.15/5.49 = ( tan_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % tan_periodic_nat
% 5.15/5.49 thf(fact_8393_tan__periodic__int,axiom,
% 5.15/5.49 ! [X: real,I: int] :
% 5.15/5.49 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.15/5.49 = ( tan_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % tan_periodic_int
% 5.15/5.49 thf(fact_8394_tan__periodic,axiom,
% 5.15/5.49 ! [X: real] :
% 5.15/5.49 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.15/5.49 = ( tan_real @ X ) ) ).
% 5.15/5.49
% 5.15/5.49 % tan_periodic
% 5.15/5.49 thf(fact_8395_complex__exp__exists,axiom,
% 5.15/5.49 ! [Z: complex] :
% 5.15/5.49 ? [A5: complex,R3: real] :
% 5.15/5.49 ( Z
% 5.15/5.49 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A5 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % complex_exp_exists
% 5.15/5.49 thf(fact_8396_fact__ge__zero,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_ge_zero
% 5.15/5.49 thf(fact_8397_fact__ge__zero,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_ge_zero
% 5.15/5.49 thf(fact_8398_fact__ge__zero,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_ge_zero
% 5.15/5.49 thf(fact_8399_fact__ge__zero,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_ge_zero
% 5.15/5.49 thf(fact_8400_fact__gt__zero,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_gt_zero
% 5.15/5.49 thf(fact_8401_fact__gt__zero,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_gt_zero
% 5.15/5.49 thf(fact_8402_fact__gt__zero,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_gt_zero
% 5.15/5.49 thf(fact_8403_fact__gt__zero,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_gt_zero
% 5.15/5.49 thf(fact_8404_fact__not__neg,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ zero_zero_rat ) ).
% 5.15/5.49
% 5.15/5.49 % fact_not_neg
% 5.15/5.49 thf(fact_8405_fact__not__neg,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 5.15/5.49
% 5.15/5.49 % fact_not_neg
% 5.15/5.49 thf(fact_8406_fact__not__neg,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N2 ) @ zero_zero_real ) ).
% 5.15/5.49
% 5.15/5.49 % fact_not_neg
% 5.15/5.49 thf(fact_8407_fact__not__neg,axiom,
% 5.15/5.49 ! [N2: nat] :
% 5.15/5.49 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 5.15/5.49
% 5.15/5.49 % fact_not_neg
% 5.15/5.49 thf(fact_8408_fact__ge__1,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_ge_1
% 5.15/5.49 thf(fact_8409_fact__ge__1,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_ge_1
% 5.15/5.49 thf(fact_8410_fact__ge__1,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_ge_1
% 5.15/5.49 thf(fact_8411_fact__ge__1,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_ge_1
% 5.15/5.49 thf(fact_8412_fact__mono,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.49 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_mono
% 5.15/5.49 thf(fact_8413_fact__mono,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.49 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_mono
% 5.15/5.49 thf(fact_8414_fact__mono,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.49 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_mono
% 5.15/5.49 thf(fact_8415_fact__mono,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.49 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_mono
% 5.15/5.49 thf(fact_8416_fact__dvd,axiom,
% 5.15/5.49 ! [N2: nat,M: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.49 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_dvd
% 5.15/5.49 thf(fact_8417_fact__dvd,axiom,
% 5.15/5.49 ! [N2: nat,M: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.49 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_dvd
% 5.15/5.49 thf(fact_8418_fact__dvd,axiom,
% 5.15/5.49 ! [N2: nat,M: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.49 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_dvd
% 5.15/5.49 thf(fact_8419_fact__dvd,axiom,
% 5.15/5.49 ! [N2: nat,M: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.49 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_dvd
% 5.15/5.49 thf(fact_8420_fact__less__mono,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.49 => ( ( ord_less_nat @ M @ N2 )
% 5.15/5.49 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_less_mono
% 5.15/5.49 thf(fact_8421_fact__less__mono,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.49 => ( ( ord_less_nat @ M @ N2 )
% 5.15/5.49 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_less_mono
% 5.15/5.49 thf(fact_8422_fact__less__mono,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.49 => ( ( ord_less_nat @ M @ N2 )
% 5.15/5.49 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_less_mono
% 5.15/5.49 thf(fact_8423_fact__less__mono,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.49 => ( ( ord_less_nat @ M @ N2 )
% 5.15/5.49 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_less_mono
% 5.15/5.49 thf(fact_8424_fact__fact__dvd__fact,axiom,
% 5.15/5.49 ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_fact_dvd_fact
% 5.15/5.49 thf(fact_8425_fact__fact__dvd__fact,axiom,
% 5.15/5.49 ! [K: nat,N2: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N2 ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_fact_dvd_fact
% 5.15/5.49 thf(fact_8426_fact__fact__dvd__fact,axiom,
% 5.15/5.49 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_fact_dvd_fact
% 5.15/5.49 thf(fact_8427_fact__fact__dvd__fact,axiom,
% 5.15/5.49 ! [K: nat,N2: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_fact_dvd_fact
% 5.15/5.49 thf(fact_8428_fact__fact__dvd__fact,axiom,
% 5.15/5.49 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_fact_dvd_fact
% 5.15/5.49 thf(fact_8429_fact__mod,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.49 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.15/5.49 = zero_zero_int ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_mod
% 5.15/5.49 thf(fact_8430_fact__mod,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.49 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.15/5.49 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_mod
% 5.15/5.49 thf(fact_8431_fact__mod,axiom,
% 5.15/5.49 ! [M: nat,N2: nat] :
% 5.15/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.49 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.15/5.49 = zero_zero_nat ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_mod
% 5.15/5.49 thf(fact_8432_fact__le__power,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_le_power
% 5.15/5.49 thf(fact_8433_fact__le__power,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_le_power
% 5.15/5.49 thf(fact_8434_fact__le__power,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_le_power
% 5.15/5.49 thf(fact_8435_fact__le__power,axiom,
% 5.15/5.49 ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % fact_le_power
% 5.15/5.49 thf(fact_8436_tan__def,axiom,
% 5.15/5.49 ( tan_complex
% 5.15/5.49 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.15/5.49
% 5.15/5.49 % tan_def
% 5.15/5.49 thf(fact_8437_tan__def,axiom,
% 5.15/5.49 ( tan_real
% 5.15/5.50 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_def
% 5.15/5.50 thf(fact_8438_choose__dvd,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % choose_dvd
% 5.15/5.50 thf(fact_8439_choose__dvd,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % choose_dvd
% 5.15/5.50 thf(fact_8440_choose__dvd,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % choose_dvd
% 5.15/5.50 thf(fact_8441_choose__dvd,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % choose_dvd
% 5.15/5.50 thf(fact_8442_choose__dvd,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % choose_dvd
% 5.15/5.50 thf(fact_8443_fact__numeral,axiom,
% 5.15/5.50 ! [K: num] :
% 5.15/5.50 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.15/5.50 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_numeral
% 5.15/5.50 thf(fact_8444_fact__numeral,axiom,
% 5.15/5.50 ! [K: num] :
% 5.15/5.50 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.15/5.50 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_numeral
% 5.15/5.50 thf(fact_8445_fact__numeral,axiom,
% 5.15/5.50 ! [K: num] :
% 5.15/5.50 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.15/5.50 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_numeral
% 5.15/5.50 thf(fact_8446_fact__numeral,axiom,
% 5.15/5.50 ! [K: num] :
% 5.15/5.50 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.15/5.50 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_numeral
% 5.15/5.50 thf(fact_8447_fact__numeral,axiom,
% 5.15/5.50 ! [K: num] :
% 5.15/5.50 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.15/5.50 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_numeral
% 5.15/5.50 thf(fact_8448_square__fact__le__2__fact,axiom,
% 5.15/5.50 ! [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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % square_fact_le_2_fact
% 5.15/5.50 thf(fact_8449_tan__45,axiom,
% 5.15/5.50 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.50 = one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % tan_45
% 5.15/5.50 thf(fact_8450_tan__60,axiom,
% 5.15/5.50 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.15/5.50 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_60
% 5.15/5.50 thf(fact_8451_fact__num__eq__if,axiom,
% 5.15/5.50 ( semiri773545260158071498ct_rat
% 5.15/5.50 = ( ^ [M5: nat] : ( if_rat @ ( M5 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M5 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_num_eq_if
% 5.15/5.50 thf(fact_8452_fact__num__eq__if,axiom,
% 5.15/5.50 ( semiri1406184849735516958ct_int
% 5.15/5.50 = ( ^ [M5: nat] : ( if_int @ ( M5 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_num_eq_if
% 5.15/5.50 thf(fact_8453_fact__num__eq__if,axiom,
% 5.15/5.50 ( semiri5044797733671781792omplex
% 5.15/5.50 = ( ^ [M5: nat] : ( if_complex @ ( M5 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M5 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_num_eq_if
% 5.15/5.50 thf(fact_8454_fact__num__eq__if,axiom,
% 5.15/5.50 ( semiri2265585572941072030t_real
% 5.15/5.50 = ( ^ [M5: nat] : ( if_real @ ( M5 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_num_eq_if
% 5.15/5.50 thf(fact_8455_fact__num__eq__if,axiom,
% 5.15/5.50 ( semiri1408675320244567234ct_nat
% 5.15/5.50 = ( ^ [M5: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M5 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_num_eq_if
% 5.15/5.50 thf(fact_8456_fact__reduce,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 => ( ( semiri773545260158071498ct_rat @ N2 )
% 5.15/5.50 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_reduce
% 5.15/5.50 thf(fact_8457_fact__reduce,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 => ( ( semiri1406184849735516958ct_int @ N2 )
% 5.15/5.50 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_reduce
% 5.15/5.50 thf(fact_8458_fact__reduce,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 => ( ( semiri5044797733671781792omplex @ N2 )
% 5.15/5.50 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_reduce
% 5.15/5.50 thf(fact_8459_fact__reduce,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 => ( ( semiri2265585572941072030t_real @ N2 )
% 5.15/5.50 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_reduce
% 5.15/5.50 thf(fact_8460_fact__reduce,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 5.15/5.50 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_reduce
% 5.15/5.50 thf(fact_8461_lemma__tan__total,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.15/5.50 => ? [X3: real] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.15/5.50 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 & ( ord_less_real @ Y @ ( tan_real @ X3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % lemma_tan_total
% 5.15/5.50 thf(fact_8462_tan__gt__zero,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_gt_zero
% 5.15/5.50 thf(fact_8463_lemma__tan__total1,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ? [X3: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.15/5.50 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 & ( ( tan_real @ X3 )
% 5.15/5.50 = Y ) ) ).
% 5.15/5.50
% 5.15/5.50 % lemma_tan_total1
% 5.15/5.50 thf(fact_8464_tan__mono__lt__eq,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.50 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.15/5.50 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_mono_lt_eq
% 5.15/5.50 thf(fact_8465_tan__monotone_H,axiom,
% 5.15/5.50 ! [Y: real,X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.50 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ord_less_real @ Y @ X )
% 5.15/5.50 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_monotone'
% 5.15/5.50 thf(fact_8466_tan__monotone,axiom,
% 5.15/5.50 ! [Y: real,X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.50 => ( ( ord_less_real @ Y @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_monotone
% 5.15/5.50 thf(fact_8467_tan__total,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ? [X3: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.15/5.50 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 & ( ( tan_real @ X3 )
% 5.15/5.50 = Y )
% 5.15/5.50 & ! [Y4: real] :
% 5.15/5.50 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.15/5.50 & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 & ( ( tan_real @ Y4 )
% 5.15/5.50 = Y ) )
% 5.15/5.50 => ( Y4 = X3 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_total
% 5.15/5.50 thf(fact_8468_tan__minus__45,axiom,
% 5.15/5.50 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.50 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_minus_45
% 5.15/5.50 thf(fact_8469_tan__inverse,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.15/5.50 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_inverse
% 5.15/5.50 thf(fact_8470_add__tan__eq,axiom,
% 5.15/5.50 ! [X: complex,Y: complex] :
% 5.15/5.50 ( ( ( cos_complex @ X )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( ( cos_complex @ Y )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) )
% 5.15/5.50 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % add_tan_eq
% 5.15/5.50 thf(fact_8471_add__tan__eq,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ( cos_real @ X )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( ( cos_real @ Y )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.15/5.50 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % add_tan_eq
% 5.15/5.50 thf(fact_8472_tan__total__pos,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.50 => ? [X3: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.15/5.50 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 & ( ( tan_real @ X3 )
% 5.15/5.50 = Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_total_pos
% 5.15/5.50 thf(fact_8473_tan__pos__pi2__le,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_pos_pi2_le
% 5.15/5.50 thf(fact_8474_tan__less__zero,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.50 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_less_zero
% 5.15/5.50 thf(fact_8475_tan__mono__le,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.50 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_mono_le
% 5.15/5.50 thf(fact_8476_tan__mono__le__eq,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.15/5.50 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.15/5.50 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_mono_le_eq
% 5.15/5.50 thf(fact_8477_tan__bound__pi2,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.50 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_bound_pi2
% 5.15/5.50 thf(fact_8478_tan__30,axiom,
% 5.15/5.50 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.15/5.50 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_30
% 5.15/5.50 thf(fact_8479_arctan__unique,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ( tan_real @ X )
% 5.15/5.50 = Y )
% 5.15/5.50 => ( ( arctan @ Y )
% 5.15/5.50 = X ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arctan_unique
% 5.15/5.50 thf(fact_8480_arctan__tan,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( arctan @ ( tan_real @ X ) )
% 5.15/5.50 = X ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arctan_tan
% 5.15/5.50 thf(fact_8481_arctan,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.15/5.50 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 & ( ( tan_real @ ( arctan @ Y ) )
% 5.15/5.50 = Y ) ) ).
% 5.15/5.50
% 5.15/5.50 % arctan
% 5.15/5.50 thf(fact_8482_Maclaurin__zero,axiom,
% 5.15/5.50 ! [X: real,N2: nat,Diff: nat > complex > real] :
% 5.15/5.50 ( ( X = zero_zero_real )
% 5.15/5.50 => ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_zero
% 5.15/5.50 thf(fact_8483_Maclaurin__zero,axiom,
% 5.15/5.50 ! [X: real,N2: nat,Diff: nat > real > real] :
% 5.15/5.50 ( ( X = zero_zero_real )
% 5.15/5.50 => ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_zero
% 5.15/5.50 thf(fact_8484_Maclaurin__zero,axiom,
% 5.15/5.50 ! [X: real,N2: nat,Diff: nat > rat > real] :
% 5.15/5.50 ( ( X = zero_zero_real )
% 5.15/5.50 => ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_zero
% 5.15/5.50 thf(fact_8485_Maclaurin__zero,axiom,
% 5.15/5.50 ! [X: real,N2: nat,Diff: nat > nat > real] :
% 5.15/5.50 ( ( X = zero_zero_real )
% 5.15/5.50 => ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_zero
% 5.15/5.50 thf(fact_8486_Maclaurin__zero,axiom,
% 5.15/5.50 ! [X: real,N2: nat,Diff: nat > int > real] :
% 5.15/5.50 ( ( X = zero_zero_real )
% 5.15/5.50 => ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_zero
% 5.15/5.50 thf(fact_8487_Maclaurin__lemma,axiom,
% 5.15/5.50 ! [H2: real,F: real > real,J: nat > real,N2: nat] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.15/5.50 => ? [B8: real] :
% 5.15/5.50 ( ( F @ H2 )
% 5.15/5.50 = ( plus_plus_real
% 5.15/5.50 @ ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_lemma
% 5.15/5.50 thf(fact_8488_lemma__tan__add1,axiom,
% 5.15/5.50 ! [X: complex,Y: complex] :
% 5.15/5.50 ( ( ( cos_complex @ X )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( ( cos_complex @ Y )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) )
% 5.15/5.50 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % lemma_tan_add1
% 5.15/5.50 thf(fact_8489_lemma__tan__add1,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ( cos_real @ X )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( ( cos_real @ Y )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) )
% 5.15/5.50 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % lemma_tan_add1
% 5.15/5.50 thf(fact_8490_tan__diff,axiom,
% 5.15/5.50 ! [X: complex,Y: complex] :
% 5.15/5.50 ( ( ( cos_complex @ X )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( ( cos_complex @ Y )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( tan_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.15/5.50 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_diff
% 5.15/5.50 thf(fact_8491_tan__diff,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ( cos_real @ X )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( ( cos_real @ Y )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( tan_real @ ( minus_minus_real @ X @ Y ) )
% 5.15/5.50 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_diff
% 5.15/5.50 thf(fact_8492_tan__add,axiom,
% 5.15/5.50 ! [X: complex,Y: complex] :
% 5.15/5.50 ( ( ( cos_complex @ X )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( ( cos_complex @ Y )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( tan_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.15/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_add
% 5.15/5.50 thf(fact_8493_tan__add,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ( cos_real @ X )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( ( cos_real @ Y )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( tan_real @ ( plus_plus_real @ X @ Y ) )
% 5.15/5.50 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_add
% 5.15/5.50 thf(fact_8494_tan__total__pi4,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.50 => ? [Z2: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 5.15/5.50 & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.50 & ( ( tan_real @ Z2 )
% 5.15/5.50 = X ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_total_pi4
% 5.15/5.50 thf(fact_8495_Maclaurin__exp__le,axiom,
% 5.15/5.50 ! [X: real,N2: nat] :
% 5.15/5.50 ? [T3: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.15/5.50 & ( ( exp_real @ X )
% 5.15/5.50 = ( plus_plus_real
% 5.15/5.50 @ ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_exp_le
% 5.15/5.50 thf(fact_8496_tan__half,axiom,
% 5.15/5.50 ( tan_complex
% 5.15/5.50 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_half
% 5.15/5.50 thf(fact_8497_tan__half,axiom,
% 5.15/5.50 ( tan_real
% 5.15/5.50 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % tan_half
% 5.15/5.50 thf(fact_8498_cos__coeff__def,axiom,
% 5.15/5.50 ( cos_coeff
% 5.15/5.50 = ( ^ [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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % cos_coeff_def
% 5.15/5.50 thf(fact_8499_Maclaurin__exp__lt,axiom,
% 5.15/5.50 ! [X: real,N2: nat] :
% 5.15/5.50 ( ( X != zero_zero_real )
% 5.15/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 => ? [T3: real] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.15/5.50 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.15/5.50 & ( ( exp_real @ X )
% 5.15/5.50 = ( plus_plus_real
% 5.15/5.50 @ ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_exp_lt
% 5.15/5.50 thf(fact_8500_cos__tan,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( cos_real @ X )
% 5.15/5.50 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % cos_tan
% 5.15/5.50 thf(fact_8501_Maclaurin__sin__expansion3,axiom,
% 5.15/5.50 ! [N2: nat,X: real] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.50 => ? [T3: real] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.15/5.50 & ( ord_less_real @ T3 @ X )
% 5.15/5.50 & ( ( sin_real @ X )
% 5.15/5.50 = ( plus_plus_real
% 5.15/5.50 @ ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 @ ( 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 @ X @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_sin_expansion3
% 5.15/5.50 thf(fact_8502_Maclaurin__sin__expansion4,axiom,
% 5.15/5.50 ! [X: real,N2: nat] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.50 => ? [T3: real] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.15/5.50 & ( ord_less_eq_real @ T3 @ X )
% 5.15/5.50 & ( ( sin_real @ X )
% 5.15/5.50 = ( plus_plus_real
% 5.15/5.50 @ ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 @ ( 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 @ X @ N2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_sin_expansion4
% 5.15/5.50 thf(fact_8503_Maclaurin__sin__expansion2,axiom,
% 5.15/5.50 ! [X: real,N2: nat] :
% 5.15/5.50 ? [T3: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.15/5.50 & ( ( sin_real @ X )
% 5.15/5.50 = ( plus_plus_real
% 5.15/5.50 @ ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 @ ( 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 @ X @ N2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_sin_expansion2
% 5.15/5.50 thf(fact_8504_Maclaurin__sin__expansion,axiom,
% 5.15/5.50 ! [X: real,N2: nat] :
% 5.15/5.50 ? [T3: real] :
% 5.15/5.50 ( ( sin_real @ X )
% 5.15/5.50 = ( plus_plus_real
% 5.15/5.50 @ ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.50 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.50 @ ( 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 @ X @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Maclaurin_sin_expansion
% 5.15/5.50 thf(fact_8505_sin__coeff__def,axiom,
% 5.15/5.50 ( sin_coeff
% 5.15/5.50 = ( ^ [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 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sin_coeff_def
% 5.15/5.50 thf(fact_8506_fact__ge__self,axiom,
% 5.15/5.50 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_ge_self
% 5.15/5.50 thf(fact_8507_fact__mono__nat,axiom,
% 5.15/5.50 ! [M: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.50 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_mono_nat
% 5.15/5.50 thf(fact_8508_fact__less__mono__nat,axiom,
% 5.15/5.50 ! [M: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.50 => ( ( ord_less_nat @ M @ N2 )
% 5.15/5.50 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_less_mono_nat
% 5.15/5.50 thf(fact_8509_fact__ge__Suc__0__nat,axiom,
% 5.15/5.50 ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_ge_Suc_0_nat
% 5.15/5.50 thf(fact_8510_dvd__fact,axiom,
% 5.15/5.50 ! [M: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.15/5.50 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.50 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % dvd_fact
% 5.15/5.50 thf(fact_8511_fact__diff__Suc,axiom,
% 5.15/5.50 ! [N2: nat,M: nat] :
% 5.15/5.50 ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.15/5.50 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 5.15/5.50 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_diff_Suc
% 5.15/5.50 thf(fact_8512_fact__div__fact__le__pow,axiom,
% 5.15/5.50 ! [R2: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ R2 @ N2 )
% 5.15/5.50 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R2 ) ) ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_div_fact_le_pow
% 5.15/5.50 thf(fact_8513_sin__coeff__Suc,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( sin_coeff @ ( suc @ N2 ) )
% 5.15/5.50 = ( divide_divide_real @ ( cos_coeff @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sin_coeff_Suc
% 5.15/5.50 thf(fact_8514_cos__coeff__Suc,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( cos_coeff @ ( suc @ N2 ) )
% 5.15/5.50 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N2 ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % cos_coeff_Suc
% 5.15/5.50 thf(fact_8515_complex__unimodular__polar,axiom,
% 5.15/5.50 ! [Z: complex] :
% 5.15/5.50 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.15/5.50 = one_one_real )
% 5.15/5.50 => ~ ! [T3: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.15/5.50 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.15/5.50 => ( Z
% 5.15/5.50 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_unimodular_polar
% 5.15/5.50 thf(fact_8516_sin__paired,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( sums_real
% 5.15/5.50 @ ^ [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 @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.15/5.50 @ ( sin_real @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % sin_paired
% 5.15/5.50 thf(fact_8517_cos__arcsin,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.50 => ( ( cos_real @ ( arcsin @ X ) )
% 5.15/5.50 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % cos_arcsin
% 5.15/5.50 thf(fact_8518_sin__arccos__abs,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.15/5.50 => ( ( sin_real @ ( arccos @ Y ) )
% 5.15/5.50 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sin_arccos_abs
% 5.15/5.50 thf(fact_8519_sums__zero,axiom,
% 5.15/5.50 ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : zero_zero_complex
% 5.15/5.50 @ zero_zero_complex ) ).
% 5.15/5.50
% 5.15/5.50 % sums_zero
% 5.15/5.50 thf(fact_8520_sums__zero,axiom,
% 5.15/5.50 ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : zero_zero_real
% 5.15/5.50 @ zero_zero_real ) ).
% 5.15/5.50
% 5.15/5.50 % sums_zero
% 5.15/5.50 thf(fact_8521_sums__zero,axiom,
% 5.15/5.50 ( sums_nat
% 5.15/5.50 @ ^ [N3: nat] : zero_zero_nat
% 5.15/5.50 @ zero_zero_nat ) ).
% 5.15/5.50
% 5.15/5.50 % sums_zero
% 5.15/5.50 thf(fact_8522_sums__zero,axiom,
% 5.15/5.50 ( sums_int
% 5.15/5.50 @ ^ [N3: nat] : zero_zero_int
% 5.15/5.50 @ zero_zero_int ) ).
% 5.15/5.50
% 5.15/5.50 % sums_zero
% 5.15/5.50 thf(fact_8523_arccos__1,axiom,
% 5.15/5.50 ( ( arccos @ one_one_real )
% 5.15/5.50 = zero_zero_real ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_1
% 5.15/5.50 thf(fact_8524_arccos__minus__1,axiom,
% 5.15/5.50 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.50 = pi ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_minus_1
% 5.15/5.50 thf(fact_8525_cos__arccos,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( cos_real @ ( arccos @ Y ) )
% 5.15/5.50 = Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % cos_arccos
% 5.15/5.50 thf(fact_8526_sin__arcsin,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.15/5.50 = Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sin_arcsin
% 5.15/5.50 thf(fact_8527_powser__sums__zero__iff,axiom,
% 5.15/5.50 ! [A: nat > complex,X: complex] :
% 5.15/5.50 ( ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( A @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) )
% 5.15/5.50 @ X )
% 5.15/5.50 = ( ( A @ zero_zero_nat )
% 5.15/5.50 = X ) ) ).
% 5.15/5.50
% 5.15/5.50 % powser_sums_zero_iff
% 5.15/5.50 thf(fact_8528_powser__sums__zero__iff,axiom,
% 5.15/5.50 ! [A: nat > real,X: real] :
% 5.15/5.50 ( ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( A @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) )
% 5.15/5.50 @ X )
% 5.15/5.50 = ( ( A @ zero_zero_nat )
% 5.15/5.50 = X ) ) ).
% 5.15/5.50
% 5.15/5.50 % powser_sums_zero_iff
% 5.15/5.50 thf(fact_8529_norm__cos__sin,axiom,
% 5.15/5.50 ! [T: real] :
% 5.15/5.50 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.15/5.50 = one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % norm_cos_sin
% 5.15/5.50 thf(fact_8530_arccos__0,axiom,
% 5.15/5.50 ( ( arccos @ zero_zero_real )
% 5.15/5.50 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_0
% 5.15/5.50 thf(fact_8531_arcsin__1,axiom,
% 5.15/5.50 ( ( arcsin @ one_one_real )
% 5.15/5.50 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_1
% 5.15/5.50 thf(fact_8532_arcsin__minus__1,axiom,
% 5.15/5.50 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.50 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_minus_1
% 5.15/5.50 thf(fact_8533_sums__mult,axiom,
% 5.15/5.50 ! [F: nat > complex,A: complex,C: complex] :
% 5.15/5.50 ( ( sums_complex @ F @ A )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) )
% 5.15/5.50 @ ( times_times_complex @ C @ A ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult
% 5.15/5.50 thf(fact_8534_sums__mult,axiom,
% 5.15/5.50 ! [F: nat > real,A: real,C: real] :
% 5.15/5.50 ( ( sums_real @ F @ A )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.15/5.50 @ ( times_times_real @ C @ A ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult
% 5.15/5.50 thf(fact_8535_sums__mult2,axiom,
% 5.15/5.50 ! [F: nat > complex,A: complex,C: complex] :
% 5.15/5.50 ( ( sums_complex @ F @ A )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ C )
% 5.15/5.50 @ ( times_times_complex @ A @ C ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult2
% 5.15/5.50 thf(fact_8536_sums__mult2,axiom,
% 5.15/5.50 ! [F: nat > real,A: real,C: real] :
% 5.15/5.50 ( ( sums_real @ F @ A )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C )
% 5.15/5.50 @ ( times_times_real @ A @ C ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult2
% 5.15/5.50 thf(fact_8537_sums__diff,axiom,
% 5.15/5.50 ! [F: nat > complex,A: complex,G: nat > complex,B: complex] :
% 5.15/5.50 ( ( sums_complex @ F @ A )
% 5.15/5.50 => ( ( sums_complex @ G @ B )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( minus_minus_complex @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_diff
% 5.15/5.50 thf(fact_8538_sums__diff,axiom,
% 5.15/5.50 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.15/5.50 ( ( sums_real @ F @ A )
% 5.15/5.50 => ( ( sums_real @ G @ B )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_diff
% 5.15/5.50 thf(fact_8539_sums__divide,axiom,
% 5.15/5.50 ! [F: nat > complex,A: complex,C: complex] :
% 5.15/5.50 ( ( sums_complex @ F @ A )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C )
% 5.15/5.50 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_divide
% 5.15/5.50 thf(fact_8540_sums__divide,axiom,
% 5.15/5.50 ! [F: nat > real,A: real,C: real] :
% 5.15/5.50 ( ( sums_real @ F @ A )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C )
% 5.15/5.50 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_divide
% 5.15/5.50 thf(fact_8541_sums__minus,axiom,
% 5.15/5.50 ! [F: nat > real,A: real] :
% 5.15/5.50 ( ( sums_real @ F @ A )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( uminus_uminus_real @ ( F @ N3 ) )
% 5.15/5.50 @ ( uminus_uminus_real @ A ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_minus
% 5.15/5.50 thf(fact_8542_sums__minus,axiom,
% 5.15/5.50 ! [F: nat > complex,A: complex] :
% 5.15/5.50 ( ( sums_complex @ F @ A )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( uminus1482373934393186551omplex @ ( F @ N3 ) )
% 5.15/5.50 @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_minus
% 5.15/5.50 thf(fact_8543_complex__diff,axiom,
% 5.15/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.50 ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.15/5.50 = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_diff
% 5.15/5.50 thf(fact_8544_sums__le,axiom,
% 5.15/5.50 ! [F: nat > real,G: nat > real,S: real,T: real] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( G @ N ) )
% 5.15/5.50 => ( ( sums_real @ F @ S )
% 5.15/5.50 => ( ( sums_real @ G @ T )
% 5.15/5.50 => ( ord_less_eq_real @ S @ T ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_le
% 5.15/5.50 thf(fact_8545_sums__le,axiom,
% 5.15/5.50 ! [F: nat > nat,G: nat > nat,S: nat,T: nat] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ ( G @ N ) )
% 5.15/5.50 => ( ( sums_nat @ F @ S )
% 5.15/5.50 => ( ( sums_nat @ G @ T )
% 5.15/5.50 => ( ord_less_eq_nat @ S @ T ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_le
% 5.15/5.50 thf(fact_8546_sums__le,axiom,
% 5.15/5.50 ! [F: nat > int,G: nat > int,S: int,T: int] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_int @ ( F @ N ) @ ( G @ N ) )
% 5.15/5.50 => ( ( sums_int @ F @ S )
% 5.15/5.50 => ( ( sums_int @ G @ T )
% 5.15/5.50 => ( ord_less_eq_int @ S @ T ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_le
% 5.15/5.50 thf(fact_8547_sums__add,axiom,
% 5.15/5.50 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.15/5.50 ( ( sums_real @ F @ A )
% 5.15/5.50 => ( ( sums_real @ G @ B )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_add
% 5.15/5.50 thf(fact_8548_sums__add,axiom,
% 5.15/5.50 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.15/5.50 ( ( sums_nat @ F @ A )
% 5.15/5.50 => ( ( sums_nat @ G @ B )
% 5.15/5.50 => ( sums_nat
% 5.15/5.50 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_add
% 5.15/5.50 thf(fact_8549_sums__add,axiom,
% 5.15/5.50 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.15/5.50 ( ( sums_int @ F @ A )
% 5.15/5.50 => ( ( sums_int @ G @ B )
% 5.15/5.50 => ( sums_int
% 5.15/5.50 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_add
% 5.15/5.50 thf(fact_8550_sums__add,axiom,
% 5.15/5.50 ! [F: nat > complex,A: complex,G: nat > complex,B: complex] :
% 5.15/5.50 ( ( sums_complex @ F @ A )
% 5.15/5.50 => ( ( sums_complex @ G @ B )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( plus_plus_complex @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_add
% 5.15/5.50 thf(fact_8551_sums__single,axiom,
% 5.15/5.50 ! [I: nat,F: nat > complex] :
% 5.15/5.50 ( sums_complex
% 5.15/5.50 @ ^ [R5: nat] : ( if_complex @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.15/5.50 @ ( F @ I ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_single
% 5.15/5.50 thf(fact_8552_sums__single,axiom,
% 5.15/5.50 ! [I: nat,F: nat > real] :
% 5.15/5.50 ( sums_real
% 5.15/5.50 @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real )
% 5.15/5.50 @ ( F @ I ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_single
% 5.15/5.50 thf(fact_8553_sums__single,axiom,
% 5.15/5.50 ! [I: nat,F: nat > nat] :
% 5.15/5.50 ( sums_nat
% 5.15/5.50 @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.15/5.50 @ ( F @ I ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_single
% 5.15/5.50 thf(fact_8554_sums__single,axiom,
% 5.15/5.50 ! [I: nat,F: nat > int] :
% 5.15/5.50 ( sums_int
% 5.15/5.50 @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int )
% 5.15/5.50 @ ( F @ I ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_single
% 5.15/5.50 thf(fact_8555_sums__of__real,axiom,
% 5.15/5.50 ! [X8: nat > real,A: real] :
% 5.15/5.50 ( ( sums_real @ X8 @ A )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( real_V1803761363581548252l_real @ ( X8 @ N3 ) )
% 5.15/5.50 @ ( real_V1803761363581548252l_real @ A ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_of_real
% 5.15/5.50 thf(fact_8556_sums__of__real,axiom,
% 5.15/5.50 ! [X8: nat > real,A: real] :
% 5.15/5.50 ( ( sums_real @ X8 @ A )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( real_V4546457046886955230omplex @ ( X8 @ N3 ) )
% 5.15/5.50 @ ( real_V4546457046886955230omplex @ A ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_of_real
% 5.15/5.50 thf(fact_8557_sums__of__real__iff,axiom,
% 5.15/5.50 ! [F: nat > real,C: real] :
% 5.15/5.50 ( ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( real_V1803761363581548252l_real @ ( F @ N3 ) )
% 5.15/5.50 @ ( real_V1803761363581548252l_real @ C ) )
% 5.15/5.50 = ( sums_real @ F @ C ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_of_real_iff
% 5.15/5.50 thf(fact_8558_sums__of__real__iff,axiom,
% 5.15/5.50 ! [F: nat > real,C: real] :
% 5.15/5.50 ( ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( real_V4546457046886955230omplex @ ( F @ N3 ) )
% 5.15/5.50 @ ( real_V4546457046886955230omplex @ C ) )
% 5.15/5.50 = ( sums_real @ F @ C ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_of_real_iff
% 5.15/5.50 thf(fact_8559_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_complex,F: complex > nat > real,X: complex > real] :
% 5.15/5.50 ( ! [I2: complex] :
% 5.15/5.50 ( ( member_complex @ I2 @ I5 )
% 5.15/5.50 => ( sums_real @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups5808333547571424918x_real
% 5.15/5.50 @ ^ [I3: complex] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups5808333547571424918x_real @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8560_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_real,F: real > nat > real,X: real > real] :
% 5.15/5.50 ( ! [I2: real] :
% 5.15/5.50 ( ( member_real @ I2 @ I5 )
% 5.15/5.50 => ( sums_real @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups8097168146408367636l_real
% 5.15/5.50 @ ^ [I3: real] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups8097168146408367636l_real @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8561_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_int,F: int > nat > real,X: int > real] :
% 5.15/5.50 ( ! [I2: int] :
% 5.15/5.50 ( ( member_int @ I2 @ I5 )
% 5.15/5.50 => ( sums_real @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups8778361861064173332t_real
% 5.15/5.50 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups8778361861064173332t_real @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8562_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_real,F: real > nat > complex,X: real > complex] :
% 5.15/5.50 ( ! [I2: real] :
% 5.15/5.50 ( ( member_real @ I2 @ I5 )
% 5.15/5.50 => ( sums_complex @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups5754745047067104278omplex
% 5.15/5.50 @ ^ [I3: real] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups5754745047067104278omplex @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8563_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_nat,F: nat > nat > complex,X: nat > complex] :
% 5.15/5.50 ( ! [I2: nat] :
% 5.15/5.50 ( ( member_nat @ I2 @ I5 )
% 5.15/5.50 => ( sums_complex @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups2073611262835488442omplex
% 5.15/5.50 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups2073611262835488442omplex @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8564_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_int,F: int > nat > complex,X: int > complex] :
% 5.15/5.50 ( ! [I2: int] :
% 5.15/5.50 ( ( member_int @ I2 @ I5 )
% 5.15/5.50 => ( sums_complex @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups3049146728041665814omplex
% 5.15/5.50 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups3049146728041665814omplex @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8565_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_int,F: int > nat > int,X: int > int] :
% 5.15/5.50 ( ! [I2: int] :
% 5.15/5.50 ( ( member_int @ I2 @ I5 )
% 5.15/5.50 => ( sums_int @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_int
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups4538972089207619220nt_int
% 5.15/5.50 @ ^ [I3: int] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups4538972089207619220nt_int @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8566_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_complex,F: complex > nat > complex,X: complex > complex] :
% 5.15/5.50 ( ! [I2: complex] :
% 5.15/5.50 ( ( member_complex @ I2 @ I5 )
% 5.15/5.50 => ( sums_complex @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups7754918857620584856omplex
% 5.15/5.50 @ ^ [I3: complex] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups7754918857620584856omplex @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8567_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_nat,F: nat > nat > nat,X: nat > nat] :
% 5.15/5.50 ( ! [I2: nat] :
% 5.15/5.50 ( ( member_nat @ I2 @ I5 )
% 5.15/5.50 => ( sums_nat @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_nat
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups3542108847815614940at_nat
% 5.15/5.50 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups3542108847815614940at_nat @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8568_sums__sum,axiom,
% 5.15/5.50 ! [I5: set_nat,F: nat > nat > real,X: nat > real] :
% 5.15/5.50 ( ! [I2: nat] :
% 5.15/5.50 ( ( member_nat @ I2 @ I5 )
% 5.15/5.50 => ( sums_real @ ( F @ I2 ) @ ( X @ I2 ) ) )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] :
% 5.15/5.50 ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [I3: nat] : ( F @ I3 @ N3 )
% 5.15/5.50 @ I5 )
% 5.15/5.50 @ ( groups6591440286371151544t_real @ X @ I5 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_sum
% 5.15/5.50 thf(fact_8569_sums__mult2__iff,axiom,
% 5.15/5.50 ! [C: complex,F: nat > complex,D: complex] :
% 5.15/5.50 ( ( C != zero_zero_complex )
% 5.15/5.50 => ( ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ C )
% 5.15/5.50 @ ( times_times_complex @ D @ C ) )
% 5.15/5.50 = ( sums_complex @ F @ D ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult2_iff
% 5.15/5.50 thf(fact_8570_sums__mult2__iff,axiom,
% 5.15/5.50 ! [C: real,F: nat > real,D: real] :
% 5.15/5.50 ( ( C != zero_zero_real )
% 5.15/5.50 => ( ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C )
% 5.15/5.50 @ ( times_times_real @ D @ C ) )
% 5.15/5.50 = ( sums_real @ F @ D ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult2_iff
% 5.15/5.50 thf(fact_8571_sums__mult__iff,axiom,
% 5.15/5.50 ! [C: complex,F: nat > complex,D: complex] :
% 5.15/5.50 ( ( C != zero_zero_complex )
% 5.15/5.50 => ( ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) )
% 5.15/5.50 @ ( times_times_complex @ C @ D ) )
% 5.15/5.50 = ( sums_complex @ F @ D ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult_iff
% 5.15/5.50 thf(fact_8572_sums__mult__iff,axiom,
% 5.15/5.50 ! [C: real,F: nat > real,D: real] :
% 5.15/5.50 ( ( C != zero_zero_real )
% 5.15/5.50 => ( ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.15/5.50 @ ( times_times_real @ C @ D ) )
% 5.15/5.50 = ( sums_real @ F @ D ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult_iff
% 5.15/5.50 thf(fact_8573_Complex__eq__numeral,axiom,
% 5.15/5.50 ! [A: real,B: real,W: num] :
% 5.15/5.50 ( ( ( complex2 @ A @ B )
% 5.15/5.50 = ( numera6690914467698888265omplex @ W ) )
% 5.15/5.50 = ( ( A
% 5.15/5.50 = ( numeral_numeral_real @ W ) )
% 5.15/5.50 & ( B = zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_eq_numeral
% 5.15/5.50 thf(fact_8574_complex__add,axiom,
% 5.15/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.50 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.15/5.50 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_add
% 5.15/5.50 thf(fact_8575_sums__mult__D,axiom,
% 5.15/5.50 ! [C: complex,F: nat > complex,A: complex] :
% 5.15/5.50 ( ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) )
% 5.15/5.50 @ A )
% 5.15/5.50 => ( ( C != zero_zero_complex )
% 5.15/5.50 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult_D
% 5.15/5.50 thf(fact_8576_sums__mult__D,axiom,
% 5.15/5.50 ! [C: real,F: nat > real,A: real] :
% 5.15/5.50 ( ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.15/5.50 @ A )
% 5.15/5.50 => ( ( C != zero_zero_real )
% 5.15/5.50 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_mult_D
% 5.15/5.50 thf(fact_8577_sums__Suc__imp,axiom,
% 5.15/5.50 ! [F: nat > complex,S: complex] :
% 5.15/5.50 ( ( ( F @ zero_zero_nat )
% 5.15/5.50 = zero_zero_complex )
% 5.15/5.50 => ( ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.15/5.50 @ S )
% 5.15/5.50 => ( sums_complex @ F @ S ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_Suc_imp
% 5.15/5.50 thf(fact_8578_sums__Suc__imp,axiom,
% 5.15/5.50 ! [F: nat > real,S: real] :
% 5.15/5.50 ( ( ( F @ zero_zero_nat )
% 5.15/5.50 = zero_zero_real )
% 5.15/5.50 => ( ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.15/5.50 @ S )
% 5.15/5.50 => ( sums_real @ F @ S ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_Suc_imp
% 5.15/5.50 thf(fact_8579_sums__Suc,axiom,
% 5.15/5.50 ! [F: nat > real,L: real] :
% 5.15/5.50 ( ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.15/5.50 @ L )
% 5.15/5.50 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_Suc
% 5.15/5.50 thf(fact_8580_sums__Suc,axiom,
% 5.15/5.50 ! [F: nat > nat,L: nat] :
% 5.15/5.50 ( ( sums_nat
% 5.15/5.50 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.15/5.50 @ L )
% 5.15/5.50 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_Suc
% 5.15/5.50 thf(fact_8581_sums__Suc,axiom,
% 5.15/5.50 ! [F: nat > int,L: int] :
% 5.15/5.50 ( ( sums_int
% 5.15/5.50 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.15/5.50 @ L )
% 5.15/5.50 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_Suc
% 5.15/5.50 thf(fact_8582_sums__Suc,axiom,
% 5.15/5.50 ! [F: nat > complex,L: complex] :
% 5.15/5.50 ( ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.15/5.50 @ L )
% 5.15/5.50 => ( sums_complex @ F @ ( plus_plus_complex @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_Suc
% 5.15/5.50 thf(fact_8583_sums__Suc__iff,axiom,
% 5.15/5.50 ! [F: nat > real,S: real] :
% 5.15/5.50 ( ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.15/5.50 @ S )
% 5.15/5.50 = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_Suc_iff
% 5.15/5.50 thf(fact_8584_sums__Suc__iff,axiom,
% 5.15/5.50 ! [F: nat > complex,S: complex] :
% 5.15/5.50 ( ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.15/5.50 @ S )
% 5.15/5.50 = ( sums_complex @ F @ ( plus_plus_complex @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_Suc_iff
% 5.15/5.50 thf(fact_8585_sums__zero__iff__shift,axiom,
% 5.15/5.50 ! [N2: nat,F: nat > complex,S: complex] :
% 5.15/5.50 ( ! [I2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ I2 @ N2 )
% 5.15/5.50 => ( ( F @ I2 )
% 5.15/5.50 = zero_zero_complex ) )
% 5.15/5.50 => ( ( sums_complex
% 5.15/5.50 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.15/5.50 @ S )
% 5.15/5.50 = ( sums_complex @ F @ S ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_zero_iff_shift
% 5.15/5.50 thf(fact_8586_sums__zero__iff__shift,axiom,
% 5.15/5.50 ! [N2: nat,F: nat > real,S: real] :
% 5.15/5.50 ( ! [I2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ I2 @ N2 )
% 5.15/5.50 => ( ( F @ I2 )
% 5.15/5.50 = zero_zero_real ) )
% 5.15/5.50 => ( ( sums_real
% 5.15/5.50 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.15/5.50 @ S )
% 5.15/5.50 = ( sums_real @ F @ S ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_zero_iff_shift
% 5.15/5.50 thf(fact_8587_Complex__eq__neg__numeral,axiom,
% 5.15/5.50 ! [A: real,B: real,W: num] :
% 5.15/5.50 ( ( ( complex2 @ A @ B )
% 5.15/5.50 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.50 = ( ( A
% 5.15/5.50 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.15/5.50 & ( B = zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_eq_neg_numeral
% 5.15/5.50 thf(fact_8588_sums__If__finite__set,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > complex] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.15/5.50 @ ( groups2073611262835488442omplex @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite_set
% 5.15/5.50 thf(fact_8589_sums__If__finite__set,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > int] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( sums_int
% 5.15/5.50 @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.15/5.50 @ ( groups3539618377306564664at_int @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite_set
% 5.15/5.50 thf(fact_8590_sums__If__finite__set,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > nat] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( sums_nat
% 5.15/5.50 @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.15/5.50 @ ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite_set
% 5.15/5.50 thf(fact_8591_sums__If__finite__set,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > real] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.15/5.50 @ ( groups6591440286371151544t_real @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite_set
% 5.15/5.50 thf(fact_8592_sums__If__finite,axiom,
% 5.15/5.50 ! [P: nat > $o,F: nat > complex] :
% 5.15/5.50 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.15/5.50 @ ( groups2073611262835488442omplex @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite
% 5.15/5.50 thf(fact_8593_sums__If__finite,axiom,
% 5.15/5.50 ! [P: nat > $o,F: nat > int] :
% 5.15/5.50 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.50 => ( sums_int
% 5.15/5.50 @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.15/5.50 @ ( groups3539618377306564664at_int @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite
% 5.15/5.50 thf(fact_8594_sums__If__finite,axiom,
% 5.15/5.50 ! [P: nat > $o,F: nat > nat] :
% 5.15/5.50 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.50 => ( sums_nat
% 5.15/5.50 @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.15/5.50 @ ( groups3542108847815614940at_nat @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite
% 5.15/5.50 thf(fact_8595_sums__If__finite,axiom,
% 5.15/5.50 ! [P: nat > $o,F: nat > real] :
% 5.15/5.50 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.15/5.50 @ ( groups6591440286371151544t_real @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite
% 5.15/5.50 thf(fact_8596_sums__finite,axiom,
% 5.15/5.50 ! [N5: set_nat,F: nat > complex] :
% 5.15/5.50 ( ( finite_finite_nat @ N5 )
% 5.15/5.50 => ( ! [N: nat] :
% 5.15/5.50 ( ~ ( member_nat @ N @ N5 )
% 5.15/5.50 => ( ( F @ N )
% 5.15/5.50 = zero_zero_complex ) )
% 5.15/5.50 => ( sums_complex @ F @ ( groups2073611262835488442omplex @ F @ N5 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_finite
% 5.15/5.50 thf(fact_8597_sums__finite,axiom,
% 5.15/5.50 ! [N5: set_nat,F: nat > int] :
% 5.15/5.50 ( ( finite_finite_nat @ N5 )
% 5.15/5.50 => ( ! [N: nat] :
% 5.15/5.50 ( ~ ( member_nat @ N @ N5 )
% 5.15/5.50 => ( ( F @ N )
% 5.15/5.50 = zero_zero_int ) )
% 5.15/5.50 => ( sums_int @ F @ ( groups3539618377306564664at_int @ F @ N5 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_finite
% 5.15/5.50 thf(fact_8598_sums__finite,axiom,
% 5.15/5.50 ! [N5: set_nat,F: nat > nat] :
% 5.15/5.50 ( ( finite_finite_nat @ N5 )
% 5.15/5.50 => ( ! [N: nat] :
% 5.15/5.50 ( ~ ( member_nat @ N @ N5 )
% 5.15/5.50 => ( ( F @ N )
% 5.15/5.50 = zero_zero_nat ) )
% 5.15/5.50 => ( sums_nat @ F @ ( groups3542108847815614940at_nat @ F @ N5 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_finite
% 5.15/5.50 thf(fact_8599_sums__finite,axiom,
% 5.15/5.50 ! [N5: set_nat,F: nat > real] :
% 5.15/5.50 ( ( finite_finite_nat @ N5 )
% 5.15/5.50 => ( ! [N: nat] :
% 5.15/5.50 ( ~ ( member_nat @ N @ N5 )
% 5.15/5.50 => ( ( F @ N )
% 5.15/5.50 = zero_zero_real ) )
% 5.15/5.50 => ( sums_real @ F @ ( groups6591440286371151544t_real @ F @ N5 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_finite
% 5.15/5.50 thf(fact_8600_one__complex_Ocode,axiom,
% 5.15/5.50 ( one_one_complex
% 5.15/5.50 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % one_complex.code
% 5.15/5.50 thf(fact_8601_Complex__eq__1,axiom,
% 5.15/5.50 ! [A: real,B: real] :
% 5.15/5.50 ( ( ( complex2 @ A @ B )
% 5.15/5.50 = one_one_complex )
% 5.15/5.50 = ( ( A = one_one_real )
% 5.15/5.50 & ( B = zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_eq_1
% 5.15/5.50 thf(fact_8602_complex__of__real__mult__Complex,axiom,
% 5.15/5.50 ! [R2: real,X: real,Y: real] :
% 5.15/5.50 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y ) )
% 5.15/5.50 = ( complex2 @ ( times_times_real @ R2 @ X ) @ ( times_times_real @ R2 @ Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_of_real_mult_Complex
% 5.15/5.50 thf(fact_8603_Complex__mult__complex__of__real,axiom,
% 5.15/5.50 ! [X: real,Y: real,R2: real] :
% 5.15/5.50 ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.15/5.50 = ( complex2 @ ( times_times_real @ X @ R2 ) @ ( times_times_real @ Y @ R2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_mult_complex_of_real
% 5.15/5.50 thf(fact_8604_complex__of__real__add__Complex,axiom,
% 5.15/5.50 ! [R2: real,X: real,Y: real] :
% 5.15/5.50 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y ) )
% 5.15/5.50 = ( complex2 @ ( plus_plus_real @ R2 @ X ) @ Y ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_of_real_add_Complex
% 5.15/5.50 thf(fact_8605_Complex__add__complex__of__real,axiom,
% 5.15/5.50 ! [X: real,Y: real,R2: real] :
% 5.15/5.50 ( ( plus_plus_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.15/5.50 = ( complex2 @ ( plus_plus_real @ X @ R2 ) @ Y ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_add_complex_of_real
% 5.15/5.50 thf(fact_8606_arccos__le__arccos,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_le_arccos
% 5.15/5.50 thf(fact_8607_arccos__eq__iff,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.50 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.15/5.50 => ( ( ( arccos @ X )
% 5.15/5.50 = ( arccos @ Y ) )
% 5.15/5.50 = ( X = Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_eq_iff
% 5.15/5.50 thf(fact_8608_arccos__le__mono,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.15/5.50 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_le_mono
% 5.15/5.50 thf(fact_8609_arcsin__minus,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.50 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 5.15/5.50 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_minus
% 5.15/5.50 thf(fact_8610_arcsin__le__arcsin,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_le_arcsin
% 5.15/5.50 thf(fact_8611_arcsin__eq__iff,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.15/5.50 => ( ( ( arcsin @ X )
% 5.15/5.50 = ( arcsin @ Y ) )
% 5.15/5.50 = ( X = Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_eq_iff
% 5.15/5.50 thf(fact_8612_arcsin__le__mono,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.15/5.50 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_le_mono
% 5.15/5.50 thf(fact_8613_powser__sums__if,axiom,
% 5.15/5.50 ! [M: nat,Z: complex] :
% 5.15/5.50 ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( if_complex @ ( N3 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N3 ) )
% 5.15/5.50 @ ( power_power_complex @ Z @ M ) ) ).
% 5.15/5.50
% 5.15/5.50 % powser_sums_if
% 5.15/5.50 thf(fact_8614_powser__sums__if,axiom,
% 5.15/5.50 ! [M: nat,Z: real] :
% 5.15/5.50 ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( if_real @ ( N3 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N3 ) )
% 5.15/5.50 @ ( power_power_real @ Z @ M ) ) ).
% 5.15/5.50
% 5.15/5.50 % powser_sums_if
% 5.15/5.50 thf(fact_8615_powser__sums__if,axiom,
% 5.15/5.50 ! [M: nat,Z: int] :
% 5.15/5.50 ( sums_int
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_int @ ( if_int @ ( N3 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N3 ) )
% 5.15/5.50 @ ( power_power_int @ Z @ M ) ) ).
% 5.15/5.50
% 5.15/5.50 % powser_sums_if
% 5.15/5.50 thf(fact_8616_powser__sums__zero,axiom,
% 5.15/5.50 ! [A: nat > complex] :
% 5.15/5.50 ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( A @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) )
% 5.15/5.50 @ ( A @ zero_zero_nat ) ) ).
% 5.15/5.50
% 5.15/5.50 % powser_sums_zero
% 5.15/5.50 thf(fact_8617_powser__sums__zero,axiom,
% 5.15/5.50 ! [A: nat > real] :
% 5.15/5.50 ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( A @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) )
% 5.15/5.50 @ ( A @ zero_zero_nat ) ) ).
% 5.15/5.50
% 5.15/5.50 % powser_sums_zero
% 5.15/5.50 thf(fact_8618_sums__iff__shift,axiom,
% 5.15/5.50 ! [F: nat > complex,N2: nat,S: complex] :
% 5.15/5.50 ( ( sums_complex
% 5.15/5.50 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.15/5.50 @ S )
% 5.15/5.50 = ( sums_complex @ F @ ( plus_plus_complex @ S @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_iff_shift
% 5.15/5.50 thf(fact_8619_sums__iff__shift,axiom,
% 5.15/5.50 ! [F: nat > real,N2: nat,S: real] :
% 5.15/5.50 ( ( sums_real
% 5.15/5.50 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.15/5.50 @ S )
% 5.15/5.50 = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_iff_shift
% 5.15/5.50 thf(fact_8620_sums__iff__shift_H,axiom,
% 5.15/5.50 ! [F: nat > complex,N2: nat,S: complex] :
% 5.15/5.50 ( ( sums_complex
% 5.15/5.50 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.15/5.50 @ ( minus_minus_complex @ S @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.15/5.50 = ( sums_complex @ F @ S ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_iff_shift'
% 5.15/5.50 thf(fact_8621_sums__iff__shift_H,axiom,
% 5.15/5.50 ! [F: nat > real,N2: nat,S: real] :
% 5.15/5.50 ( ( sums_real
% 5.15/5.50 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.15/5.50 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.15/5.50 = ( sums_real @ F @ S ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_iff_shift'
% 5.15/5.50 thf(fact_8622_sums__split__initial__segment,axiom,
% 5.15/5.50 ! [F: nat > complex,S: complex,N2: nat] :
% 5.15/5.50 ( ( sums_complex @ F @ S )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.15/5.50 @ ( minus_minus_complex @ S @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_split_initial_segment
% 5.15/5.50 thf(fact_8623_sums__split__initial__segment,axiom,
% 5.15/5.50 ! [F: nat > real,S: real,N2: nat] :
% 5.15/5.50 ( ( sums_real @ F @ S )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.15/5.50 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_split_initial_segment
% 5.15/5.50 thf(fact_8624_sums__If__finite__set_H,axiom,
% 5.15/5.50 ! [G: nat > complex,S3: complex,A2: set_nat,S5: complex,F: nat > complex] :
% 5.15/5.50 ( ( sums_complex @ G @ S3 )
% 5.15/5.50 => ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( S5
% 5.15/5.50 = ( plus_plus_complex @ S3
% 5.15/5.50 @ ( groups2073611262835488442omplex
% 5.15/5.50 @ ^ [N3: nat] : ( minus_minus_complex @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ A2 ) ) )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( if_complex @ ( member_nat @ N3 @ A2 ) @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ S5 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite_set'
% 5.15/5.50 thf(fact_8625_sums__If__finite__set_H,axiom,
% 5.15/5.50 ! [G: nat > real,S3: real,A2: set_nat,S5: real,F: nat > real] :
% 5.15/5.50 ( ( sums_real @ G @ S3 )
% 5.15/5.50 => ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( S5
% 5.15/5.50 = ( plus_plus_real @ S3
% 5.15/5.50 @ ( groups6591440286371151544t_real
% 5.15/5.50 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ A2 ) ) )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( if_real @ ( member_nat @ N3 @ A2 ) @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.50 @ S5 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_If_finite_set'
% 5.15/5.50 thf(fact_8626_Complex__sum_H,axiom,
% 5.15/5.50 ! [F: nat > real,S: set_nat] :
% 5.15/5.50 ( ( groups2073611262835488442omplex
% 5.15/5.50 @ ^ [X2: nat] : ( complex2 @ ( F @ X2 ) @ zero_zero_real )
% 5.15/5.50 @ S )
% 5.15/5.50 = ( complex2 @ ( groups6591440286371151544t_real @ F @ S ) @ zero_zero_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_sum'
% 5.15/5.50 thf(fact_8627_Complex__sum_H,axiom,
% 5.15/5.50 ! [F: complex > real,S: set_complex] :
% 5.15/5.50 ( ( groups7754918857620584856omplex
% 5.15/5.50 @ ^ [X2: complex] : ( complex2 @ ( F @ X2 ) @ zero_zero_real )
% 5.15/5.50 @ S )
% 5.15/5.50 = ( complex2 @ ( groups5808333547571424918x_real @ F @ S ) @ zero_zero_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_sum'
% 5.15/5.50 thf(fact_8628_Complex__eq__neg__1,axiom,
% 5.15/5.50 ! [A: real,B: real] :
% 5.15/5.50 ( ( ( complex2 @ A @ B )
% 5.15/5.50 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.15/5.50 = ( ( A
% 5.15/5.50 = ( uminus_uminus_real @ one_one_real ) )
% 5.15/5.50 & ( B = zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_eq_neg_1
% 5.15/5.50 thf(fact_8629_complex__mult,axiom,
% 5.15/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.15/5.50 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.15/5.50 = ( 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 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_mult
% 5.15/5.50 thf(fact_8630_arccos__lbound,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_lbound
% 5.15/5.50 thf(fact_8631_arccos__less__arccos,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_less_arccos
% 5.15/5.50 thf(fact_8632_arccos__less__mono,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.15/5.50 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_less_mono
% 5.15/5.50 thf(fact_8633_arccos__ubound,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_ubound
% 5.15/5.50 thf(fact_8634_arccos__cos,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ pi )
% 5.15/5.50 => ( ( arccos @ ( cos_real @ X ) )
% 5.15/5.50 = X ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_cos
% 5.15/5.50 thf(fact_8635_arcsin__less__arcsin,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_less_arcsin
% 5.15/5.50 thf(fact_8636_arcsin__less__mono,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.15/5.50 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.15/5.50 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_less_mono
% 5.15/5.50 thf(fact_8637_cos__arccos__abs,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.15/5.50 => ( ( cos_real @ ( arccos @ Y ) )
% 5.15/5.50 = Y ) ) ).
% 5.15/5.50
% 5.15/5.50 % cos_arccos_abs
% 5.15/5.50 thf(fact_8638_arccos__cos__eq__abs,axiom,
% 5.15/5.50 ! [Theta: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.15/5.50 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.15/5.50 = ( abs_abs_real @ Theta ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_cos_eq_abs
% 5.15/5.50 thf(fact_8639_arccos__lt__bounded,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.15/5.50 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_lt_bounded
% 5.15/5.50 thf(fact_8640_arccos__bounded,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_bounded
% 5.15/5.50 thf(fact_8641_sin__arccos__nonzero,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.50 => ( ( sin_real @ ( arccos @ X ) )
% 5.15/5.50 != zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sin_arccos_nonzero
% 5.15/5.50 thf(fact_8642_arccos__cos2,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.15/5.50 => ( ( arccos @ ( cos_real @ X ) )
% 5.15/5.50 = ( uminus_uminus_real @ X ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_cos2
% 5.15/5.50 thf(fact_8643_arccos__minus,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.50 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.15/5.50 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_minus
% 5.15/5.50 thf(fact_8644_cos__arcsin__nonzero,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.50 => ( ( cos_real @ ( arcsin @ X ) )
% 5.15/5.50 != zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % cos_arcsin_nonzero
% 5.15/5.50 thf(fact_8645_geometric__sums,axiom,
% 5.15/5.50 ! [C: real] :
% 5.15/5.50 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.15/5.50 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % geometric_sums
% 5.15/5.50 thf(fact_8646_geometric__sums,axiom,
% 5.15/5.50 ! [C: complex] :
% 5.15/5.50 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.15/5.50 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % geometric_sums
% 5.15/5.50 thf(fact_8647_power__half__series,axiom,
% 5.15/5.50 ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N3 ) )
% 5.15/5.50 @ one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % power_half_series
% 5.15/5.50 thf(fact_8648_arccos,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.15/5.50 & ( ( cos_real @ ( arccos @ Y ) )
% 5.15/5.50 = Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos
% 5.15/5.50 thf(fact_8649_arccos__minus__abs,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.50 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.15/5.50 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_minus_abs
% 5.15/5.50 thf(fact_8650_complex__norm,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y ) )
% 5.15/5.50 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_norm
% 5.15/5.50 thf(fact_8651_sums__if_H,axiom,
% 5.15/5.50 ! [G: nat > real,X: real] :
% 5.15/5.50 ( ( sums_real @ G @ X )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [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 ) ) ) ) )
% 5.15/5.50 @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_if'
% 5.15/5.50 thf(fact_8652_sums__if,axiom,
% 5.15/5.50 ! [G: nat > real,X: real,F: nat > real,Y: real] :
% 5.15/5.50 ( ( sums_real @ G @ X )
% 5.15/5.50 => ( ( sums_real @ F @ Y )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [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 ) ) ) ) )
% 5.15/5.50 @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sums_if
% 5.15/5.50 thf(fact_8653_arccos__le__pi2,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_le_pi2
% 5.15/5.50 thf(fact_8654_arcsin__lt__bounded,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.15/5.50 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_lt_bounded
% 5.15/5.50 thf(fact_8655_arcsin__lbound,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_lbound
% 5.15/5.50 thf(fact_8656_arcsin__ubound,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_ubound
% 5.15/5.50 thf(fact_8657_arcsin__bounded,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_bounded
% 5.15/5.50 thf(fact_8658_arcsin__sin,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( arcsin @ ( sin_real @ X ) )
% 5.15/5.50 = X ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_sin
% 5.15/5.50 thf(fact_8659_cos__paired,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( sums_real
% 5.15/5.50 @ ^ [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 @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.15/5.50 @ ( cos_real @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % cos_paired
% 5.15/5.50 thf(fact_8660_arcsin,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.15/5.50 = Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin
% 5.15/5.50 thf(fact_8661_arcsin__pi,axiom,
% 5.15/5.50 ! [Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.15/5.50 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.15/5.50 = Y ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_pi
% 5.15/5.50 thf(fact_8662_arcsin__le__iff,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 5.15/5.50 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arcsin_le_iff
% 5.15/5.50 thf(fact_8663_le__arcsin__iff,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.50 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % le_arcsin_iff
% 5.15/5.50 thf(fact_8664_arccos__cos__eq__abs__2pi,axiom,
% 5.15/5.50 ! [Theta: real] :
% 5.15/5.50 ~ ! [K3: int] :
% 5.15/5.50 ( ( arccos @ ( cos_real @ Theta ) )
% 5.15/5.50 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % arccos_cos_eq_abs_2pi
% 5.15/5.50 thf(fact_8665_geometric__deriv__sums,axiom,
% 5.15/5.50 ! [Z: real] :
% 5.15/5.50 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) )
% 5.15/5.50 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % geometric_deriv_sums
% 5.15/5.50 thf(fact_8666_geometric__deriv__sums,axiom,
% 5.15/5.50 ! [Z: complex] :
% 5.15/5.50 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) )
% 5.15/5.50 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % geometric_deriv_sums
% 5.15/5.50 thf(fact_8667_sin__arccos,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.50 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.50 => ( ( sin_real @ ( arccos @ X ) )
% 5.15/5.50 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % sin_arccos
% 5.15/5.50 thf(fact_8668_diffs__equiv,axiom,
% 5.15/5.50 ! [C: nat > real,X: real] :
% 5.15/5.50 ( ( summable_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X @ N3 ) ) )
% 5.15/5.50 => ( sums_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( C @ N3 ) ) @ ( power_power_real @ X @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) ) )
% 5.15/5.50 @ ( suminf_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_equiv
% 5.15/5.50 thf(fact_8669_diffs__equiv,axiom,
% 5.15/5.50 ! [C: nat > complex,X: complex] :
% 5.15/5.50 ( ( summable_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X @ N3 ) ) )
% 5.15/5.50 => ( sums_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N3 ) @ ( C @ N3 ) ) @ ( power_power_complex @ X @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) ) )
% 5.15/5.50 @ ( suminf_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_equiv
% 5.15/5.50 thf(fact_8670_monoI1,axiom,
% 5.15/5.50 ! [X8: nat > real] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_real @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.15/5.50 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI1
% 5.15/5.50 thf(fact_8671_monoI1,axiom,
% 5.15/5.50 ! [X8: nat > set_nat] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_set_nat @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.15/5.50 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI1
% 5.15/5.50 thf(fact_8672_monoI1,axiom,
% 5.15/5.50 ! [X8: nat > rat] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_rat @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.15/5.50 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI1
% 5.15/5.50 thf(fact_8673_monoI1,axiom,
% 5.15/5.50 ! [X8: nat > num] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_num @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.15/5.50 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI1
% 5.15/5.50 thf(fact_8674_monoI1,axiom,
% 5.15/5.50 ! [X8: nat > nat] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_nat @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.15/5.50 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI1
% 5.15/5.50 thf(fact_8675_monoI1,axiom,
% 5.15/5.50 ! [X8: nat > int] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_int @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.15/5.50 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI1
% 5.15/5.50 thf(fact_8676_monoI2,axiom,
% 5.15/5.50 ! [X8: nat > real] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_real @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.15/5.50 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI2
% 5.15/5.50 thf(fact_8677_monoI2,axiom,
% 5.15/5.50 ! [X8: nat > set_nat] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_set_nat @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.15/5.50 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI2
% 5.15/5.50 thf(fact_8678_monoI2,axiom,
% 5.15/5.50 ! [X8: nat > rat] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_rat @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.15/5.50 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI2
% 5.15/5.50 thf(fact_8679_monoI2,axiom,
% 5.15/5.50 ! [X8: nat > num] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_num @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.15/5.50 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI2
% 5.15/5.50 thf(fact_8680_monoI2,axiom,
% 5.15/5.50 ! [X8: nat > nat] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_nat @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.15/5.50 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI2
% 5.15/5.50 thf(fact_8681_monoI2,axiom,
% 5.15/5.50 ! [X8: nat > int] :
% 5.15/5.50 ( ! [M3: nat,N: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M3 @ N )
% 5.15/5.50 => ( ord_less_eq_int @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.15/5.50 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoI2
% 5.15/5.50 thf(fact_8682_monoseq__def,axiom,
% 5.15/5.50 ( topolo6980174941875973593q_real
% 5.15/5.50 = ( ^ [X4: nat > real] :
% 5.15/5.50 ( ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_real @ ( X4 @ M5 ) @ ( X4 @ N3 ) ) )
% 5.15/5.50 | ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_real @ ( X4 @ N3 ) @ ( X4 @ M5 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_def
% 5.15/5.50 thf(fact_8683_monoseq__def,axiom,
% 5.15/5.50 ( topolo7278393974255667507et_nat
% 5.15/5.50 = ( ^ [X4: nat > set_nat] :
% 5.15/5.50 ( ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_set_nat @ ( X4 @ M5 ) @ ( X4 @ N3 ) ) )
% 5.15/5.50 | ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_set_nat @ ( X4 @ N3 ) @ ( X4 @ M5 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_def
% 5.15/5.50 thf(fact_8684_monoseq__def,axiom,
% 5.15/5.50 ( topolo4267028734544971653eq_rat
% 5.15/5.50 = ( ^ [X4: nat > rat] :
% 5.15/5.50 ( ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_rat @ ( X4 @ M5 ) @ ( X4 @ N3 ) ) )
% 5.15/5.50 | ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_rat @ ( X4 @ N3 ) @ ( X4 @ M5 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_def
% 5.15/5.50 thf(fact_8685_monoseq__def,axiom,
% 5.15/5.50 ( topolo1459490580787246023eq_num
% 5.15/5.50 = ( ^ [X4: nat > num] :
% 5.15/5.50 ( ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_num @ ( X4 @ M5 ) @ ( X4 @ N3 ) ) )
% 5.15/5.50 | ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_num @ ( X4 @ N3 ) @ ( X4 @ M5 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_def
% 5.15/5.50 thf(fact_8686_monoseq__def,axiom,
% 5.15/5.50 ( topolo4902158794631467389eq_nat
% 5.15/5.50 = ( ^ [X4: nat > nat] :
% 5.15/5.50 ( ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_nat @ ( X4 @ M5 ) @ ( X4 @ N3 ) ) )
% 5.15/5.50 | ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_nat @ ( X4 @ N3 ) @ ( X4 @ M5 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_def
% 5.15/5.50 thf(fact_8687_monoseq__def,axiom,
% 5.15/5.50 ( topolo4899668324122417113eq_int
% 5.15/5.50 = ( ^ [X4: nat > int] :
% 5.15/5.50 ( ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_int @ ( X4 @ M5 ) @ ( X4 @ N3 ) ) )
% 5.15/5.50 | ! [M5: nat,N3: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.50 => ( ord_less_eq_int @ ( X4 @ N3 ) @ ( X4 @ M5 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_def
% 5.15/5.50 thf(fact_8688_diffs__of__real,axiom,
% 5.15/5.50 ! [F: nat > real] :
% 5.15/5.50 ( ( diffs_complex
% 5.15/5.50 @ ^ [N3: nat] : ( real_V4546457046886955230omplex @ ( F @ N3 ) ) )
% 5.15/5.50 = ( ^ [N3: nat] : ( real_V4546457046886955230omplex @ ( diffs_real @ F @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_of_real
% 5.15/5.50 thf(fact_8689_diffs__minus,axiom,
% 5.15/5.50 ! [C: nat > int] :
% 5.15/5.50 ( ( diffs_int
% 5.15/5.50 @ ^ [N3: nat] : ( uminus_uminus_int @ ( C @ N3 ) ) )
% 5.15/5.50 = ( ^ [N3: nat] : ( uminus_uminus_int @ ( diffs_int @ C @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_minus
% 5.15/5.50 thf(fact_8690_diffs__minus,axiom,
% 5.15/5.50 ! [C: nat > real] :
% 5.15/5.50 ( ( diffs_real
% 5.15/5.50 @ ^ [N3: nat] : ( uminus_uminus_real @ ( C @ N3 ) ) )
% 5.15/5.50 = ( ^ [N3: nat] : ( uminus_uminus_real @ ( diffs_real @ C @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_minus
% 5.15/5.50 thf(fact_8691_diffs__minus,axiom,
% 5.15/5.50 ! [C: nat > complex] :
% 5.15/5.50 ( ( diffs_complex
% 5.15/5.50 @ ^ [N3: nat] : ( uminus1482373934393186551omplex @ ( C @ N3 ) ) )
% 5.15/5.50 = ( ^ [N3: nat] : ( uminus1482373934393186551omplex @ ( diffs_complex @ C @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_minus
% 5.15/5.50 thf(fact_8692_diffs__minus,axiom,
% 5.15/5.50 ! [C: nat > rat] :
% 5.15/5.50 ( ( diffs_rat
% 5.15/5.50 @ ^ [N3: nat] : ( uminus_uminus_rat @ ( C @ N3 ) ) )
% 5.15/5.50 = ( ^ [N3: nat] : ( uminus_uminus_rat @ ( diffs_rat @ C @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_minus
% 5.15/5.50 thf(fact_8693_diffs__minus,axiom,
% 5.15/5.50 ! [C: nat > code_integer] :
% 5.15/5.50 ( ( diffs_Code_integer
% 5.15/5.50 @ ^ [N3: nat] : ( uminus1351360451143612070nteger @ ( C @ N3 ) ) )
% 5.15/5.50 = ( ^ [N3: nat] : ( uminus1351360451143612070nteger @ ( diffs_Code_integer @ C @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_minus
% 5.15/5.50 thf(fact_8694_diffs__def,axiom,
% 5.15/5.50 ( diffs_rat
% 5.15/5.50 = ( ^ [C3: nat > rat,N3: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) @ ( C3 @ ( suc @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_def
% 5.15/5.50 thf(fact_8695_diffs__def,axiom,
% 5.15/5.50 ( diffs_int
% 5.15/5.50 = ( ^ [C3: nat > int,N3: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) @ ( C3 @ ( suc @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_def
% 5.15/5.50 thf(fact_8696_diffs__def,axiom,
% 5.15/5.50 ( diffs_real
% 5.15/5.50 = ( ^ [C3: nat > real,N3: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) @ ( C3 @ ( suc @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_def
% 5.15/5.50 thf(fact_8697_diffs__def,axiom,
% 5.15/5.50 ( diffs_complex
% 5.15/5.50 = ( ^ [C3: nat > complex,N3: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N3 ) ) @ ( C3 @ ( suc @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % diffs_def
% 5.15/5.50 thf(fact_8698_termdiff__converges__all,axiom,
% 5.15/5.50 ! [C: nat > complex,X: complex] :
% 5.15/5.50 ( ! [X3: complex] :
% 5.15/5.50 ( summable_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( C @ N3 ) @ ( power_power_complex @ X3 @ N3 ) ) )
% 5.15/5.50 => ( summable_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % termdiff_converges_all
% 5.15/5.50 thf(fact_8699_termdiff__converges__all,axiom,
% 5.15/5.50 ! [C: nat > real,X: real] :
% 5.15/5.50 ( ! [X3: real] :
% 5.15/5.50 ( summable_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( C @ N3 ) @ ( power_power_real @ X3 @ N3 ) ) )
% 5.15/5.50 => ( summable_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % termdiff_converges_all
% 5.15/5.50 thf(fact_8700_termdiff__converges,axiom,
% 5.15/5.50 ! [X: real,K5: real,C: nat > real] :
% 5.15/5.50 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ K5 )
% 5.15/5.50 => ( ! [X3: real] :
% 5.15/5.50 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 5.15/5.50 => ( summable_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( C @ N3 ) @ ( power_power_real @ X3 @ N3 ) ) ) )
% 5.15/5.50 => ( summable_real
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % termdiff_converges
% 5.15/5.50 thf(fact_8701_termdiff__converges,axiom,
% 5.15/5.50 ! [X: complex,K5: real,C: nat > complex] :
% 5.15/5.50 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ K5 )
% 5.15/5.50 => ( ! [X3: complex] :
% 5.15/5.50 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 5.15/5.50 => ( summable_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( C @ N3 ) @ ( power_power_complex @ X3 @ N3 ) ) ) )
% 5.15/5.50 => ( summable_complex
% 5.15/5.50 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % termdiff_converges
% 5.15/5.50 thf(fact_8702_monoseq__minus,axiom,
% 5.15/5.50 ! [A: nat > int] :
% 5.15/5.50 ( ( topolo4899668324122417113eq_int @ A )
% 5.15/5.50 => ( topolo4899668324122417113eq_int
% 5.15/5.50 @ ^ [N3: nat] : ( uminus_uminus_int @ ( A @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_minus
% 5.15/5.50 thf(fact_8703_monoseq__minus,axiom,
% 5.15/5.50 ! [A: nat > rat] :
% 5.15/5.50 ( ( topolo4267028734544971653eq_rat @ A )
% 5.15/5.50 => ( topolo4267028734544971653eq_rat
% 5.15/5.50 @ ^ [N3: nat] : ( uminus_uminus_rat @ ( A @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_minus
% 5.15/5.50 thf(fact_8704_monoseq__minus,axiom,
% 5.15/5.50 ! [A: nat > code_integer] :
% 5.15/5.50 ( ( topolo2919662092509805066nteger @ A )
% 5.15/5.50 => ( topolo2919662092509805066nteger
% 5.15/5.50 @ ^ [N3: nat] : ( uminus1351360451143612070nteger @ ( A @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_minus
% 5.15/5.50 thf(fact_8705_monoseq__minus,axiom,
% 5.15/5.50 ! [A: nat > real] :
% 5.15/5.50 ( ( topolo6980174941875973593q_real @ A )
% 5.15/5.50 => ( topolo6980174941875973593q_real
% 5.15/5.50 @ ^ [N3: nat] : ( uminus_uminus_real @ ( A @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_minus
% 5.15/5.50 thf(fact_8706_monoseq__Suc,axiom,
% 5.15/5.50 ( topolo6980174941875973593q_real
% 5.15/5.50 = ( ^ [X4: nat > real] :
% 5.15/5.50 ( ! [N3: nat] : ( ord_less_eq_real @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.15/5.50 | ! [N3: nat] : ( ord_less_eq_real @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_Suc
% 5.15/5.50 thf(fact_8707_monoseq__Suc,axiom,
% 5.15/5.50 ( topolo7278393974255667507et_nat
% 5.15/5.50 = ( ^ [X4: nat > set_nat] :
% 5.15/5.50 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.15/5.50 | ! [N3: nat] : ( ord_less_eq_set_nat @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_Suc
% 5.15/5.50 thf(fact_8708_monoseq__Suc,axiom,
% 5.15/5.50 ( topolo4267028734544971653eq_rat
% 5.15/5.50 = ( ^ [X4: nat > rat] :
% 5.15/5.50 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.15/5.50 | ! [N3: nat] : ( ord_less_eq_rat @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_Suc
% 5.15/5.50 thf(fact_8709_monoseq__Suc,axiom,
% 5.15/5.50 ( topolo1459490580787246023eq_num
% 5.15/5.50 = ( ^ [X4: nat > num] :
% 5.15/5.50 ( ! [N3: nat] : ( ord_less_eq_num @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.15/5.50 | ! [N3: nat] : ( ord_less_eq_num @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_Suc
% 5.15/5.50 thf(fact_8710_monoseq__Suc,axiom,
% 5.15/5.50 ( topolo4902158794631467389eq_nat
% 5.15/5.50 = ( ^ [X4: nat > nat] :
% 5.15/5.50 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.15/5.50 | ! [N3: nat] : ( ord_less_eq_nat @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_Suc
% 5.15/5.50 thf(fact_8711_monoseq__Suc,axiom,
% 5.15/5.50 ( topolo4899668324122417113eq_int
% 5.15/5.50 = ( ^ [X4: nat > int] :
% 5.15/5.50 ( ! [N3: nat] : ( ord_less_eq_int @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.15/5.50 | ! [N3: nat] : ( ord_less_eq_int @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % monoseq_Suc
% 5.15/5.50 thf(fact_8712_mono__SucI2,axiom,
% 5.15/5.50 ! [X8: nat > real] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.15/5.50 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI2
% 5.15/5.50 thf(fact_8713_mono__SucI2,axiom,
% 5.15/5.50 ! [X8: nat > set_nat] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.15/5.50 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI2
% 5.15/5.50 thf(fact_8714_mono__SucI2,axiom,
% 5.15/5.50 ! [X8: nat > rat] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.15/5.50 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI2
% 5.15/5.50 thf(fact_8715_mono__SucI2,axiom,
% 5.15/5.50 ! [X8: nat > num] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.15/5.50 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI2
% 5.15/5.50 thf(fact_8716_mono__SucI2,axiom,
% 5.15/5.50 ! [X8: nat > nat] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.15/5.50 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI2
% 5.15/5.50 thf(fact_8717_mono__SucI2,axiom,
% 5.15/5.50 ! [X8: nat > int] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.15/5.50 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI2
% 5.15/5.50 thf(fact_8718_mono__SucI1,axiom,
% 5.15/5.50 ! [X8: nat > real] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_real @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.15/5.50 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI1
% 5.15/5.50 thf(fact_8719_mono__SucI1,axiom,
% 5.15/5.50 ! [X8: nat > set_nat] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.15/5.50 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI1
% 5.15/5.50 thf(fact_8720_mono__SucI1,axiom,
% 5.15/5.50 ! [X8: nat > rat] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_rat @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.15/5.50 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI1
% 5.15/5.50 thf(fact_8721_mono__SucI1,axiom,
% 5.15/5.50 ! [X8: nat > num] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_num @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.15/5.50 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI1
% 5.15/5.50 thf(fact_8722_mono__SucI1,axiom,
% 5.15/5.50 ! [X8: nat > nat] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_nat @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.15/5.50 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI1
% 5.15/5.50 thf(fact_8723_mono__SucI1,axiom,
% 5.15/5.50 ! [X8: nat > int] :
% 5.15/5.50 ( ! [N: nat] : ( ord_less_eq_int @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.15/5.50 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.15/5.50
% 5.15/5.50 % mono_SucI1
% 5.15/5.50 thf(fact_8724_exp__two__pi__i_H,axiom,
% 5.15/5.50 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.15/5.50 = one_one_complex ) ).
% 5.15/5.50
% 5.15/5.50 % exp_two_pi_i'
% 5.15/5.50 thf(fact_8725_exp__two__pi__i,axiom,
% 5.15/5.50 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.15/5.50 = one_one_complex ) ).
% 5.15/5.50
% 5.15/5.50 % exp_two_pi_i
% 5.15/5.50 thf(fact_8726_pochhammer__double,axiom,
% 5.15/5.50 ! [Z: rat,N2: nat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_double
% 5.15/5.50 thf(fact_8727_pochhammer__double,axiom,
% 5.15/5.50 ! [Z: real,N2: nat] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_double
% 5.15/5.50 thf(fact_8728_pochhammer__double,axiom,
% 5.15/5.50 ! [Z: complex,N2: nat] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_double
% 5.15/5.50 thf(fact_8729_floor__log__nat__eq__powr__iff,axiom,
% 5.15/5.50 ! [B: nat,K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.15/5.50 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.50 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.15/5.50 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.15/5.50 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.15/5.50 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_log_nat_eq_powr_iff
% 5.15/5.50 thf(fact_8730_of__int__floor__cancel,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = X )
% 5.15/5.50 = ( ? [N3: int] :
% 5.15/5.50 ( X
% 5.15/5.50 = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_floor_cancel
% 5.15/5.50 thf(fact_8731_of__int__floor__cancel,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = X )
% 5.15/5.50 = ( ? [N3: int] :
% 5.15/5.50 ( X
% 5.15/5.50 = ( ring_1_of_int_rat @ N3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_floor_cancel
% 5.15/5.50 thf(fact_8732_floor__numeral,axiom,
% 5.15/5.50 ! [V: num] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.15/5.50 = ( numeral_numeral_int @ V ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_numeral
% 5.15/5.50 thf(fact_8733_floor__numeral,axiom,
% 5.15/5.50 ! [V: num] :
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.15/5.50 = ( numeral_numeral_int @ V ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_numeral
% 5.15/5.50 thf(fact_8734_floor__one,axiom,
% 5.15/5.50 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.15/5.50 = one_one_int ) ).
% 5.15/5.50
% 5.15/5.50 % floor_one
% 5.15/5.50 thf(fact_8735_floor__one,axiom,
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.15/5.50 = one_one_int ) ).
% 5.15/5.50
% 5.15/5.50 % floor_one
% 5.15/5.50 thf(fact_8736_pochhammer__0,axiom,
% 5.15/5.50 ! [A: complex] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.15/5.50 = one_one_complex ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0
% 5.15/5.50 thf(fact_8737_pochhammer__0,axiom,
% 5.15/5.50 ! [A: real] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.15/5.50 = one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0
% 5.15/5.50 thf(fact_8738_pochhammer__0,axiom,
% 5.15/5.50 ! [A: rat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.15/5.50 = one_one_rat ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0
% 5.15/5.50 thf(fact_8739_pochhammer__0,axiom,
% 5.15/5.50 ! [A: nat] :
% 5.15/5.50 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.15/5.50 = one_one_nat ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0
% 5.15/5.50 thf(fact_8740_pochhammer__0,axiom,
% 5.15/5.50 ! [A: int] :
% 5.15/5.50 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.15/5.50 = one_one_int ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0
% 5.15/5.50 thf(fact_8741_norm__ii,axiom,
% 5.15/5.50 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.15/5.50 = one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % norm_ii
% 5.15/5.50 thf(fact_8742_complex__i__mult__minus,axiom,
% 5.15/5.50 ! [X: complex] :
% 5.15/5.50 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 5.15/5.50 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_i_mult_minus
% 5.15/5.50 thf(fact_8743_divide__i,axiom,
% 5.15/5.50 ! [X: complex] :
% 5.15/5.50 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 5.15/5.50 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % divide_i
% 5.15/5.50 thf(fact_8744_floor__diff__of__int,axiom,
% 5.15/5.50 ! [X: real,Z: int] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 5.15/5.50 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ Z ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_diff_of_int
% 5.15/5.50 thf(fact_8745_floor__diff__of__int,axiom,
% 5.15/5.50 ! [X: rat,Z: int] :
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 5.15/5.50 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ Z ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_diff_of_int
% 5.15/5.50 thf(fact_8746_i__squared,axiom,
% 5.15/5.50 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.15/5.50 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % i_squared
% 5.15/5.50 thf(fact_8747_divide__numeral__i,axiom,
% 5.15/5.50 ! [Z: complex,N2: num] :
% 5.15/5.50 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N2 ) @ imaginary_unit ) )
% 5.15/5.50 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % divide_numeral_i
% 5.15/5.50 thf(fact_8748_zero__le__floor,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % zero_le_floor
% 5.15/5.50 thf(fact_8749_zero__le__floor,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % zero_le_floor
% 5.15/5.50 thf(fact_8750_floor__less__zero,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 5.15/5.50 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_zero
% 5.15/5.50 thf(fact_8751_floor__less__zero,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 5.15/5.50 = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_zero
% 5.15/5.50 thf(fact_8752_numeral__le__floor,axiom,
% 5.15/5.50 ! [V: num,X: real] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % numeral_le_floor
% 5.15/5.50 thf(fact_8753_numeral__le__floor,axiom,
% 5.15/5.50 ! [V: num,X: rat] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % numeral_le_floor
% 5.15/5.50 thf(fact_8754_zero__less__floor,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % zero_less_floor
% 5.15/5.50 thf(fact_8755_zero__less__floor,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % zero_less_floor
% 5.15/5.50 thf(fact_8756_floor__le__zero,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 5.15/5.50 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_zero
% 5.15/5.50 thf(fact_8757_floor__le__zero,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 5.15/5.50 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_zero
% 5.15/5.50 thf(fact_8758_floor__less__numeral,axiom,
% 5.15/5.50 ! [X: real,V: num] :
% 5.15/5.50 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.50 = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_numeral
% 5.15/5.50 thf(fact_8759_floor__less__numeral,axiom,
% 5.15/5.50 ! [X: rat,V: num] :
% 5.15/5.50 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.50 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_numeral
% 5.15/5.50 thf(fact_8760_one__le__floor,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % one_le_floor
% 5.15/5.50 thf(fact_8761_one__le__floor,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % one_le_floor
% 5.15/5.50 thf(fact_8762_floor__less__one,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.15/5.50 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_one
% 5.15/5.50 thf(fact_8763_floor__less__one,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.15/5.50 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_one
% 5.15/5.50 thf(fact_8764_floor__neg__numeral,axiom,
% 5.15/5.50 ! [V: num] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_neg_numeral
% 5.15/5.50 thf(fact_8765_floor__neg__numeral,axiom,
% 5.15/5.50 ! [V: num] :
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_neg_numeral
% 5.15/5.50 thf(fact_8766_floor__diff__numeral,axiom,
% 5.15/5.50 ! [X: real,V: num] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.15/5.50 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_diff_numeral
% 5.15/5.50 thf(fact_8767_floor__diff__numeral,axiom,
% 5.15/5.50 ! [X: rat,V: num] :
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.15/5.50 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_diff_numeral
% 5.15/5.50 thf(fact_8768_floor__diff__one,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.15/5.50 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_diff_one
% 5.15/5.50 thf(fact_8769_floor__diff__one,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 5.15/5.50 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_diff_one
% 5.15/5.50 thf(fact_8770_floor__numeral__power,axiom,
% 5.15/5.50 ! [X: num,N2: nat] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.15/5.50 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_numeral_power
% 5.15/5.50 thf(fact_8771_floor__numeral__power,axiom,
% 5.15/5.50 ! [X: num,N2: nat] :
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.15/5.50 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_numeral_power
% 5.15/5.50 thf(fact_8772_floor__divide__eq__div__numeral,axiom,
% 5.15/5.50 ! [A: num,B: num] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.15/5.50 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_eq_div_numeral
% 5.15/5.50 thf(fact_8773_numeral__less__floor,axiom,
% 5.15/5.50 ! [V: num,X: real] :
% 5.15/5.50 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % numeral_less_floor
% 5.15/5.50 thf(fact_8774_numeral__less__floor,axiom,
% 5.15/5.50 ! [V: num,X: rat] :
% 5.15/5.50 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % numeral_less_floor
% 5.15/5.50 thf(fact_8775_floor__le__numeral,axiom,
% 5.15/5.50 ! [X: real,V: num] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.50 = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_numeral
% 5.15/5.50 thf(fact_8776_floor__le__numeral,axiom,
% 5.15/5.50 ! [X: rat,V: num] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.15/5.50 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_numeral
% 5.15/5.50 thf(fact_8777_one__less__floor,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % one_less_floor
% 5.15/5.50 thf(fact_8778_one__less__floor,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % one_less_floor
% 5.15/5.50 thf(fact_8779_floor__le__one,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.15/5.50 = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_one
% 5.15/5.50 thf(fact_8780_floor__le__one,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.15/5.50 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_one
% 5.15/5.50 thf(fact_8781_neg__numeral__le__floor,axiom,
% 5.15/5.50 ! [V: num,X: real] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % neg_numeral_le_floor
% 5.15/5.50 thf(fact_8782_neg__numeral__le__floor,axiom,
% 5.15/5.50 ! [V: num,X: rat] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % neg_numeral_le_floor
% 5.15/5.50 thf(fact_8783_floor__less__neg__numeral,axiom,
% 5.15/5.50 ! [X: real,V: num] :
% 5.15/5.50 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.50 = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_neg_numeral
% 5.15/5.50 thf(fact_8784_floor__less__neg__numeral,axiom,
% 5.15/5.50 ! [X: rat,V: num] :
% 5.15/5.50 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.50 = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_neg_numeral
% 5.15/5.50 thf(fact_8785_floor__one__divide__eq__div__numeral,axiom,
% 5.15/5.50 ! [B: num] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.15/5.50 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_one_divide_eq_div_numeral
% 5.15/5.50 thf(fact_8786_floor__minus__divide__eq__div__numeral,axiom,
% 5.15/5.50 ! [A: num,B: num] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.15/5.50 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_minus_divide_eq_div_numeral
% 5.15/5.50 thf(fact_8787_power2__i,axiom,
% 5.15/5.50 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.50 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % power2_i
% 5.15/5.50 thf(fact_8788_exp__pi__i,axiom,
% 5.15/5.50 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.15/5.50 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % exp_pi_i
% 5.15/5.50 thf(fact_8789_exp__pi__i_H,axiom,
% 5.15/5.50 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.15/5.50 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % exp_pi_i'
% 5.15/5.50 thf(fact_8790_i__even__power,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.50 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % i_even_power
% 5.15/5.50 thf(fact_8791_neg__numeral__less__floor,axiom,
% 5.15/5.50 ! [V: num,X: real] :
% 5.15/5.50 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % neg_numeral_less_floor
% 5.15/5.50 thf(fact_8792_neg__numeral__less__floor,axiom,
% 5.15/5.50 ! [V: num,X: rat] :
% 5.15/5.50 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % neg_numeral_less_floor
% 5.15/5.50 thf(fact_8793_floor__le__neg__numeral,axiom,
% 5.15/5.50 ! [X: real,V: num] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.50 = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_neg_numeral
% 5.15/5.50 thf(fact_8794_floor__le__neg__numeral,axiom,
% 5.15/5.50 ! [X: rat,V: num] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.15/5.50 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_neg_numeral
% 5.15/5.50 thf(fact_8795_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.15/5.50 ! [B: num] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.15/5.50 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_minus_one_divide_eq_div_numeral
% 5.15/5.50 thf(fact_8796_floor__mono,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.50 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_mono
% 5.15/5.50 thf(fact_8797_floor__mono,axiom,
% 5.15/5.50 ! [X: rat,Y: rat] :
% 5.15/5.50 ( ( ord_less_eq_rat @ X @ Y )
% 5.15/5.50 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_mono
% 5.15/5.50 thf(fact_8798_of__int__floor__le,axiom,
% 5.15/5.50 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_floor_le
% 5.15/5.50 thf(fact_8799_of__int__floor__le,axiom,
% 5.15/5.50 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_floor_le
% 5.15/5.50 thf(fact_8800_floor__less__cancel,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) )
% 5.15/5.50 => ( ord_less_real @ X @ Y ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_cancel
% 5.15/5.50 thf(fact_8801_floor__less__cancel,axiom,
% 5.15/5.50 ! [X: rat,Y: rat] :
% 5.15/5.50 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) )
% 5.15/5.50 => ( ord_less_rat @ X @ Y ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_cancel
% 5.15/5.50 thf(fact_8802_pochhammer__pos,axiom,
% 5.15/5.50 ! [X: real,N2: nat] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.50 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_pos
% 5.15/5.50 thf(fact_8803_pochhammer__pos,axiom,
% 5.15/5.50 ! [X: rat,N2: nat] :
% 5.15/5.50 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.15/5.50 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_pos
% 5.15/5.50 thf(fact_8804_pochhammer__pos,axiom,
% 5.15/5.50 ! [X: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.15/5.50 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_pos
% 5.15/5.50 thf(fact_8805_pochhammer__pos,axiom,
% 5.15/5.50 ! [X: int,N2: nat] :
% 5.15/5.50 ( ( ord_less_int @ zero_zero_int @ X )
% 5.15/5.50 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_pos
% 5.15/5.50 thf(fact_8806_pochhammer__eq__0__mono,axiom,
% 5.15/5.50 ! [A: complex,N2: nat,M: nat] :
% 5.15/5.50 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.15/5.50 = zero_zero_complex )
% 5.15/5.50 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.50 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.15/5.50 = zero_zero_complex ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_eq_0_mono
% 5.15/5.50 thf(fact_8807_pochhammer__eq__0__mono,axiom,
% 5.15/5.50 ! [A: real,N2: nat,M: nat] :
% 5.15/5.50 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.15/5.50 = zero_zero_real )
% 5.15/5.50 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.50 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.15/5.50 = zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_eq_0_mono
% 5.15/5.50 thf(fact_8808_pochhammer__eq__0__mono,axiom,
% 5.15/5.50 ! [A: rat,N2: nat,M: nat] :
% 5.15/5.50 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.15/5.50 = zero_zero_rat )
% 5.15/5.50 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.50 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.15/5.50 = zero_zero_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_eq_0_mono
% 5.15/5.50 thf(fact_8809_pochhammer__neq__0__mono,axiom,
% 5.15/5.50 ! [A: complex,M: nat,N2: nat] :
% 5.15/5.50 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.15/5.50 != zero_zero_complex )
% 5.15/5.50 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.50 => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.15/5.50 != zero_zero_complex ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_neq_0_mono
% 5.15/5.50 thf(fact_8810_pochhammer__neq__0__mono,axiom,
% 5.15/5.50 ! [A: real,M: nat,N2: nat] :
% 5.15/5.50 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.15/5.50 != zero_zero_real )
% 5.15/5.50 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.50 => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.15/5.50 != zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_neq_0_mono
% 5.15/5.50 thf(fact_8811_pochhammer__neq__0__mono,axiom,
% 5.15/5.50 ! [A: rat,M: nat,N2: nat] :
% 5.15/5.50 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.15/5.50 != zero_zero_rat )
% 5.15/5.50 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.50 => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.15/5.50 != zero_zero_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_neq_0_mono
% 5.15/5.50 thf(fact_8812_pochhammer__fact,axiom,
% 5.15/5.50 ( semiri5044797733671781792omplex
% 5.15/5.50 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_fact
% 5.15/5.50 thf(fact_8813_pochhammer__fact,axiom,
% 5.15/5.50 ( semiri773545260158071498ct_rat
% 5.15/5.50 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_fact
% 5.15/5.50 thf(fact_8814_pochhammer__fact,axiom,
% 5.15/5.50 ( semiri1406184849735516958ct_int
% 5.15/5.50 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_fact
% 5.15/5.50 thf(fact_8815_pochhammer__fact,axiom,
% 5.15/5.50 ( semiri2265585572941072030t_real
% 5.15/5.50 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_fact
% 5.15/5.50 thf(fact_8816_pochhammer__fact,axiom,
% 5.15/5.50 ( semiri1408675320244567234ct_nat
% 5.15/5.50 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_fact
% 5.15/5.50 thf(fact_8817_i__times__eq__iff,axiom,
% 5.15/5.50 ! [W: complex,Z: complex] :
% 5.15/5.50 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.15/5.50 = Z )
% 5.15/5.50 = ( W
% 5.15/5.50 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % i_times_eq_iff
% 5.15/5.50 thf(fact_8818_le__floor__iff,axiom,
% 5.15/5.50 ! [Z: int,X: real] :
% 5.15/5.50 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % le_floor_iff
% 5.15/5.50 thf(fact_8819_le__floor__iff,axiom,
% 5.15/5.50 ! [Z: int,X: rat] :
% 5.15/5.50 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % le_floor_iff
% 5.15/5.50 thf(fact_8820_floor__less__iff,axiom,
% 5.15/5.50 ! [X: real,Z: int] :
% 5.15/5.50 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 5.15/5.50 = ( ord_less_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_iff
% 5.15/5.50 thf(fact_8821_floor__less__iff,axiom,
% 5.15/5.50 ! [X: rat,Z: int] :
% 5.15/5.50 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 5.15/5.50 = ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_less_iff
% 5.15/5.50 thf(fact_8822_le__floor__add,axiom,
% 5.15/5.50 ! [X: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % le_floor_add
% 5.15/5.50 thf(fact_8823_le__floor__add,axiom,
% 5.15/5.50 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % le_floor_add
% 5.15/5.50 thf(fact_8824_int__add__floor,axiom,
% 5.15/5.50 ! [Z: int,X: real] :
% 5.15/5.50 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % int_add_floor
% 5.15/5.50 thf(fact_8825_int__add__floor,axiom,
% 5.15/5.50 ! [Z: int,X: rat] :
% 5.15/5.50 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % int_add_floor
% 5.15/5.50 thf(fact_8826_floor__add__int,axiom,
% 5.15/5.50 ! [X: real,Z: int] :
% 5.15/5.50 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 5.15/5.50 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_add_int
% 5.15/5.50 thf(fact_8827_floor__add__int,axiom,
% 5.15/5.50 ! [X: rat,Z: int] :
% 5.15/5.50 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 5.15/5.50 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_add_int
% 5.15/5.50 thf(fact_8828_floor__divide__of__int__eq,axiom,
% 5.15/5.50 ! [K: int,L: int] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 5.15/5.50 = ( divide_divide_int @ K @ L ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_of_int_eq
% 5.15/5.50 thf(fact_8829_floor__divide__of__int__eq,axiom,
% 5.15/5.50 ! [K: int,L: int] :
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 5.15/5.50 = ( divide_divide_int @ K @ L ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_of_int_eq
% 5.15/5.50 thf(fact_8830_floor__power,axiom,
% 5.15/5.50 ! [X: real,N2: nat] :
% 5.15/5.50 ( ( X
% 5.15/5.50 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 5.15/5.50 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X @ N2 ) )
% 5.15/5.50 = ( power_power_int @ ( archim6058952711729229775r_real @ X ) @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_power
% 5.15/5.50 thf(fact_8831_floor__power,axiom,
% 5.15/5.50 ! [X: rat,N2: nat] :
% 5.15/5.50 ( ( X
% 5.15/5.50 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 5.15/5.50 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X @ N2 ) )
% 5.15/5.50 = ( power_power_int @ ( archim3151403230148437115or_rat @ X ) @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_power
% 5.15/5.50 thf(fact_8832_pochhammer__nonneg,axiom,
% 5.15/5.50 ! [X: real,N2: nat] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_nonneg
% 5.15/5.50 thf(fact_8833_pochhammer__nonneg,axiom,
% 5.15/5.50 ! [X: rat,N2: nat] :
% 5.15/5.50 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.15/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_nonneg
% 5.15/5.50 thf(fact_8834_pochhammer__nonneg,axiom,
% 5.15/5.50 ! [X: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.15/5.50 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_nonneg
% 5.15/5.50 thf(fact_8835_pochhammer__nonneg,axiom,
% 5.15/5.50 ! [X: int,N2: nat] :
% 5.15/5.50 ( ( ord_less_int @ zero_zero_int @ X )
% 5.15/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_nonneg
% 5.15/5.50 thf(fact_8836_pochhammer__0__left,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ( N2 = zero_zero_nat )
% 5.15/5.50 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.15/5.50 = one_one_complex ) )
% 5.15/5.50 & ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.15/5.50 = zero_zero_complex ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0_left
% 5.15/5.50 thf(fact_8837_pochhammer__0__left,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ( N2 = zero_zero_nat )
% 5.15/5.50 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.15/5.50 = one_one_real ) )
% 5.15/5.50 & ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.15/5.50 = zero_zero_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0_left
% 5.15/5.50 thf(fact_8838_pochhammer__0__left,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ( N2 = zero_zero_nat )
% 5.15/5.50 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 5.15/5.50 = one_one_rat ) )
% 5.15/5.50 & ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 5.15/5.50 = zero_zero_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0_left
% 5.15/5.50 thf(fact_8839_pochhammer__0__left,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ( N2 = zero_zero_nat )
% 5.15/5.50 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 = one_one_nat ) )
% 5.15/5.50 & ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.15/5.50 = zero_zero_nat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0_left
% 5.15/5.50 thf(fact_8840_pochhammer__0__left,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ( N2 = zero_zero_nat )
% 5.15/5.50 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.15/5.50 = one_one_int ) )
% 5.15/5.50 & ( ( N2 != zero_zero_nat )
% 5.15/5.50 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.15/5.50 = zero_zero_int ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_0_left
% 5.15/5.50 thf(fact_8841_imaginary__unit_Ocode,axiom,
% 5.15/5.50 ( imaginary_unit
% 5.15/5.50 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % imaginary_unit.code
% 5.15/5.50 thf(fact_8842_Complex__eq__i,axiom,
% 5.15/5.50 ! [X: real,Y: real] :
% 5.15/5.50 ( ( ( complex2 @ X @ Y )
% 5.15/5.50 = imaginary_unit )
% 5.15/5.50 = ( ( X = zero_zero_real )
% 5.15/5.50 & ( Y = one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_eq_i
% 5.15/5.50 thf(fact_8843_one__add__floor,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.15/5.50 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % one_add_floor
% 5.15/5.50 thf(fact_8844_one__add__floor,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.15/5.50 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % one_add_floor
% 5.15/5.50 thf(fact_8845_floor__divide__of__nat__eq,axiom,
% 5.15/5.50 ! [M: nat,N2: nat] :
% 5.15/5.50 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.15/5.50 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_of_nat_eq
% 5.15/5.50 thf(fact_8846_floor__divide__of__nat__eq,axiom,
% 5.15/5.50 ! [M: nat,N2: nat] :
% 5.15/5.50 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) )
% 5.15/5.50 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_of_nat_eq
% 5.15/5.50 thf(fact_8847_i__mult__Complex,axiom,
% 5.15/5.50 ! [A: real,B: real] :
% 5.15/5.50 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.15/5.50 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.15/5.50
% 5.15/5.50 % i_mult_Complex
% 5.15/5.50 thf(fact_8848_Complex__mult__i,axiom,
% 5.15/5.50 ! [A: real,B: real] :
% 5.15/5.50 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.15/5.50 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_mult_i
% 5.15/5.50 thf(fact_8849_real__of__int__floor__add__one__gt,axiom,
% 5.15/5.50 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % real_of_int_floor_add_one_gt
% 5.15/5.50 thf(fact_8850_floor__eq,axiom,
% 5.15/5.50 ! [N2: int,X: real] :
% 5.15/5.50 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.15/5.50 => ( ( archim6058952711729229775r_real @ X )
% 5.15/5.50 = N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_eq
% 5.15/5.50 thf(fact_8851_real__of__int__floor__add__one__ge,axiom,
% 5.15/5.50 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % real_of_int_floor_add_one_ge
% 5.15/5.50 thf(fact_8852_real__of__int__floor__gt__diff__one,axiom,
% 5.15/5.50 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % real_of_int_floor_gt_diff_one
% 5.15/5.50 thf(fact_8853_real__of__int__floor__ge__diff__one,axiom,
% 5.15/5.50 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % real_of_int_floor_ge_diff_one
% 5.15/5.50 thf(fact_8854_pochhammer__rec,axiom,
% 5.15/5.50 ! [A: complex,N2: nat] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec
% 5.15/5.50 thf(fact_8855_pochhammer__rec,axiom,
% 5.15/5.50 ! [A: real,N2: nat] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec
% 5.15/5.50 thf(fact_8856_pochhammer__rec,axiom,
% 5.15/5.50 ! [A: rat,N2: nat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec
% 5.15/5.50 thf(fact_8857_pochhammer__rec,axiom,
% 5.15/5.50 ! [A: nat,N2: nat] :
% 5.15/5.50 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec
% 5.15/5.50 thf(fact_8858_pochhammer__rec,axiom,
% 5.15/5.50 ! [A: int,N2: nat] :
% 5.15/5.50 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec
% 5.15/5.50 thf(fact_8859_pochhammer__rec_H,axiom,
% 5.15/5.50 ! [Z: rat,N2: nat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec'
% 5.15/5.50 thf(fact_8860_pochhammer__rec_H,axiom,
% 5.15/5.50 ! [Z: int,N2: nat] :
% 5.15/5.50 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec'
% 5.15/5.50 thf(fact_8861_pochhammer__rec_H,axiom,
% 5.15/5.50 ! [Z: real,N2: nat] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec'
% 5.15/5.50 thf(fact_8862_pochhammer__rec_H,axiom,
% 5.15/5.50 ! [Z: nat,N2: nat] :
% 5.15/5.50 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec'
% 5.15/5.50 thf(fact_8863_pochhammer__rec_H,axiom,
% 5.15/5.50 ! [Z: complex,N2: nat] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_rec'
% 5.15/5.50 thf(fact_8864_pochhammer__Suc,axiom,
% 5.15/5.50 ! [A: rat,N2: nat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_Suc
% 5.15/5.50 thf(fact_8865_pochhammer__Suc,axiom,
% 5.15/5.50 ! [A: int,N2: nat] :
% 5.15/5.50 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_Suc
% 5.15/5.50 thf(fact_8866_pochhammer__Suc,axiom,
% 5.15/5.50 ! [A: real,N2: nat] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_Suc
% 5.15/5.50 thf(fact_8867_pochhammer__Suc,axiom,
% 5.15/5.50 ! [A: nat,N2: nat] :
% 5.15/5.50 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_Suc
% 5.15/5.50 thf(fact_8868_pochhammer__Suc,axiom,
% 5.15/5.50 ! [A: complex,N2: nat] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.15/5.50 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N2 ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_Suc
% 5.15/5.50 thf(fact_8869_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ord_less_nat @ N2 @ K )
% 5.15/5.50 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.15/5.50 = zero_zero_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma
% 5.15/5.50 thf(fact_8870_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ord_less_nat @ N2 @ K )
% 5.15/5.50 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.15/5.50 = zero_z3403309356797280102nteger ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma
% 5.15/5.50 thf(fact_8871_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ord_less_nat @ N2 @ K )
% 5.15/5.50 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.15/5.50 = zero_zero_int ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma
% 5.15/5.50 thf(fact_8872_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ord_less_nat @ N2 @ K )
% 5.15/5.50 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.15/5.50 = zero_zero_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma
% 5.15/5.50 thf(fact_8873_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ord_less_nat @ N2 @ K )
% 5.15/5.50 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.15/5.50 = zero_zero_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma
% 5.15/5.50 thf(fact_8874_pochhammer__of__nat__eq__0__iff,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.15/5.50 = zero_zero_rat )
% 5.15/5.50 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_iff
% 5.15/5.50 thf(fact_8875_pochhammer__of__nat__eq__0__iff,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.15/5.50 = zero_z3403309356797280102nteger )
% 5.15/5.50 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_iff
% 5.15/5.50 thf(fact_8876_pochhammer__of__nat__eq__0__iff,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.15/5.50 = zero_zero_int )
% 5.15/5.50 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_iff
% 5.15/5.50 thf(fact_8877_pochhammer__of__nat__eq__0__iff,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.15/5.50 = zero_zero_real )
% 5.15/5.50 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_iff
% 5.15/5.50 thf(fact_8878_pochhammer__of__nat__eq__0__iff,axiom,
% 5.15/5.50 ! [N2: nat,K: nat] :
% 5.15/5.50 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.15/5.50 = zero_zero_complex )
% 5.15/5.50 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_iff
% 5.15/5.50 thf(fact_8879_pochhammer__eq__0__iff,axiom,
% 5.15/5.50 ! [A: rat,N2: nat] :
% 5.15/5.50 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.15/5.50 = zero_zero_rat )
% 5.15/5.50 = ( ? [K2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ K2 @ N2 )
% 5.15/5.50 & ( A
% 5.15/5.50 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_eq_0_iff
% 5.15/5.50 thf(fact_8880_pochhammer__eq__0__iff,axiom,
% 5.15/5.50 ! [A: real,N2: nat] :
% 5.15/5.50 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.15/5.50 = zero_zero_real )
% 5.15/5.50 = ( ? [K2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ K2 @ N2 )
% 5.15/5.50 & ( A
% 5.15/5.50 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_eq_0_iff
% 5.15/5.50 thf(fact_8881_pochhammer__eq__0__iff,axiom,
% 5.15/5.50 ! [A: complex,N2: nat] :
% 5.15/5.50 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.15/5.50 = zero_zero_complex )
% 5.15/5.50 = ( ? [K2: nat] :
% 5.15/5.50 ( ( ord_less_nat @ K2 @ N2 )
% 5.15/5.50 & ( A
% 5.15/5.50 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_eq_0_iff
% 5.15/5.50 thf(fact_8882_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.15/5.50 != zero_zero_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma'
% 5.15/5.50 thf(fact_8883_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.15/5.50 != zero_z3403309356797280102nteger ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma'
% 5.15/5.50 thf(fact_8884_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.15/5.50 != zero_zero_int ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma'
% 5.15/5.50 thf(fact_8885_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.15/5.50 != zero_zero_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma'
% 5.15/5.50 thf(fact_8886_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.15/5.50 ! [K: nat,N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.50 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.15/5.50 != zero_zero_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_of_nat_eq_0_lemma'
% 5.15/5.50 thf(fact_8887_pochhammer__product_H,axiom,
% 5.15/5.50 ! [Z: rat,N2: nat,M: nat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.50 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product'
% 5.15/5.50 thf(fact_8888_pochhammer__product_H,axiom,
% 5.15/5.50 ! [Z: int,N2: nat,M: nat] :
% 5.15/5.50 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.50 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product'
% 5.15/5.50 thf(fact_8889_pochhammer__product_H,axiom,
% 5.15/5.50 ! [Z: real,N2: nat,M: nat] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.50 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product'
% 5.15/5.50 thf(fact_8890_pochhammer__product_H,axiom,
% 5.15/5.50 ! [Z: nat,N2: nat,M: nat] :
% 5.15/5.50 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.50 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product'
% 5.15/5.50 thf(fact_8891_pochhammer__product_H,axiom,
% 5.15/5.50 ! [Z: complex,N2: nat,M: nat] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.15/5.50 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ M ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product'
% 5.15/5.50 thf(fact_8892_floor__unique,axiom,
% 5.15/5.50 ! [Z: int,X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.15/5.50 => ( ( archim6058952711729229775r_real @ X )
% 5.15/5.50 = Z ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_unique
% 5.15/5.50 thf(fact_8893_floor__unique,axiom,
% 5.15/5.50 ! [Z: int,X: rat] :
% 5.15/5.50 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 5.15/5.50 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.15/5.50 => ( ( archim3151403230148437115or_rat @ X )
% 5.15/5.50 = Z ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_unique
% 5.15/5.50 thf(fact_8894_floor__eq__iff,axiom,
% 5.15/5.50 ! [X: real,A: int] :
% 5.15/5.50 ( ( ( archim6058952711729229775r_real @ X )
% 5.15/5.50 = A )
% 5.15/5.50 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 5.15/5.50 & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_eq_iff
% 5.15/5.50 thf(fact_8895_floor__eq__iff,axiom,
% 5.15/5.50 ! [X: rat,A: int] :
% 5.15/5.50 ( ( ( archim3151403230148437115or_rat @ X )
% 5.15/5.50 = A )
% 5.15/5.50 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 5.15/5.50 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_eq_iff
% 5.15/5.50 thf(fact_8896_floor__split,axiom,
% 5.15/5.50 ! [P: int > $o,T: real] :
% 5.15/5.50 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.15/5.50 = ( ! [I3: int] :
% 5.15/5.50 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I3 ) @ T )
% 5.15/5.50 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) ) )
% 5.15/5.50 => ( P @ I3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_split
% 5.15/5.50 thf(fact_8897_floor__split,axiom,
% 5.15/5.50 ! [P: int > $o,T: rat] :
% 5.15/5.50 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.15/5.50 = ( ! [I3: int] :
% 5.15/5.50 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T )
% 5.15/5.50 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 5.15/5.50 => ( P @ I3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_split
% 5.15/5.50 thf(fact_8898_le__mult__floor,axiom,
% 5.15/5.50 ! [A: real,B: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.15/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.15/5.50 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % le_mult_floor
% 5.15/5.50 thf(fact_8899_le__mult__floor,axiom,
% 5.15/5.50 ! [A: rat,B: rat] :
% 5.15/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.15/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.15/5.50 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % le_mult_floor
% 5.15/5.50 thf(fact_8900_less__floor__iff,axiom,
% 5.15/5.50 ! [Z: int,X: real] :
% 5.15/5.50 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.50 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % less_floor_iff
% 5.15/5.50 thf(fact_8901_less__floor__iff,axiom,
% 5.15/5.50 ! [Z: int,X: rat] :
% 5.15/5.50 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 5.15/5.50 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 5.15/5.50
% 5.15/5.50 % less_floor_iff
% 5.15/5.50 thf(fact_8902_floor__le__iff,axiom,
% 5.15/5.50 ! [X: real,Z: int] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 5.15/5.50 = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_iff
% 5.15/5.50 thf(fact_8903_floor__le__iff,axiom,
% 5.15/5.50 ! [X: rat,Z: int] :
% 5.15/5.50 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 5.15/5.50 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_le_iff
% 5.15/5.50 thf(fact_8904_floor__correct,axiom,
% 5.15/5.50 ! [X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 5.15/5.50 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_correct
% 5.15/5.50 thf(fact_8905_floor__correct,axiom,
% 5.15/5.50 ! [X: rat] :
% 5.15/5.50 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 5.15/5.50 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_correct
% 5.15/5.50 thf(fact_8906_floor__eq2,axiom,
% 5.15/5.50 ! [N2: int,X: real] :
% 5.15/5.50 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 5.15/5.50 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.15/5.50 => ( ( archim6058952711729229775r_real @ X )
% 5.15/5.50 = N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_eq2
% 5.15/5.50 thf(fact_8907_floor__divide__real__eq__div,axiom,
% 5.15/5.50 ! [B: int,A: real] :
% 5.15/5.50 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.15/5.50 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.15/5.50 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_real_eq_div
% 5.15/5.50 thf(fact_8908_complex__of__real__i,axiom,
% 5.15/5.50 ! [R2: real] :
% 5.15/5.50 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.15/5.50 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_of_real_i
% 5.15/5.50 thf(fact_8909_i__complex__of__real,axiom,
% 5.15/5.50 ! [R2: real] :
% 5.15/5.50 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.15/5.50 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % i_complex_of_real
% 5.15/5.50 thf(fact_8910_pochhammer__product,axiom,
% 5.15/5.50 ! [M: nat,N2: nat,Z: rat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.50 => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 5.15/5.50 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product
% 5.15/5.50 thf(fact_8911_pochhammer__product,axiom,
% 5.15/5.50 ! [M: nat,N2: nat,Z: int] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.50 => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 5.15/5.50 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product
% 5.15/5.50 thf(fact_8912_pochhammer__product,axiom,
% 5.15/5.50 ! [M: nat,N2: nat,Z: real] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.50 => ( ( comm_s7457072308508201937r_real @ Z @ N2 )
% 5.15/5.50 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product
% 5.15/5.50 thf(fact_8913_pochhammer__product,axiom,
% 5.15/5.50 ! [M: nat,N2: nat,Z: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.50 => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 5.15/5.50 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product
% 5.15/5.50 thf(fact_8914_pochhammer__product,axiom,
% 5.15/5.50 ! [M: nat,N2: nat,Z: complex] :
% 5.15/5.50 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.50 => ( ( comm_s2602460028002588243omplex @ Z @ N2 )
% 5.15/5.50 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_product
% 5.15/5.50 thf(fact_8915_Complex__eq,axiom,
% 5.15/5.50 ( complex2
% 5.15/5.50 = ( ^ [A3: real,B2: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A3 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Complex_eq
% 5.15/5.50 thf(fact_8916_floor__divide__lower,axiom,
% 5.15/5.50 ! [Q3: real,P2: real] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.15/5.50 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_lower
% 5.15/5.50 thf(fact_8917_floor__divide__lower,axiom,
% 5.15/5.50 ! [Q3: rat,P2: rat] :
% 5.15/5.50 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.15/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_lower
% 5.15/5.50 thf(fact_8918_pochhammer__absorb__comp,axiom,
% 5.15/5.50 ! [R2: rat,K: nat] :
% 5.15/5.50 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.15/5.50 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_absorb_comp
% 5.15/5.50 thf(fact_8919_pochhammer__absorb__comp,axiom,
% 5.15/5.50 ! [R2: code_integer,K: nat] :
% 5.15/5.50 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.15/5.50 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_absorb_comp
% 5.15/5.50 thf(fact_8920_pochhammer__absorb__comp,axiom,
% 5.15/5.50 ! [R2: int,K: nat] :
% 5.15/5.50 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.15/5.50 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_absorb_comp
% 5.15/5.50 thf(fact_8921_pochhammer__absorb__comp,axiom,
% 5.15/5.50 ! [R2: real,K: nat] :
% 5.15/5.50 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.15/5.50 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_absorb_comp
% 5.15/5.50 thf(fact_8922_pochhammer__absorb__comp,axiom,
% 5.15/5.50 ! [R2: complex,K: nat] :
% 5.15/5.50 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.15/5.50 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_absorb_comp
% 5.15/5.50 thf(fact_8923_floor__divide__upper,axiom,
% 5.15/5.50 ! [Q3: real,P2: real] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.15/5.50 => ( ord_less_real @ P2 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_upper
% 5.15/5.50 thf(fact_8924_floor__divide__upper,axiom,
% 5.15/5.50 ! [Q3: rat,P2: rat] :
% 5.15/5.50 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.15/5.50 => ( ord_less_rat @ P2 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_divide_upper
% 5.15/5.50 thf(fact_8925_pochhammer__same,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 5.15/5.50 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_same
% 5.15/5.50 thf(fact_8926_pochhammer__same,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 5.15/5.50 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_same
% 5.15/5.50 thf(fact_8927_pochhammer__same,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 5.15/5.50 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_same
% 5.15/5.50 thf(fact_8928_pochhammer__same,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ N2 )
% 5.15/5.50 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_same
% 5.15/5.50 thf(fact_8929_pochhammer__same,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ N2 )
% 5.15/5.50 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_same
% 5.15/5.50 thf(fact_8930_complex__split__polar,axiom,
% 5.15/5.50 ! [Z: complex] :
% 5.15/5.50 ? [R3: real,A5: real] :
% 5.15/5.50 ( Z
% 5.15/5.50 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A5 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A5 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % complex_split_polar
% 5.15/5.50 thf(fact_8931_round__def,axiom,
% 5.15/5.50 ( archim8280529875227126926d_real
% 5.15/5.50 = ( ^ [X2: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % round_def
% 5.15/5.50 thf(fact_8932_round__def,axiom,
% 5.15/5.50 ( archim7778729529865785530nd_rat
% 5.15/5.50 = ( ^ [X2: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % round_def
% 5.15/5.50 thf(fact_8933_pochhammer__minus,axiom,
% 5.15/5.50 ! [B: rat,K: nat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus
% 5.15/5.50 thf(fact_8934_pochhammer__minus,axiom,
% 5.15/5.50 ! [B: code_integer,K: nat] :
% 5.15/5.50 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.15/5.50 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus
% 5.15/5.50 thf(fact_8935_pochhammer__minus,axiom,
% 5.15/5.50 ! [B: int,K: nat] :
% 5.15/5.50 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus
% 5.15/5.50 thf(fact_8936_pochhammer__minus,axiom,
% 5.15/5.50 ! [B: real,K: nat] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus
% 5.15/5.50 thf(fact_8937_pochhammer__minus,axiom,
% 5.15/5.50 ! [B: complex,K: nat] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus
% 5.15/5.50 thf(fact_8938_pochhammer__minus_H,axiom,
% 5.15/5.50 ! [B: rat,K: nat] :
% 5.15/5.50 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.15/5.50 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus'
% 5.15/5.50 thf(fact_8939_pochhammer__minus_H,axiom,
% 5.15/5.50 ! [B: code_integer,K: nat] :
% 5.15/5.50 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.15/5.50 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus'
% 5.15/5.50 thf(fact_8940_pochhammer__minus_H,axiom,
% 5.15/5.50 ! [B: int,K: nat] :
% 5.15/5.50 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.15/5.50 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus'
% 5.15/5.50 thf(fact_8941_pochhammer__minus_H,axiom,
% 5.15/5.50 ! [B: real,K: nat] :
% 5.15/5.50 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.15/5.50 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus'
% 5.15/5.50 thf(fact_8942_pochhammer__minus_H,axiom,
% 5.15/5.50 ! [B: complex,K: nat] :
% 5.15/5.50 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.15/5.50 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_minus'
% 5.15/5.50 thf(fact_8943_floor__log__eq__powr__iff,axiom,
% 5.15/5.50 ! [X: real,B: real,K: int] :
% 5.15/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.50 => ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.50 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 5.15/5.50 = K )
% 5.15/5.50 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 5.15/5.50 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_log_eq_powr_iff
% 5.15/5.50 thf(fact_8944_cmod__unit__one,axiom,
% 5.15/5.50 ! [A: real] :
% 5.15/5.50 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.15/5.50 = one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % cmod_unit_one
% 5.15/5.50 thf(fact_8945_cmod__complex__polar,axiom,
% 5.15/5.50 ! [R2: real,A: real] :
% 5.15/5.50 ( ( 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 ) ) ) ) ) )
% 5.15/5.50 = ( abs_abs_real @ R2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % cmod_complex_polar
% 5.15/5.50 thf(fact_8946_floor__log2__div2,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.50 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_log2_div2
% 5.15/5.50 thf(fact_8947_fact__double,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_double
% 5.15/5.50 thf(fact_8948_fact__double,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_double
% 5.15/5.50 thf(fact_8949_fact__double,axiom,
% 5.15/5.50 ! [N2: nat] :
% 5.15/5.50 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.50 = ( 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 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % fact_double
% 5.15/5.50 thf(fact_8950_floor__log__nat__eq__if,axiom,
% 5.15/5.50 ! [B: nat,N2: nat,K: nat] :
% 5.15/5.50 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.15/5.50 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.15/5.50 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.15/5.50 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.15/5.50 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % floor_log_nat_eq_if
% 5.15/5.50 thf(fact_8951_Arg__minus__ii,axiom,
% 5.15/5.50 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.15/5.50 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Arg_minus_ii
% 5.15/5.50 thf(fact_8952_csqrt__ii,axiom,
% 5.15/5.50 ( ( csqrt @ imaginary_unit )
% 5.15/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % csqrt_ii
% 5.15/5.50 thf(fact_8953_pochhammer__times__pochhammer__half,axiom,
% 5.15/5.50 ! [Z: rat,N2: nat] :
% 5.15/5.50 ( ( 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 ) ) )
% 5.15/5.50 = ( groups73079841787564623at_rat
% 5.15/5.50 @ ^ [K2: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.15/5.50 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_times_pochhammer_half
% 5.15/5.50 thf(fact_8954_pochhammer__times__pochhammer__half,axiom,
% 5.15/5.50 ! [Z: real,N2: nat] :
% 5.15/5.50 ( ( 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 ) ) )
% 5.15/5.50 = ( groups129246275422532515t_real
% 5.15/5.50 @ ^ [K2: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.50 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_times_pochhammer_half
% 5.15/5.50 thf(fact_8955_pochhammer__times__pochhammer__half,axiom,
% 5.15/5.50 ! [Z: complex,N2: nat] :
% 5.15/5.50 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( groups6464643781859351333omplex
% 5.15/5.50 @ ^ [K2: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.15/5.50 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_times_pochhammer_half
% 5.15/5.50 thf(fact_8956_pochhammer__code,axiom,
% 5.15/5.50 ( comm_s4028243227959126397er_rat
% 5.15/5.50 = ( ^ [A3: rat,N3: nat] :
% 5.15/5.50 ( if_rat @ ( N3 = zero_zero_nat ) @ one_one_rat
% 5.15/5.50 @ ( set_fo1949268297981939178at_rat
% 5.15/5.50 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.15/5.50 @ zero_zero_nat
% 5.15/5.50 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.15/5.50 @ one_one_rat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_code
% 5.15/5.50 thf(fact_8957_pochhammer__code,axiom,
% 5.15/5.50 ( comm_s4660882817536571857er_int
% 5.15/5.50 = ( ^ [A3: int,N3: nat] :
% 5.15/5.50 ( if_int @ ( N3 = zero_zero_nat ) @ one_one_int
% 5.15/5.50 @ ( set_fo2581907887559384638at_int
% 5.15/5.50 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.15/5.50 @ zero_zero_nat
% 5.15/5.50 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.15/5.50 @ one_one_int ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_code
% 5.15/5.50 thf(fact_8958_pochhammer__code,axiom,
% 5.15/5.50 ( comm_s7457072308508201937r_real
% 5.15/5.50 = ( ^ [A3: real,N3: nat] :
% 5.15/5.50 ( if_real @ ( N3 = zero_zero_nat ) @ one_one_real
% 5.15/5.50 @ ( set_fo3111899725591712190t_real
% 5.15/5.50 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.15/5.50 @ zero_zero_nat
% 5.15/5.50 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.15/5.50 @ one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_code
% 5.15/5.50 thf(fact_8959_pochhammer__code,axiom,
% 5.15/5.50 ( comm_s2602460028002588243omplex
% 5.15/5.50 = ( ^ [A3: complex,N3: nat] :
% 5.15/5.50 ( if_complex @ ( N3 = zero_zero_nat ) @ one_one_complex
% 5.15/5.50 @ ( set_fo1517530859248394432omplex
% 5.15/5.50 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.15/5.50 @ zero_zero_nat
% 5.15/5.50 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.15/5.50 @ one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_code
% 5.15/5.50 thf(fact_8960_pochhammer__code,axiom,
% 5.15/5.50 ( comm_s4663373288045622133er_nat
% 5.15/5.50 = ( ^ [A3: nat,N3: nat] :
% 5.15/5.50 ( if_nat @ ( N3 = zero_zero_nat ) @ one_one_nat
% 5.15/5.50 @ ( set_fo2584398358068434914at_nat
% 5.15/5.50 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.15/5.50 @ zero_zero_nat
% 5.15/5.50 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.15/5.50 @ one_one_nat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % pochhammer_code
% 5.15/5.50 thf(fact_8961_prod_Oneutral__const,axiom,
% 5.15/5.50 ! [A2: set_nat] :
% 5.15/5.50 ( ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [Uu3: nat] : one_one_nat
% 5.15/5.50 @ A2 )
% 5.15/5.50 = one_one_nat ) ).
% 5.15/5.50
% 5.15/5.50 % prod.neutral_const
% 5.15/5.50 thf(fact_8962_prod_Oneutral__const,axiom,
% 5.15/5.50 ! [A2: set_nat] :
% 5.15/5.50 ( ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [Uu3: nat] : one_one_int
% 5.15/5.50 @ A2 )
% 5.15/5.50 = one_one_int ) ).
% 5.15/5.50
% 5.15/5.50 % prod.neutral_const
% 5.15/5.50 thf(fact_8963_prod_Oneutral__const,axiom,
% 5.15/5.50 ! [A2: set_int] :
% 5.15/5.50 ( ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [Uu3: int] : one_one_int
% 5.15/5.50 @ A2 )
% 5.15/5.50 = one_one_int ) ).
% 5.15/5.50
% 5.15/5.50 % prod.neutral_const
% 5.15/5.50 thf(fact_8964_of__nat__prod,axiom,
% 5.15/5.50 ! [F: int > nat,A2: set_int] :
% 5.15/5.50 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 5.15/5.50 = ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_nat_prod
% 5.15/5.50 thf(fact_8965_of__nat__prod,axiom,
% 5.15/5.50 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.50 ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.15/5.50 = ( groups129246275422532515t_real
% 5.15/5.50 @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_nat_prod
% 5.15/5.50 thf(fact_8966_of__nat__prod,axiom,
% 5.15/5.50 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.50 ( ( semiri8010041392384452111omplex @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.15/5.50 = ( groups6464643781859351333omplex
% 5.15/5.50 @ ^ [X2: nat] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_nat_prod
% 5.15/5.50 thf(fact_8967_of__nat__prod,axiom,
% 5.15/5.50 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.50 ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.15/5.50 = ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_nat_prod
% 5.15/5.50 thf(fact_8968_of__nat__prod,axiom,
% 5.15/5.50 ! [F: nat > nat,A2: set_nat] :
% 5.15/5.50 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.15/5.50 = ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_nat_prod
% 5.15/5.50 thf(fact_8969_of__int__prod,axiom,
% 5.15/5.50 ! [F: nat > int,A2: set_nat] :
% 5.15/5.50 ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.15/5.50 = ( groups129246275422532515t_real
% 5.15/5.50 @ ^ [X2: nat] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_prod
% 5.15/5.50 thf(fact_8970_of__int__prod,axiom,
% 5.15/5.50 ! [F: nat > int,A2: set_nat] :
% 5.15/5.50 ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.15/5.50 = ( groups73079841787564623at_rat
% 5.15/5.50 @ ^ [X2: nat] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_prod
% 5.15/5.50 thf(fact_8971_of__int__prod,axiom,
% 5.15/5.50 ! [F: nat > int,A2: set_nat] :
% 5.15/5.50 ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.15/5.50 = ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [X2: nat] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_prod
% 5.15/5.50 thf(fact_8972_of__int__prod,axiom,
% 5.15/5.50 ! [F: int > int,A2: set_int] :
% 5.15/5.50 ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.15/5.50 = ( groups2316167850115554303t_real
% 5.15/5.50 @ ^ [X2: int] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_prod
% 5.15/5.50 thf(fact_8973_of__int__prod,axiom,
% 5.15/5.50 ! [F: int > int,A2: set_int] :
% 5.15/5.50 ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.15/5.50 = ( groups1072433553688619179nt_rat
% 5.15/5.50 @ ^ [X2: int] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_prod
% 5.15/5.50 thf(fact_8974_of__int__prod,axiom,
% 5.15/5.50 ! [F: int > int,A2: set_int] :
% 5.15/5.50 ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.15/5.50 = ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [X2: int] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % of_int_prod
% 5.15/5.50 thf(fact_8975_prod_Oempty,axiom,
% 5.15/5.50 ! [G: nat > complex] :
% 5.15/5.50 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.15/5.50 = one_one_complex ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8976_prod_Oempty,axiom,
% 5.15/5.50 ! [G: nat > real] :
% 5.15/5.50 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.15/5.50 = one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8977_prod_Oempty,axiom,
% 5.15/5.50 ! [G: nat > rat] :
% 5.15/5.50 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.15/5.50 = one_one_rat ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8978_prod_Oempty,axiom,
% 5.15/5.50 ! [G: int > complex] :
% 5.15/5.50 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.15/5.50 = one_one_complex ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8979_prod_Oempty,axiom,
% 5.15/5.50 ! [G: int > real] :
% 5.15/5.50 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.15/5.50 = one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8980_prod_Oempty,axiom,
% 5.15/5.50 ! [G: int > rat] :
% 5.15/5.50 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.15/5.50 = one_one_rat ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8981_prod_Oempty,axiom,
% 5.15/5.50 ! [G: int > nat] :
% 5.15/5.50 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.15/5.50 = one_one_nat ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8982_prod_Oempty,axiom,
% 5.15/5.50 ! [G: real > complex] :
% 5.15/5.50 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 5.15/5.50 = one_one_complex ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8983_prod_Oempty,axiom,
% 5.15/5.50 ! [G: real > real] :
% 5.15/5.50 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 5.15/5.50 = one_one_real ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8984_prod_Oempty,axiom,
% 5.15/5.50 ! [G: real > rat] :
% 5.15/5.50 ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 5.15/5.50 = one_one_rat ) ).
% 5.15/5.50
% 5.15/5.50 % prod.empty
% 5.15/5.50 thf(fact_8985_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_nat,G: nat > complex] :
% 5.15/5.50 ( ~ ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.15/5.50 = one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8986_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_complex,G: complex > complex] :
% 5.15/5.50 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.15/5.50 = one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8987_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_int,G: int > complex] :
% 5.15/5.50 ( ~ ( finite_finite_int @ A2 )
% 5.15/5.50 => ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.15/5.50 = one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8988_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_nat,G: nat > real] :
% 5.15/5.50 ( ~ ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( groups129246275422532515t_real @ G @ A2 )
% 5.15/5.50 = one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8989_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_complex,G: complex > real] :
% 5.15/5.50 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ( groups766887009212190081x_real @ G @ A2 )
% 5.15/5.50 = one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8990_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_int,G: int > real] :
% 5.15/5.50 ( ~ ( finite_finite_int @ A2 )
% 5.15/5.50 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.15/5.50 = one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8991_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_nat,G: nat > rat] :
% 5.15/5.50 ( ~ ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.15/5.50 = one_one_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8992_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_complex,G: complex > rat] :
% 5.15/5.50 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.15/5.50 = one_one_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8993_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_int,G: int > rat] :
% 5.15/5.50 ( ~ ( finite_finite_int @ A2 )
% 5.15/5.50 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 5.15/5.50 = one_one_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8994_prod_Oinfinite,axiom,
% 5.15/5.50 ! [A2: set_complex,G: complex > nat] :
% 5.15/5.50 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 5.15/5.50 = one_one_nat ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.infinite
% 5.15/5.50 thf(fact_8995_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_real,A: real,B: real > complex] :
% 5.15/5.50 ( ( finite_finite_real @ S3 )
% 5.15/5.50 => ( ( ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups713298508707869441omplex
% 5.15/5.50 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups713298508707869441omplex
% 5.15/5.50 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_8996_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.15/5.50 ( ( finite_finite_nat @ S3 )
% 5.15/5.50 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups6464643781859351333omplex
% 5.15/5.50 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups6464643781859351333omplex
% 5.15/5.50 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_8997_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.50 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.50 => ( ( groups3708469109370488835omplex
% 5.15/5.50 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.50 => ( ( groups3708469109370488835omplex
% 5.15/5.50 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_8998_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_int,A: int,B: int > complex] :
% 5.15/5.50 ( ( finite_finite_int @ S3 )
% 5.15/5.50 => ( ( ( member_int @ A @ S3 )
% 5.15/5.50 => ( ( groups7440179247065528705omplex
% 5.15/5.50 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.50 => ( ( groups7440179247065528705omplex
% 5.15/5.50 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_8999_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_real,A: real,B: real > real] :
% 5.15/5.50 ( ( finite_finite_real @ S3 )
% 5.15/5.50 => ( ( ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups1681761925125756287l_real
% 5.15/5.50 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups1681761925125756287l_real
% 5.15/5.50 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_9000_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_nat,A: nat,B: nat > real] :
% 5.15/5.50 ( ( finite_finite_nat @ S3 )
% 5.15/5.50 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups129246275422532515t_real
% 5.15/5.50 @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups129246275422532515t_real
% 5.15/5.50 @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_9001_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.50 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.50 => ( ( groups766887009212190081x_real
% 5.15/5.50 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.50 => ( ( groups766887009212190081x_real
% 5.15/5.50 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_9002_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_int,A: int,B: int > real] :
% 5.15/5.50 ( ( finite_finite_int @ S3 )
% 5.15/5.50 => ( ( ( member_int @ A @ S3 )
% 5.15/5.50 => ( ( groups2316167850115554303t_real
% 5.15/5.50 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.50 => ( ( groups2316167850115554303t_real
% 5.15/5.50 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_9003_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_real,A: real,B: real > rat] :
% 5.15/5.50 ( ( finite_finite_real @ S3 )
% 5.15/5.50 => ( ( ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups4061424788464935467al_rat
% 5.15/5.50 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups4061424788464935467al_rat
% 5.15/5.50 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_rat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_9004_prod_Odelta_H,axiom,
% 5.15/5.50 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.15/5.50 ( ( finite_finite_nat @ S3 )
% 5.15/5.50 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups73079841787564623at_rat
% 5.15/5.50 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups73079841787564623at_rat
% 5.15/5.50 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_rat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta'
% 5.15/5.50 thf(fact_9005_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_real,A: real,B: real > complex] :
% 5.15/5.50 ( ( finite_finite_real @ S3 )
% 5.15/5.50 => ( ( ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups713298508707869441omplex
% 5.15/5.50 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups713298508707869441omplex
% 5.15/5.50 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9006_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.15/5.50 ( ( finite_finite_nat @ S3 )
% 5.15/5.50 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups6464643781859351333omplex
% 5.15/5.50 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups6464643781859351333omplex
% 5.15/5.50 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9007_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.50 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.50 => ( ( groups3708469109370488835omplex
% 5.15/5.50 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.50 => ( ( groups3708469109370488835omplex
% 5.15/5.50 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9008_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_int,A: int,B: int > complex] :
% 5.15/5.50 ( ( finite_finite_int @ S3 )
% 5.15/5.50 => ( ( ( member_int @ A @ S3 )
% 5.15/5.50 => ( ( groups7440179247065528705omplex
% 5.15/5.50 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.50 => ( ( groups7440179247065528705omplex
% 5.15/5.50 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_complex ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9009_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_real,A: real,B: real > real] :
% 5.15/5.50 ( ( finite_finite_real @ S3 )
% 5.15/5.50 => ( ( ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups1681761925125756287l_real
% 5.15/5.50 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups1681761925125756287l_real
% 5.15/5.50 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9010_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_nat,A: nat,B: nat > real] :
% 5.15/5.50 ( ( finite_finite_nat @ S3 )
% 5.15/5.50 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups129246275422532515t_real
% 5.15/5.50 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups129246275422532515t_real
% 5.15/5.50 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9011_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.50 => ( ( ( member_complex @ A @ S3 )
% 5.15/5.50 => ( ( groups766887009212190081x_real
% 5.15/5.50 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_complex @ A @ S3 )
% 5.15/5.50 => ( ( groups766887009212190081x_real
% 5.15/5.50 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9012_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_int,A: int,B: int > real] :
% 5.15/5.50 ( ( finite_finite_int @ S3 )
% 5.15/5.50 => ( ( ( member_int @ A @ S3 )
% 5.15/5.50 => ( ( groups2316167850115554303t_real
% 5.15/5.50 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_int @ A @ S3 )
% 5.15/5.50 => ( ( groups2316167850115554303t_real
% 5.15/5.50 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_real ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9013_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_real,A: real,B: real > rat] :
% 5.15/5.50 ( ( finite_finite_real @ S3 )
% 5.15/5.50 => ( ( ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups4061424788464935467al_rat
% 5.15/5.50 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_real @ A @ S3 )
% 5.15/5.50 => ( ( groups4061424788464935467al_rat
% 5.15/5.50 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_rat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9014_prod_Odelta,axiom,
% 5.15/5.50 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.15/5.50 ( ( finite_finite_nat @ S3 )
% 5.15/5.50 => ( ( ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups73079841787564623at_rat
% 5.15/5.50 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = ( B @ A ) ) )
% 5.15/5.50 & ( ~ ( member_nat @ A @ S3 )
% 5.15/5.50 => ( ( groups73079841787564623at_rat
% 5.15/5.50 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.15/5.50 @ S3 )
% 5.15/5.50 = one_one_rat ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.delta
% 5.15/5.50 thf(fact_9015_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.15/5.50 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.50 => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.50 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.50 = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9016_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_real,X: real,G: real > real] :
% 5.15/5.50 ( ( finite_finite_real @ A2 )
% 5.15/5.50 => ( ~ ( member_real @ X @ A2 )
% 5.15/5.50 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.15/5.50 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9017_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_nat,X: nat,G: nat > real] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ~ ( member_nat @ X @ A2 )
% 5.15/5.50 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 5.15/5.50 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9018_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ~ ( member_complex @ X @ A2 )
% 5.15/5.50 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.50 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9019_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_int,X: int,G: int > real] :
% 5.15/5.50 ( ( finite_finite_int @ A2 )
% 5.15/5.50 => ( ~ ( member_int @ X @ A2 )
% 5.15/5.50 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.50 = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9020_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.15/5.50 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.15/5.50 => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 5.15/5.50 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 5.15/5.50 = ( times_times_rat @ ( G @ X ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9021_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_real,X: real,G: real > rat] :
% 5.15/5.50 ( ( finite_finite_real @ A2 )
% 5.15/5.50 => ( ~ ( member_real @ X @ A2 )
% 5.15/5.50 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X @ A2 ) )
% 5.15/5.50 = ( times_times_rat @ ( G @ X ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9022_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_nat,X: nat,G: nat > rat] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ~ ( member_nat @ X @ A2 )
% 5.15/5.50 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 5.15/5.50 = ( times_times_rat @ ( G @ X ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9023_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_complex,X: complex,G: complex > rat] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ~ ( member_complex @ X @ A2 )
% 5.15/5.50 => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.15/5.50 = ( times_times_rat @ ( G @ X ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9024_prod_Oinsert,axiom,
% 5.15/5.50 ! [A2: set_int,X: int,G: int > rat] :
% 5.15/5.50 ( ( finite_finite_int @ A2 )
% 5.15/5.50 => ( ~ ( member_int @ X @ A2 )
% 5.15/5.50 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 5.15/5.50 = ( times_times_rat @ ( G @ X ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.insert
% 5.15/5.50 thf(fact_9025_prod_OlessThan__Suc,axiom,
% 5.15/5.50 ! [G: nat > real,N2: nat] :
% 5.15/5.50 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.lessThan_Suc
% 5.15/5.50 thf(fact_9026_prod_OlessThan__Suc,axiom,
% 5.15/5.50 ! [G: nat > rat,N2: nat] :
% 5.15/5.50 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.lessThan_Suc
% 5.15/5.50 thf(fact_9027_prod_OlessThan__Suc,axiom,
% 5.15/5.50 ! [G: nat > nat,N2: nat] :
% 5.15/5.50 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.lessThan_Suc
% 5.15/5.50 thf(fact_9028_prod_OlessThan__Suc,axiom,
% 5.15/5.50 ! [G: nat > int,N2: nat] :
% 5.15/5.50 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.lessThan_Suc
% 5.15/5.50 thf(fact_9029_power2__csqrt,axiom,
% 5.15/5.50 ! [Z: complex] :
% 5.15/5.50 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.50 = Z ) ).
% 5.15/5.50
% 5.15/5.50 % power2_csqrt
% 5.15/5.50 thf(fact_9030_prod_Ocl__ivl__Suc,axiom,
% 5.15/5.50 ! [N2: nat,M: nat,G: nat > complex] :
% 5.15/5.50 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = one_one_complex ) )
% 5.15/5.50 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.cl_ivl_Suc
% 5.15/5.50 thf(fact_9031_prod_Ocl__ivl__Suc,axiom,
% 5.15/5.50 ! [N2: nat,M: nat,G: nat > real] :
% 5.15/5.50 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = one_one_real ) )
% 5.15/5.50 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.cl_ivl_Suc
% 5.15/5.50 thf(fact_9032_prod_Ocl__ivl__Suc,axiom,
% 5.15/5.50 ! [N2: nat,M: nat,G: nat > rat] :
% 5.15/5.50 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = one_one_rat ) )
% 5.15/5.50 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.cl_ivl_Suc
% 5.15/5.50 thf(fact_9033_prod_Ocl__ivl__Suc,axiom,
% 5.15/5.50 ! [N2: nat,M: nat,G: nat > nat] :
% 5.15/5.50 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = one_one_nat ) )
% 5.15/5.50 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.cl_ivl_Suc
% 5.15/5.50 thf(fact_9034_prod_Ocl__ivl__Suc,axiom,
% 5.15/5.50 ! [N2: nat,M: nat,G: nat > int] :
% 5.15/5.50 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = one_one_int ) )
% 5.15/5.50 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.15/5.50 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.15/5.50 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.cl_ivl_Suc
% 5.15/5.50 thf(fact_9035_Arg__ii,axiom,
% 5.15/5.50 ( ( arg @ imaginary_unit )
% 5.15/5.50 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % Arg_ii
% 5.15/5.50 thf(fact_9036_prod_Oswap,axiom,
% 5.15/5.50 ! [G: nat > nat > nat,B3: set_nat,A2: set_nat] :
% 5.15/5.50 ( ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( G @ I3 ) @ B3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [J3: nat] :
% 5.15/5.50 ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [I3: nat] : ( G @ I3 @ J3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 @ B3 ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap
% 5.15/5.50 thf(fact_9037_prod_Oswap,axiom,
% 5.15/5.50 ! [G: nat > nat > int,B3: set_nat,A2: set_nat] :
% 5.15/5.50 ( ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( G @ I3 ) @ B3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [J3: nat] :
% 5.15/5.50 ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [I3: nat] : ( G @ I3 @ J3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 @ B3 ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap
% 5.15/5.50 thf(fact_9038_prod_Oswap,axiom,
% 5.15/5.50 ! [G: nat > int > int,B3: set_int,A2: set_nat] :
% 5.15/5.50 ( ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [I3: nat] : ( groups1705073143266064639nt_int @ ( G @ I3 ) @ B3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [J3: int] :
% 5.15/5.50 ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [I3: nat] : ( G @ I3 @ J3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 @ B3 ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap
% 5.15/5.50 thf(fact_9039_prod_Oswap,axiom,
% 5.15/5.50 ! [G: int > nat > int,B3: set_nat,A2: set_int] :
% 5.15/5.50 ( ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [I3: int] : ( groups705719431365010083at_int @ ( G @ I3 ) @ B3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [J3: nat] :
% 5.15/5.50 ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [I3: int] : ( G @ I3 @ J3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 @ B3 ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap
% 5.15/5.50 thf(fact_9040_prod_Oswap,axiom,
% 5.15/5.50 ! [G: int > int > int,B3: set_int,A2: set_int] :
% 5.15/5.50 ( ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [I3: int] : ( groups1705073143266064639nt_int @ ( G @ I3 ) @ B3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [J3: int] :
% 5.15/5.50 ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [I3: int] : ( G @ I3 @ J3 )
% 5.15/5.50 @ A2 )
% 5.15/5.50 @ B3 ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap
% 5.15/5.50 thf(fact_9041_prod_Oneutral,axiom,
% 5.15/5.50 ! [A2: set_nat,G: nat > nat] :
% 5.15/5.50 ( ! [X3: nat] :
% 5.15/5.50 ( ( member_nat @ X3 @ A2 )
% 5.15/5.50 => ( ( G @ X3 )
% 5.15/5.50 = one_one_nat ) )
% 5.15/5.50 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.15/5.50 = one_one_nat ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.neutral
% 5.15/5.50 thf(fact_9042_prod_Oneutral,axiom,
% 5.15/5.50 ! [A2: set_nat,G: nat > int] :
% 5.15/5.50 ( ! [X3: nat] :
% 5.15/5.50 ( ( member_nat @ X3 @ A2 )
% 5.15/5.50 => ( ( G @ X3 )
% 5.15/5.50 = one_one_int ) )
% 5.15/5.50 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.15/5.50 = one_one_int ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.neutral
% 5.15/5.50 thf(fact_9043_prod_Oneutral,axiom,
% 5.15/5.50 ! [A2: set_int,G: int > int] :
% 5.15/5.50 ( ! [X3: int] :
% 5.15/5.50 ( ( member_int @ X3 @ A2 )
% 5.15/5.50 => ( ( G @ X3 )
% 5.15/5.50 = one_one_int ) )
% 5.15/5.50 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.15/5.50 = one_one_int ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.neutral
% 5.15/5.50 thf(fact_9044_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: complex > complex,A2: set_complex] :
% 5.15/5.50 ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.15/5.50 != one_one_complex )
% 5.15/5.50 => ~ ! [A5: complex] :
% 5.15/5.50 ( ( member_complex @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_complex ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9045_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: real > complex,A2: set_real] :
% 5.15/5.50 ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.15/5.50 != one_one_complex )
% 5.15/5.50 => ~ ! [A5: real] :
% 5.15/5.50 ( ( member_real @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_complex ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9046_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: nat > complex,A2: set_nat] :
% 5.15/5.50 ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.15/5.50 != one_one_complex )
% 5.15/5.50 => ~ ! [A5: nat] :
% 5.15/5.50 ( ( member_nat @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_complex ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9047_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: int > complex,A2: set_int] :
% 5.15/5.50 ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.15/5.50 != one_one_complex )
% 5.15/5.50 => ~ ! [A5: int] :
% 5.15/5.50 ( ( member_int @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_complex ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9048_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: complex > real,A2: set_complex] :
% 5.15/5.50 ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.15/5.50 != one_one_real )
% 5.15/5.50 => ~ ! [A5: complex] :
% 5.15/5.50 ( ( member_complex @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9049_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: real > real,A2: set_real] :
% 5.15/5.50 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.15/5.50 != one_one_real )
% 5.15/5.50 => ~ ! [A5: real] :
% 5.15/5.50 ( ( member_real @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9050_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: nat > real,A2: set_nat] :
% 5.15/5.50 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 5.15/5.50 != one_one_real )
% 5.15/5.50 => ~ ! [A5: nat] :
% 5.15/5.50 ( ( member_nat @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9051_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: int > real,A2: set_int] :
% 5.15/5.50 ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.15/5.50 != one_one_real )
% 5.15/5.50 => ~ ! [A5: int] :
% 5.15/5.50 ( ( member_int @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_real ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9052_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: complex > rat,A2: set_complex] :
% 5.15/5.50 ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.15/5.50 != one_one_rat )
% 5.15/5.50 => ~ ! [A5: complex] :
% 5.15/5.50 ( ( member_complex @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9053_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.15/5.50 ! [G: real > rat,A2: set_real] :
% 5.15/5.50 ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.15/5.50 != one_one_rat )
% 5.15/5.50 => ~ ! [A5: real] :
% 5.15/5.50 ( ( member_real @ A5 @ A2 )
% 5.15/5.50 => ( ( G @ A5 )
% 5.15/5.50 = one_one_rat ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.not_neutral_contains_not_neutral
% 5.15/5.50 thf(fact_9054_prod_Odistrib,axiom,
% 5.15/5.50 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.15/5.50 ( ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.distrib
% 5.15/5.50 thf(fact_9055_prod_Odistrib,axiom,
% 5.15/5.50 ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 5.15/5.50 ( ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [X2: nat] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.distrib
% 5.15/5.50 thf(fact_9056_prod_Odistrib,axiom,
% 5.15/5.50 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.15/5.50 ( ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [X2: int] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.distrib
% 5.15/5.50 thf(fact_9057_prod__power__distrib,axiom,
% 5.15/5.50 ! [F: nat > nat,A2: set_nat,N2: nat] :
% 5.15/5.50 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N2 )
% 5.15/5.50 = ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N2 )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_power_distrib
% 5.15/5.50 thf(fact_9058_prod__power__distrib,axiom,
% 5.15/5.50 ! [F: nat > int,A2: set_nat,N2: nat] :
% 5.15/5.50 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N2 )
% 5.15/5.50 = ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [X2: nat] : ( power_power_int @ ( F @ X2 ) @ N2 )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_power_distrib
% 5.15/5.50 thf(fact_9059_prod__power__distrib,axiom,
% 5.15/5.50 ! [F: int > int,A2: set_int,N2: nat] :
% 5.15/5.50 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N2 )
% 5.15/5.50 = ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [X2: int] : ( power_power_int @ ( F @ X2 ) @ N2 )
% 5.15/5.50 @ A2 ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_power_distrib
% 5.15/5.50 thf(fact_9060_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_real,B3: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 5.15/5.50 ( ( finite_finite_real @ A2 )
% 5.15/5.50 => ( ( finite_finite_nat @ B3 )
% 5.15/5.50 => ( ( groups4696554848551431203al_nat
% 5.15/5.50 @ ^ [X2: real] :
% 5.15/5.50 ( groups708209901874060359at_nat @ ( G @ X2 )
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( groups4696554848551431203al_nat
% 5.15/5.50 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_real
% 5.15/5.50 @ ^ [X2: real] :
% 5.15/5.50 ( ( member_real @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9061_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_complex,B3: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ( finite_finite_nat @ B3 )
% 5.15/5.50 => ( ( groups861055069439313189ex_nat
% 5.15/5.50 @ ^ [X2: complex] :
% 5.15/5.50 ( groups708209901874060359at_nat @ ( G @ X2 )
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( groups861055069439313189ex_nat
% 5.15/5.50 @ ^ [X2: complex] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_complex
% 5.15/5.50 @ ^ [X2: complex] :
% 5.15/5.50 ( ( member_complex @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9062_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_int,B3: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 5.15/5.50 ( ( finite_finite_int @ A2 )
% 5.15/5.50 => ( ( finite_finite_nat @ B3 )
% 5.15/5.50 => ( ( groups1707563613775114915nt_nat
% 5.15/5.50 @ ^ [X2: int] :
% 5.15/5.50 ( groups708209901874060359at_nat @ ( G @ X2 )
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( groups1707563613775114915nt_nat
% 5.15/5.50 @ ^ [X2: int] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_int
% 5.15/5.50 @ ^ [X2: int] :
% 5.15/5.50 ( ( member_int @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9063_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_real,B3: set_nat,G: real > nat > int,R: real > nat > $o] :
% 5.15/5.50 ( ( finite_finite_real @ A2 )
% 5.15/5.50 => ( ( finite_finite_nat @ B3 )
% 5.15/5.50 => ( ( groups4694064378042380927al_int
% 5.15/5.50 @ ^ [X2: real] :
% 5.15/5.50 ( groups705719431365010083at_int @ ( G @ X2 )
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( groups4694064378042380927al_int
% 5.15/5.50 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_real
% 5.15/5.50 @ ^ [X2: real] :
% 5.15/5.50 ( ( member_real @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9064_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_complex,B3: set_nat,G: complex > nat > int,R: complex > nat > $o] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ( finite_finite_nat @ B3 )
% 5.15/5.50 => ( ( groups858564598930262913ex_int
% 5.15/5.50 @ ^ [X2: complex] :
% 5.15/5.50 ( groups705719431365010083at_int @ ( G @ X2 )
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( ( member_nat @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [Y2: nat] :
% 5.15/5.50 ( groups858564598930262913ex_int
% 5.15/5.50 @ ^ [X2: complex] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_complex
% 5.15/5.50 @ ^ [X2: complex] :
% 5.15/5.50 ( ( member_complex @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9065_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_real,B3: set_int,G: real > int > int,R: real > int > $o] :
% 5.15/5.50 ( ( finite_finite_real @ A2 )
% 5.15/5.50 => ( ( finite_finite_int @ B3 )
% 5.15/5.50 => ( ( groups4694064378042380927al_int
% 5.15/5.50 @ ^ [X2: real] :
% 5.15/5.50 ( groups1705073143266064639nt_int @ ( G @ X2 )
% 5.15/5.50 @ ( collect_int
% 5.15/5.50 @ ^ [Y2: int] :
% 5.15/5.50 ( ( member_int @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [Y2: int] :
% 5.15/5.50 ( groups4694064378042380927al_int
% 5.15/5.50 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_real
% 5.15/5.50 @ ^ [X2: real] :
% 5.15/5.50 ( ( member_real @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9066_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_complex,B3: set_int,G: complex > int > int,R: complex > int > $o] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ( finite_finite_int @ B3 )
% 5.15/5.50 => ( ( groups858564598930262913ex_int
% 5.15/5.50 @ ^ [X2: complex] :
% 5.15/5.50 ( groups1705073143266064639nt_int @ ( G @ X2 )
% 5.15/5.50 @ ( collect_int
% 5.15/5.50 @ ^ [Y2: int] :
% 5.15/5.50 ( ( member_int @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [Y2: int] :
% 5.15/5.50 ( groups858564598930262913ex_int
% 5.15/5.50 @ ^ [X2: complex] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_complex
% 5.15/5.50 @ ^ [X2: complex] :
% 5.15/5.50 ( ( member_complex @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9067_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_nat,B3: set_real,G: nat > real > nat,R: nat > real > $o] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( finite_finite_real @ B3 )
% 5.15/5.50 => ( ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] :
% 5.15/5.50 ( groups4696554848551431203al_nat @ ( G @ X2 )
% 5.15/5.50 @ ( collect_real
% 5.15/5.50 @ ^ [Y2: real] :
% 5.15/5.50 ( ( member_real @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups4696554848551431203al_nat
% 5.15/5.50 @ ^ [Y2: real] :
% 5.15/5.50 ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [X2: nat] :
% 5.15/5.50 ( ( member_nat @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9068_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_nat,B3: set_complex,G: nat > complex > nat,R: nat > complex > $o] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( finite3207457112153483333omplex @ B3 )
% 5.15/5.50 => ( ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] :
% 5.15/5.50 ( groups861055069439313189ex_nat @ ( G @ X2 )
% 5.15/5.50 @ ( collect_complex
% 5.15/5.50 @ ^ [Y2: complex] :
% 5.15/5.50 ( ( member_complex @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups861055069439313189ex_nat
% 5.15/5.50 @ ^ [Y2: complex] :
% 5.15/5.50 ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [X2: nat] :
% 5.15/5.50 ( ( member_nat @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9069_prod_Oswap__restrict,axiom,
% 5.15/5.50 ! [A2: set_nat,B3: set_int,G: nat > int > nat,R: nat > int > $o] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( finite_finite_int @ B3 )
% 5.15/5.50 => ( ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] :
% 5.15/5.50 ( groups1707563613775114915nt_nat @ ( G @ X2 )
% 5.15/5.50 @ ( collect_int
% 5.15/5.50 @ ^ [Y2: int] :
% 5.15/5.50 ( ( member_int @ Y2 @ B3 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ A2 )
% 5.15/5.50 = ( groups1707563613775114915nt_nat
% 5.15/5.50 @ ^ [Y2: int] :
% 5.15/5.50 ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [X2: nat] : ( G @ X2 @ Y2 )
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [X2: nat] :
% 5.15/5.50 ( ( member_nat @ X2 @ A2 )
% 5.15/5.50 & ( R @ X2 @ Y2 ) ) ) )
% 5.15/5.50 @ B3 ) ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.swap_restrict
% 5.15/5.50 thf(fact_9070_mod__prod__eq,axiom,
% 5.15/5.50 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.15/5.50 ( ( modulo_modulo_nat
% 5.15/5.50 @ ( groups708209901874060359at_nat
% 5.15/5.50 @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 5.15/5.50 @ A2 )
% 5.15/5.50 @ A )
% 5.15/5.50 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 5.15/5.50
% 5.15/5.50 % mod_prod_eq
% 5.15/5.50 thf(fact_9071_mod__prod__eq,axiom,
% 5.15/5.50 ! [F: nat > int,A: int,A2: set_nat] :
% 5.15/5.50 ( ( modulo_modulo_int
% 5.15/5.50 @ ( groups705719431365010083at_int
% 5.15/5.50 @ ^ [I3: nat] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.15/5.50 @ A2 )
% 5.15/5.50 @ A )
% 5.15/5.50 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 5.15/5.50
% 5.15/5.50 % mod_prod_eq
% 5.15/5.50 thf(fact_9072_mod__prod__eq,axiom,
% 5.15/5.50 ! [F: int > int,A: int,A2: set_int] :
% 5.15/5.50 ( ( modulo_modulo_int
% 5.15/5.50 @ ( groups1705073143266064639nt_int
% 5.15/5.50 @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.15/5.50 @ A2 )
% 5.15/5.50 @ A )
% 5.15/5.50 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 5.15/5.50
% 5.15/5.50 % mod_prod_eq
% 5.15/5.50 thf(fact_9073_prod__nonneg,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > nat] :
% 5.15/5.50 ( ! [X3: nat] :
% 5.15/5.50 ( ( member_nat @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_nonneg
% 5.15/5.50 thf(fact_9074_prod__nonneg,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > int] :
% 5.15/5.50 ( ! [X3: nat] :
% 5.15/5.50 ( ( member_nat @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_nonneg
% 5.15/5.50 thf(fact_9075_prod__nonneg,axiom,
% 5.15/5.50 ! [A2: set_int,F: int > int] :
% 5.15/5.50 ( ! [X3: int] :
% 5.15/5.50 ( ( member_int @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_nonneg
% 5.15/5.50 thf(fact_9076_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.15/5.50 ( ! [I2: complex] :
% 5.15/5.50 ( ( member_complex @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9077_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_real,F: real > real,G: real > real] :
% 5.15/5.50 ( ! [I2: real] :
% 5.15/5.50 ( ( member_real @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9078_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.15/5.50 ( ! [I2: nat] :
% 5.15/5.50 ( ( member_nat @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9079_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_int,F: int > real,G: int > real] :
% 5.15/5.50 ( ! [I2: int] :
% 5.15/5.50 ( ( member_int @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9080_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.15/5.50 ( ! [I2: complex] :
% 5.15/5.50 ( ( member_complex @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9081_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.15/5.50 ( ! [I2: real] :
% 5.15/5.50 ( ( member_real @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9082_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.15/5.50 ( ! [I2: nat] :
% 5.15/5.50 ( ( member_nat @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9083_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.15/5.50 ( ! [I2: int] :
% 5.15/5.50 ( ( member_int @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9084_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.15/5.50 ( ! [I2: complex] :
% 5.15/5.50 ( ( member_complex @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9085_prod__mono,axiom,
% 5.15/5.50 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.15/5.50 ( ! [I2: real] :
% 5.15/5.50 ( ( member_real @ I2 @ A2 )
% 5.15/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.15/5.50 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.15/5.50 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_mono
% 5.15/5.50 thf(fact_9086_prod__pos,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > nat] :
% 5.15/5.50 ( ! [X3: nat] :
% 5.15/5.50 ( ( member_nat @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_pos
% 5.15/5.50 thf(fact_9087_prod__pos,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > int] :
% 5.15/5.50 ( ! [X3: nat] :
% 5.15/5.50 ( ( member_nat @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_pos
% 5.15/5.50 thf(fact_9088_prod__pos,axiom,
% 5.15/5.50 ! [A2: set_int,F: int > int] :
% 5.15/5.50 ( ! [X3: int] :
% 5.15/5.50 ( ( member_int @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_pos
% 5.15/5.50 thf(fact_9089_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_complex,F: complex > real] :
% 5.15/5.50 ( ! [X3: complex] :
% 5.15/5.50 ( ( member_complex @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9090_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_real,F: real > real] :
% 5.15/5.50 ( ! [X3: real] :
% 5.15/5.50 ( ( member_real @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9091_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > real] :
% 5.15/5.50 ( ! [X3: nat] :
% 5.15/5.50 ( ( member_nat @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9092_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_int,F: int > real] :
% 5.15/5.50 ( ! [X3: int] :
% 5.15/5.50 ( ( member_int @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9093_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_complex,F: complex > rat] :
% 5.15/5.50 ( ! [X3: complex] :
% 5.15/5.50 ( ( member_complex @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9094_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_real,F: real > rat] :
% 5.15/5.50 ( ! [X3: real] :
% 5.15/5.50 ( ( member_real @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9095_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_nat,F: nat > rat] :
% 5.15/5.50 ( ! [X3: nat] :
% 5.15/5.50 ( ( member_nat @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9096_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_int,F: int > rat] :
% 5.15/5.50 ( ! [X3: int] :
% 5.15/5.50 ( ( member_int @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9097_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_complex,F: complex > nat] :
% 5.15/5.50 ( ! [X3: complex] :
% 5.15/5.50 ( ( member_complex @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_nat @ one_one_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9098_prod__ge__1,axiom,
% 5.15/5.50 ! [A2: set_real,F: real > nat] :
% 5.15/5.50 ( ! [X3: real] :
% 5.15/5.50 ( ( member_real @ X3 @ A2 )
% 5.15/5.50 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.15/5.50 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_ge_1
% 5.15/5.50 thf(fact_9099_prod__atLeastAtMost__code,axiom,
% 5.15/5.50 ! [F: nat > complex,A: nat,B: nat] :
% 5.15/5.50 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.15/5.50 = ( set_fo1517530859248394432omplex
% 5.15/5.50 @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 5.15/5.50 @ A
% 5.15/5.50 @ B
% 5.15/5.50 @ one_one_complex ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_atLeastAtMost_code
% 5.15/5.50 thf(fact_9100_prod__atLeastAtMost__code,axiom,
% 5.15/5.50 ! [F: nat > real,A: nat,B: nat] :
% 5.15/5.50 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.15/5.50 = ( set_fo3111899725591712190t_real
% 5.15/5.50 @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 5.15/5.50 @ A
% 5.15/5.50 @ B
% 5.15/5.50 @ one_one_real ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_atLeastAtMost_code
% 5.15/5.50 thf(fact_9101_prod__atLeastAtMost__code,axiom,
% 5.15/5.50 ! [F: nat > rat,A: nat,B: nat] :
% 5.15/5.50 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.15/5.50 = ( set_fo1949268297981939178at_rat
% 5.15/5.50 @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 5.15/5.50 @ A
% 5.15/5.50 @ B
% 5.15/5.50 @ one_one_rat ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_atLeastAtMost_code
% 5.15/5.50 thf(fact_9102_prod__atLeastAtMost__code,axiom,
% 5.15/5.50 ! [F: nat > nat,A: nat,B: nat] :
% 5.15/5.50 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.15/5.50 = ( set_fo2584398358068434914at_nat
% 5.15/5.50 @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 5.15/5.50 @ A
% 5.15/5.50 @ B
% 5.15/5.50 @ one_one_nat ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_atLeastAtMost_code
% 5.15/5.50 thf(fact_9103_prod__atLeastAtMost__code,axiom,
% 5.15/5.50 ! [F: nat > int,A: nat,B: nat] :
% 5.15/5.50 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.15/5.50 = ( set_fo2581907887559384638at_int
% 5.15/5.50 @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 5.15/5.50 @ A
% 5.15/5.50 @ B
% 5.15/5.50 @ one_one_int ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod_atLeastAtMost_code
% 5.15/5.50 thf(fact_9104_prod_Ointer__filter,axiom,
% 5.15/5.50 ! [A2: set_real,G: real > complex,P: real > $o] :
% 5.15/5.50 ( ( finite_finite_real @ A2 )
% 5.15/5.50 => ( ( groups713298508707869441omplex @ G
% 5.15/5.50 @ ( collect_real
% 5.15/5.50 @ ^ [X2: real] :
% 5.15/5.50 ( ( member_real @ X2 @ A2 )
% 5.15/5.50 & ( P @ X2 ) ) ) )
% 5.15/5.50 = ( groups713298508707869441omplex
% 5.15/5.50 @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.15/5.50 @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.inter_filter
% 5.15/5.50 thf(fact_9105_prod_Ointer__filter,axiom,
% 5.15/5.50 ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( groups6464643781859351333omplex @ G
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [X2: nat] :
% 5.15/5.50 ( ( member_nat @ X2 @ A2 )
% 5.15/5.50 & ( P @ X2 ) ) ) )
% 5.15/5.50 = ( groups6464643781859351333omplex
% 5.15/5.50 @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.15/5.50 @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.inter_filter
% 5.15/5.50 thf(fact_9106_prod_Ointer__filter,axiom,
% 5.15/5.50 ! [A2: set_complex,G: complex > complex,P: complex > $o] :
% 5.15/5.50 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.50 => ( ( groups3708469109370488835omplex @ G
% 5.15/5.50 @ ( collect_complex
% 5.15/5.50 @ ^ [X2: complex] :
% 5.15/5.50 ( ( member_complex @ X2 @ A2 )
% 5.15/5.50 & ( P @ X2 ) ) ) )
% 5.15/5.50 = ( groups3708469109370488835omplex
% 5.15/5.50 @ ^ [X2: complex] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.15/5.50 @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.inter_filter
% 5.15/5.50 thf(fact_9107_prod_Ointer__filter,axiom,
% 5.15/5.50 ! [A2: set_int,G: int > complex,P: int > $o] :
% 5.15/5.50 ( ( finite_finite_int @ A2 )
% 5.15/5.50 => ( ( groups7440179247065528705omplex @ G
% 5.15/5.50 @ ( collect_int
% 5.15/5.50 @ ^ [X2: int] :
% 5.15/5.50 ( ( member_int @ X2 @ A2 )
% 5.15/5.50 & ( P @ X2 ) ) ) )
% 5.15/5.50 = ( groups7440179247065528705omplex
% 5.15/5.50 @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_complex )
% 5.15/5.50 @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.inter_filter
% 5.15/5.50 thf(fact_9108_prod_Ointer__filter,axiom,
% 5.15/5.50 ! [A2: set_real,G: real > real,P: real > $o] :
% 5.15/5.50 ( ( finite_finite_real @ A2 )
% 5.15/5.50 => ( ( groups1681761925125756287l_real @ G
% 5.15/5.50 @ ( collect_real
% 5.15/5.50 @ ^ [X2: real] :
% 5.15/5.50 ( ( member_real @ X2 @ A2 )
% 5.15/5.50 & ( P @ X2 ) ) ) )
% 5.15/5.50 = ( groups1681761925125756287l_real
% 5.15/5.50 @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.15/5.50 @ A2 ) ) ) ).
% 5.15/5.50
% 5.15/5.50 % prod.inter_filter
% 5.15/5.50 thf(fact_9109_prod_Ointer__filter,axiom,
% 5.15/5.50 ! [A2: set_nat,G: nat > real,P: nat > $o] :
% 5.15/5.50 ( ( finite_finite_nat @ A2 )
% 5.15/5.50 => ( ( groups129246275422532515t_real @ G
% 5.15/5.50 @ ( collect_nat
% 5.15/5.50 @ ^ [X2: nat] :
% 5.15/5.50 ( ( member_nat @ X2 @ A2 )
% 5.15/5.51 & ( P @ X2 ) ) ) )
% 5.15/5.51 = ( groups129246275422532515t_real
% 5.15/5.51 @ ^ [X2: nat] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.15/5.51 @ A2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.inter_filter
% 5.15/5.51 thf(fact_9110_prod_Ointer__filter,axiom,
% 5.15/5.51 ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 5.15/5.51 ( ( finite3207457112153483333omplex @ A2 )
% 5.15/5.51 => ( ( groups766887009212190081x_real @ G
% 5.15/5.51 @ ( collect_complex
% 5.15/5.51 @ ^ [X2: complex] :
% 5.15/5.51 ( ( member_complex @ X2 @ A2 )
% 5.15/5.51 & ( P @ X2 ) ) ) )
% 5.15/5.51 = ( groups766887009212190081x_real
% 5.15/5.51 @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.15/5.51 @ A2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.inter_filter
% 5.15/5.51 thf(fact_9111_prod_Ointer__filter,axiom,
% 5.15/5.51 ! [A2: set_int,G: int > real,P: int > $o] :
% 5.15/5.51 ( ( finite_finite_int @ A2 )
% 5.15/5.51 => ( ( groups2316167850115554303t_real @ G
% 5.15/5.51 @ ( collect_int
% 5.15/5.51 @ ^ [X2: int] :
% 5.15/5.51 ( ( member_int @ X2 @ A2 )
% 5.15/5.51 & ( P @ X2 ) ) ) )
% 5.15/5.51 = ( groups2316167850115554303t_real
% 5.15/5.51 @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 5.15/5.51 @ A2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.inter_filter
% 5.15/5.51 thf(fact_9112_prod_Ointer__filter,axiom,
% 5.15/5.51 ! [A2: set_real,G: real > rat,P: real > $o] :
% 5.15/5.51 ( ( finite_finite_real @ A2 )
% 5.15/5.51 => ( ( groups4061424788464935467al_rat @ G
% 5.15/5.51 @ ( collect_real
% 5.15/5.51 @ ^ [X2: real] :
% 5.15/5.51 ( ( member_real @ X2 @ A2 )
% 5.15/5.51 & ( P @ X2 ) ) ) )
% 5.15/5.51 = ( groups4061424788464935467al_rat
% 5.15/5.51 @ ^ [X2: real] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_rat )
% 5.15/5.51 @ A2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.inter_filter
% 5.15/5.51 thf(fact_9113_prod_Ointer__filter,axiom,
% 5.15/5.51 ! [A2: set_nat,G: nat > rat,P: nat > $o] :
% 5.15/5.51 ( ( finite_finite_nat @ A2 )
% 5.15/5.51 => ( ( groups73079841787564623at_rat @ G
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [X2: nat] :
% 5.15/5.51 ( ( member_nat @ X2 @ A2 )
% 5.15/5.51 & ( P @ X2 ) ) ) )
% 5.15/5.51 = ( groups73079841787564623at_rat
% 5.15/5.51 @ ^ [X2: nat] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_rat )
% 5.15/5.51 @ A2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.inter_filter
% 5.15/5.51 thf(fact_9114_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.15/5.51 ! [G: nat > nat,M: nat,N2: nat] :
% 5.15/5.51 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.15/5.51 = ( groups708209901874060359at_nat
% 5.15/5.51 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.51 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.shift_bounds_cl_Suc_ivl
% 5.15/5.51 thf(fact_9115_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.15/5.51 ! [G: nat > int,M: nat,N2: nat] :
% 5.15/5.51 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.15/5.51 = ( groups705719431365010083at_int
% 5.15/5.51 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.15/5.51 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.shift_bounds_cl_Suc_ivl
% 5.15/5.51 thf(fact_9116_power__sum,axiom,
% 5.15/5.51 ! [C: real,F: nat > nat,A2: set_nat] :
% 5.15/5.51 ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.51 = ( groups129246275422532515t_real
% 5.15/5.51 @ ^ [A3: nat] : ( power_power_real @ C @ ( F @ A3 ) )
% 5.15/5.51 @ A2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % power_sum
% 5.15/5.51 thf(fact_9117_power__sum,axiom,
% 5.15/5.51 ! [C: complex,F: nat > nat,A2: set_nat] :
% 5.15/5.51 ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.51 = ( groups6464643781859351333omplex
% 5.15/5.51 @ ^ [A3: nat] : ( power_power_complex @ C @ ( F @ A3 ) )
% 5.15/5.51 @ A2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % power_sum
% 5.15/5.51 thf(fact_9118_power__sum,axiom,
% 5.15/5.51 ! [C: nat,F: nat > nat,A2: set_nat] :
% 5.15/5.51 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.51 = ( groups708209901874060359at_nat
% 5.15/5.51 @ ^ [A3: nat] : ( power_power_nat @ C @ ( F @ A3 ) )
% 5.15/5.51 @ A2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % power_sum
% 5.15/5.51 thf(fact_9119_power__sum,axiom,
% 5.15/5.51 ! [C: int,F: nat > nat,A2: set_nat] :
% 5.15/5.51 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.15/5.51 = ( groups705719431365010083at_int
% 5.15/5.51 @ ^ [A3: nat] : ( power_power_int @ C @ ( F @ A3 ) )
% 5.15/5.51 @ A2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % power_sum
% 5.15/5.51 thf(fact_9120_power__sum,axiom,
% 5.15/5.51 ! [C: int,F: int > nat,A2: set_int] :
% 5.15/5.51 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.15/5.51 = ( groups1705073143266064639nt_int
% 5.15/5.51 @ ^ [A3: int] : ( power_power_int @ C @ ( F @ A3 ) )
% 5.15/5.51 @ A2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % power_sum
% 5.15/5.51 thf(fact_9121_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.15/5.51 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.15/5.51 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.15/5.51 = ( groups708209901874060359at_nat
% 5.15/5.51 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.15/5.51 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.shift_bounds_cl_nat_ivl
% 5.15/5.51 thf(fact_9122_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.15/5.51 ! [G: nat > int,M: nat,K: nat,N2: nat] :
% 5.15/5.51 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.15/5.51 = ( groups705719431365010083at_int
% 5.15/5.51 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.15/5.51 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.shift_bounds_cl_nat_ivl
% 5.15/5.51 thf(fact_9123_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_complex,F: complex > real] :
% 5.15/5.51 ( ! [X3: complex] :
% 5.15/5.51 ( ( member_complex @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.15/5.51 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9124_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_real,F: real > real] :
% 5.15/5.51 ( ! [X3: real] :
% 5.15/5.51 ( ( member_real @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.15/5.51 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9125_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_nat,F: nat > real] :
% 5.15/5.51 ( ! [X3: nat] :
% 5.15/5.51 ( ( member_nat @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.15/5.51 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9126_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_int,F: int > real] :
% 5.15/5.51 ( ! [X3: int] :
% 5.15/5.51 ( ( member_int @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.15/5.51 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9127_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_complex,F: complex > rat] :
% 5.15/5.51 ( ! [X3: complex] :
% 5.15/5.51 ( ( member_complex @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.15/5.51 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9128_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_real,F: real > rat] :
% 5.15/5.51 ( ! [X3: real] :
% 5.15/5.51 ( ( member_real @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.15/5.51 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9129_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_nat,F: nat > rat] :
% 5.15/5.51 ( ! [X3: nat] :
% 5.15/5.51 ( ( member_nat @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.15/5.51 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9130_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_int,F: int > rat] :
% 5.15/5.51 ( ! [X3: int] :
% 5.15/5.51 ( ( member_int @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.15/5.51 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9131_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_complex,F: complex > nat] :
% 5.15/5.51 ( ! [X3: complex] :
% 5.15/5.51 ( ( member_complex @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.15/5.51 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9132_prod__le__1,axiom,
% 5.15/5.51 ! [A2: set_real,F: real > nat] :
% 5.15/5.51 ( ! [X3: real] :
% 5.15/5.51 ( ( member_real @ X3 @ A2 )
% 5.15/5.51 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.15/5.51 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.15/5.51 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_le_1
% 5.15/5.51 thf(fact_9133_prod_Orelated,axiom,
% 5.15/5.51 ! [R: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.15/5.51 ( ( R @ one_one_real @ one_one_real )
% 5.15/5.51 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_real @ X16 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite_finite_int @ S3 )
% 5.15/5.51 => ( ! [X3: int] :
% 5.15/5.51 ( ( member_int @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups2316167850115554303t_real @ H2 @ S3 ) @ ( groups2316167850115554303t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9134_prod_Orelated,axiom,
% 5.15/5.51 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.15/5.51 ( ( R @ one_one_rat @ one_one_rat )
% 5.15/5.51 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_rat @ X16 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite_finite_nat @ S3 )
% 5.15/5.51 => ( ! [X3: nat] :
% 5.15/5.51 ( ( member_nat @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups73079841787564623at_rat @ H2 @ S3 ) @ ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9135_prod_Orelated,axiom,
% 5.15/5.51 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.15/5.51 ( ( R @ one_one_rat @ one_one_rat )
% 5.15/5.51 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_rat @ X16 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.51 => ( ! [X3: complex] :
% 5.15/5.51 ( ( member_complex @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups225925009352817453ex_rat @ H2 @ S3 ) @ ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9136_prod_Orelated,axiom,
% 5.15/5.51 ! [R: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.15/5.51 ( ( R @ one_one_rat @ one_one_rat )
% 5.15/5.51 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_rat @ X16 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite_finite_int @ S3 )
% 5.15/5.51 => ( ! [X3: int] :
% 5.15/5.51 ( ( member_int @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups1072433553688619179nt_rat @ H2 @ S3 ) @ ( groups1072433553688619179nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9137_prod_Orelated,axiom,
% 5.15/5.51 ! [R: nat > nat > $o,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.15/5.51 ( ( R @ one_one_nat @ one_one_nat )
% 5.15/5.51 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_nat @ X16 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.51 => ( ! [X3: complex] :
% 5.15/5.51 ( ( member_complex @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups861055069439313189ex_nat @ H2 @ S3 ) @ ( groups861055069439313189ex_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9138_prod_Orelated,axiom,
% 5.15/5.51 ! [R: nat > nat > $o,S3: set_int,H2: int > nat,G: int > nat] :
% 5.15/5.51 ( ( R @ one_one_nat @ one_one_nat )
% 5.15/5.51 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_nat @ X16 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite_finite_int @ S3 )
% 5.15/5.51 => ( ! [X3: int] :
% 5.15/5.51 ( ( member_int @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups1707563613775114915nt_nat @ H2 @ S3 ) @ ( groups1707563613775114915nt_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9139_prod_Orelated,axiom,
% 5.15/5.51 ! [R: int > int > $o,S3: set_complex,H2: complex > int,G: complex > int] :
% 5.15/5.51 ( ( R @ one_one_int @ one_one_int )
% 5.15/5.51 => ( ! [X16: int,Y15: int,X23: int,Y23: int] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_int @ X16 @ Y15 ) @ ( times_times_int @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite3207457112153483333omplex @ S3 )
% 5.15/5.51 => ( ! [X3: complex] :
% 5.15/5.51 ( ( member_complex @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups858564598930262913ex_int @ H2 @ S3 ) @ ( groups858564598930262913ex_int @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9140_prod_Orelated,axiom,
% 5.15/5.51 ! [R: nat > nat > $o,S3: set_nat,H2: nat > nat,G: nat > nat] :
% 5.15/5.51 ( ( R @ one_one_nat @ one_one_nat )
% 5.15/5.51 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_nat @ X16 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite_finite_nat @ S3 )
% 5.15/5.51 => ( ! [X3: nat] :
% 5.15/5.51 ( ( member_nat @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups708209901874060359at_nat @ H2 @ S3 ) @ ( groups708209901874060359at_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9141_prod_Orelated,axiom,
% 5.15/5.51 ! [R: int > int > $o,S3: set_nat,H2: nat > int,G: nat > int] :
% 5.15/5.51 ( ( R @ one_one_int @ one_one_int )
% 5.15/5.51 => ( ! [X16: int,Y15: int,X23: int,Y23: int] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_int @ X16 @ Y15 ) @ ( times_times_int @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite_finite_nat @ S3 )
% 5.15/5.51 => ( ! [X3: nat] :
% 5.15/5.51 ( ( member_nat @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups705719431365010083at_int @ H2 @ S3 ) @ ( groups705719431365010083at_int @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9142_prod_Orelated,axiom,
% 5.15/5.51 ! [R: int > int > $o,S3: set_int,H2: int > int,G: int > int] :
% 5.15/5.51 ( ( R @ one_one_int @ one_one_int )
% 5.15/5.51 => ( ! [X16: int,Y15: int,X23: int,Y23: int] :
% 5.15/5.51 ( ( ( R @ X16 @ X23 )
% 5.15/5.51 & ( R @ Y15 @ Y23 ) )
% 5.15/5.51 => ( R @ ( times_times_int @ X16 @ Y15 ) @ ( times_times_int @ X23 @ Y23 ) ) )
% 5.15/5.51 => ( ( finite_finite_int @ S3 )
% 5.15/5.51 => ( ! [X3: int] :
% 5.15/5.51 ( ( member_int @ X3 @ S3 )
% 5.15/5.51 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.15/5.51 => ( R @ ( groups1705073143266064639nt_int @ H2 @ S3 ) @ ( groups1705073143266064639nt_int @ G @ S3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod.related
% 5.15/5.51 thf(fact_9143_fact__eq__fact__times,axiom,
% 5.15/5.51 ! [N2: nat,M: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.51 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.15/5.51 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 5.15/5.51 @ ( groups708209901874060359at_nat
% 5.15/5.51 @ ^ [X2: nat] : X2
% 5.15/5.51 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % fact_eq_fact_times
% 5.15/5.51 thf(fact_9144_of__real__sqrt,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 5.15/5.51 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % of_real_sqrt
% 5.15/5.51 thf(fact_9145_fact__div__fact,axiom,
% 5.15/5.51 ! [N2: nat,M: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.51 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 5.15/5.51 = ( groups708209901874060359at_nat
% 5.15/5.51 @ ^ [X2: nat] : X2
% 5.15/5.51 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % fact_div_fact
% 5.15/5.51 thf(fact_9146_Arg__bounded,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.15/5.51 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.15/5.51
% 5.15/5.51 % Arg_bounded
% 5.15/5.51 thf(fact_9147_cis__minus__pi__half,axiom,
% 5.15/5.51 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.15/5.51 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.15/5.51
% 5.15/5.51 % cis_minus_pi_half
% 5.15/5.51 thf(fact_9148_norm__cis,axiom,
% 5.15/5.51 ! [A: real] :
% 5.15/5.51 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.15/5.51 = one_one_real ) ).
% 5.15/5.51
% 5.15/5.51 % norm_cis
% 5.15/5.51 thf(fact_9149_cis__pi__half,axiom,
% 5.15/5.51 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.51 = imaginary_unit ) ).
% 5.15/5.51
% 5.15/5.51 % cis_pi_half
% 5.15/5.51 thf(fact_9150_cis__2pi,axiom,
% 5.15/5.51 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.15/5.51 = one_one_complex ) ).
% 5.15/5.51
% 5.15/5.51 % cis_2pi
% 5.15/5.51 thf(fact_9151_cis__mult,axiom,
% 5.15/5.51 ! [A: real,B: real] :
% 5.15/5.51 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.15/5.51 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cis_mult
% 5.15/5.51 thf(fact_9152_cis__divide,axiom,
% 5.15/5.51 ! [A: real,B: real] :
% 5.15/5.51 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 5.15/5.51 = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cis_divide
% 5.15/5.51 thf(fact_9153_prod__int__eq,axiom,
% 5.15/5.51 ! [I: nat,J: nat] :
% 5.15/5.51 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.15/5.51 = ( groups1705073143266064639nt_int
% 5.15/5.51 @ ^ [X2: int] : X2
% 5.15/5.51 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_int_eq
% 5.15/5.51 thf(fact_9154_DeMoivre,axiom,
% 5.15/5.51 ! [A: real,N2: nat] :
% 5.15/5.51 ( ( power_power_complex @ ( cis @ A ) @ N2 )
% 5.15/5.51 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % DeMoivre
% 5.15/5.51 thf(fact_9155_prod__int__plus__eq,axiom,
% 5.15/5.51 ! [I: nat,J: nat] :
% 5.15/5.51 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.15/5.51 = ( groups1705073143266064639nt_int
% 5.15/5.51 @ ^ [X2: int] : X2
% 5.15/5.51 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_int_plus_eq
% 5.15/5.51 thf(fact_9156_cis__conv__exp,axiom,
% 5.15/5.51 ( cis
% 5.15/5.51 = ( ^ [B2: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cis_conv_exp
% 5.15/5.51 thf(fact_9157_bij__betw__roots__unity,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( bij_betw_nat_complex
% 5.15/5.51 @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.15/5.51 @ ( set_ord_lessThan_nat @ N2 )
% 5.15/5.51 @ ( collect_complex
% 5.15/5.51 @ ^ [Z3: complex] :
% 5.15/5.51 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.51 = one_one_complex ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bij_betw_roots_unity
% 5.15/5.51 thf(fact_9158_binomial__code,axiom,
% 5.15/5.51 ( binomial
% 5.15/5.51 = ( ^ [N3: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K2 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_code
% 5.15/5.51 thf(fact_9159_binomial__Suc__n,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( binomial @ ( suc @ N2 ) @ N2 )
% 5.15/5.51 = ( suc @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_Suc_n
% 5.15/5.51 thf(fact_9160_binomial__n__n,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( binomial @ N2 @ N2 )
% 5.15/5.51 = one_one_nat ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_n_n
% 5.15/5.51 thf(fact_9161_binomial__1,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 5.15/5.51 = N2 ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_1
% 5.15/5.51 thf(fact_9162_binomial__0__Suc,axiom,
% 5.15/5.51 ! [K: nat] :
% 5.15/5.51 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.15/5.51 = zero_zero_nat ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_0_Suc
% 5.15/5.51 thf(fact_9163_binomial__eq__0__iff,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( ( binomial @ N2 @ K )
% 5.15/5.51 = zero_zero_nat )
% 5.15/5.51 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_eq_0_iff
% 5.15/5.51 thf(fact_9164_binomial__Suc__Suc,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.15/5.51 = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_Suc_Suc
% 5.15/5.51 thf(fact_9165_binomial__n__0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( binomial @ N2 @ zero_zero_nat )
% 5.15/5.51 = one_one_nat ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_n_0
% 5.15/5.51 thf(fact_9166_zero__less__binomial__iff,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 5.15/5.51 = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % zero_less_binomial_iff
% 5.15/5.51 thf(fact_9167_choose__one,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( binomial @ N2 @ one_one_nat )
% 5.15/5.51 = N2 ) ).
% 5.15/5.51
% 5.15/5.51 % choose_one
% 5.15/5.51 thf(fact_9168_sum__choose__upper,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [K2: nat] : ( binomial @ K2 @ M )
% 5.15/5.51 @ ( set_ord_atMost_nat @ N2 ) )
% 5.15/5.51 = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sum_choose_upper
% 5.15/5.51 thf(fact_9169_sum__choose__lower,axiom,
% 5.15/5.51 ! [R2: nat,N2: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K2 ) @ K2 )
% 5.15/5.51 @ ( set_ord_atMost_nat @ N2 ) )
% 5.15/5.51 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % sum_choose_lower
% 5.15/5.51 thf(fact_9170_choose__rising__sum_I2_J,axiom,
% 5.15/5.51 ! [N2: nat,M: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.15/5.51 @ ( set_ord_atMost_nat @ M ) )
% 5.15/5.51 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_rising_sum(2)
% 5.15/5.51 thf(fact_9171_choose__rising__sum_I1_J,axiom,
% 5.15/5.51 ! [N2: nat,M: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.15/5.51 @ ( set_ord_atMost_nat @ M ) )
% 5.15/5.51 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_rising_sum(1)
% 5.15/5.51 thf(fact_9172_binomial__eq__0,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( ord_less_nat @ N2 @ K )
% 5.15/5.51 => ( ( binomial @ N2 @ K )
% 5.15/5.51 = zero_zero_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_eq_0
% 5.15/5.51 thf(fact_9173_Suc__times__binomial,axiom,
% 5.15/5.51 ! [K: nat,N2: nat] :
% 5.15/5.51 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) )
% 5.15/5.51 = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_times_binomial
% 5.15/5.51 thf(fact_9174_Suc__times__binomial__eq,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) )
% 5.15/5.51 = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_times_binomial_eq
% 5.15/5.51 thf(fact_9175_binomial__symmetric,axiom,
% 5.15/5.51 ! [K: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.51 => ( ( binomial @ N2 @ K )
% 5.15/5.51 = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_symmetric
% 5.15/5.51 thf(fact_9176_choose__mult__lemma,axiom,
% 5.15/5.51 ! [M: nat,R2: nat,K: nat] :
% 5.15/5.51 ( ( 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 ) )
% 5.15/5.51 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_mult_lemma
% 5.15/5.51 thf(fact_9177_binomial__le__pow,axiom,
% 5.15/5.51 ! [R2: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ R2 @ N2 )
% 5.15/5.51 => ( ord_less_eq_nat @ ( binomial @ N2 @ R2 ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_le_pow
% 5.15/5.51 thf(fact_9178_lessThan__Suc__atMost,axiom,
% 5.15/5.51 ! [K: nat] :
% 5.15/5.51 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.15/5.51 = ( set_ord_atMost_nat @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % lessThan_Suc_atMost
% 5.15/5.51 thf(fact_9179_sum__choose__diagonal,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.51 => ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ M ) )
% 5.15/5.51 = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sum_choose_diagonal
% 5.15/5.51 thf(fact_9180_vandermonde,axiom,
% 5.15/5.51 ! [M: nat,N2: nat,R2: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K2 ) ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ R2 ) )
% 5.15/5.51 = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % vandermonde
% 5.15/5.51 thf(fact_9181_atMost__Suc,axiom,
% 5.15/5.51 ! [K: nat] :
% 5.15/5.51 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.15/5.51 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atMost_Suc
% 5.15/5.51 thf(fact_9182_choose__row__sum,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.15/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_row_sum
% 5.15/5.51 thf(fact_9183_binomial,axiom,
% 5.15/5.51 ! [A: nat,B: nat,N2: nat] :
% 5.15/5.51 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.15/5.51 = ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K2 ) ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial
% 5.15/5.51 thf(fact_9184_zero__less__binomial,axiom,
% 5.15/5.51 ! [K: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.51 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % zero_less_binomial
% 5.15/5.51 thf(fact_9185_Suc__times__binomial__add,axiom,
% 5.15/5.51 ! [A: nat,B: nat] :
% 5.15/5.51 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.15/5.51 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_times_binomial_add
% 5.15/5.51 thf(fact_9186_binomial__Suc__Suc__eq__times,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.15/5.51 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) @ ( suc @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_Suc_Suc_eq_times
% 5.15/5.51 thf(fact_9187_choose__mult,axiom,
% 5.15/5.51 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ K @ M )
% 5.15/5.51 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.51 => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 5.15/5.51 = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_mult
% 5.15/5.51 thf(fact_9188_binomial__absorb__comp,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 5.15/5.51 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_absorb_comp
% 5.15/5.51 thf(fact_9189_choose__square__sum,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N2 @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ N2 ) )
% 5.15/5.51 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_square_sum
% 5.15/5.51 thf(fact_9190_atMost__nat__numeral,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.15/5.51 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atMost_nat_numeral
% 5.15/5.51 thf(fact_9191_binomial__absorption,axiom,
% 5.15/5.51 ! [K: nat,N2: nat] :
% 5.15/5.51 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 5.15/5.51 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_absorption
% 5.15/5.51 thf(fact_9192_binomial__r__part__sum,axiom,
% 5.15/5.51 ! [M: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.15/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_r_part_sum
% 5.15/5.51 thf(fact_9193_choose__linear__sum,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N2 @ I3 ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ N2 ) )
% 5.15/5.51 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_linear_sum
% 5.15/5.51 thf(fact_9194_binomial__fact__lemma,axiom,
% 5.15/5.51 ! [K: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.51 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 5.15/5.51 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_fact_lemma
% 5.15/5.51 thf(fact_9195_binomial__mono,axiom,
% 5.15/5.51 ! [K: nat,K6: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ K @ K6 )
% 5.15/5.51 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.15/5.51 => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_mono
% 5.15/5.51 thf(fact_9196_binomial__maximum_H,axiom,
% 5.15/5.51 ! [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 ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_maximum'
% 5.15/5.51 thf(fact_9197_binomial__maximum,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_maximum
% 5.15/5.51 thf(fact_9198_binomial__antimono,axiom,
% 5.15/5.51 ! [K: nat,K6: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ K @ K6 )
% 5.15/5.51 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.15/5.51 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.15/5.51 => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_antimono
% 5.15/5.51 thf(fact_9199_binomial__le__pow2,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_le_pow2
% 5.15/5.51 thf(fact_9200_choose__reduce__nat,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.51 => ( ( binomial @ N2 @ K )
% 5.15/5.51 = ( 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 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_reduce_nat
% 5.15/5.51 thf(fact_9201_times__binomial__minus1__eq,axiom,
% 5.15/5.51 ! [K: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.15/5.51 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 5.15/5.51 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % times_binomial_minus1_eq
% 5.15/5.51 thf(fact_9202_binomial__altdef__nat,axiom,
% 5.15/5.51 ! [K: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ K @ N2 )
% 5.15/5.51 => ( ( binomial @ N2 @ K )
% 5.15/5.51 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_altdef_nat
% 5.15/5.51 thf(fact_9203_atLeast1__atMost__eq__remove0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.51 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeast1_atMost_eq_remove0
% 5.15/5.51 thf(fact_9204_binomial__less__binomial__Suc,axiom,
% 5.15/5.51 ! [K: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.51 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_less_binomial_Suc
% 5.15/5.51 thf(fact_9205_binomial__strict__mono,axiom,
% 5.15/5.51 ! [K: nat,K6: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ K @ K6 )
% 5.15/5.51 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.15/5.51 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_strict_mono
% 5.15/5.51 thf(fact_9206_binomial__strict__antimono,axiom,
% 5.15/5.51 ! [K: nat,K6: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ K @ K6 )
% 5.15/5.51 => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.15/5.51 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.15/5.51 => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_strict_antimono
% 5.15/5.51 thf(fact_9207_central__binomial__odd,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.51 => ( ( binomial @ N2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.51 = ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % central_binomial_odd
% 5.15/5.51 thf(fact_9208_binomial__addition__formula,axiom,
% 5.15/5.51 ! [N2: nat,K: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( binomial @ N2 @ ( suc @ K ) )
% 5.15/5.51 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_addition_formula
% 5.15/5.51 thf(fact_9209_choose__two,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.51 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % choose_two
% 5.15/5.51 thf(fact_9210_polynomial__product__nat,axiom,
% 5.15/5.51 ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X: nat] :
% 5.15/5.51 ( ! [I2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ M @ I2 )
% 5.15/5.51 => ( ( A @ I2 )
% 5.15/5.51 = zero_zero_nat ) )
% 5.15/5.51 => ( ! [J2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ N2 @ J2 )
% 5.15/5.51 => ( ( B @ J2 )
% 5.15/5.51 = zero_zero_nat ) )
% 5.15/5.51 => ( ( times_times_nat
% 5.15/5.51 @ ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X @ I3 ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ M ) )
% 5.15/5.51 @ ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.15/5.51 = ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [R5: nat] :
% 5.15/5.51 ( times_times_nat
% 5.15/5.51 @ ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ R5 ) )
% 5.15/5.51 @ ( power_power_nat @ X @ R5 ) )
% 5.15/5.51 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % polynomial_product_nat
% 5.15/5.51 thf(fact_9211_central__binomial__lower__bound,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( 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 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % central_binomial_lower_bound
% 5.15/5.51 thf(fact_9212_Maclaurin__sin__bound,axiom,
% 5.15/5.51 ! [X: real,N2: nat] :
% 5.15/5.51 ( ord_less_eq_real
% 5.15/5.51 @ ( abs_abs_real
% 5.15/5.51 @ ( minus_minus_real @ ( sin_real @ X )
% 5.15/5.51 @ ( groups6591440286371151544t_real
% 5.15/5.51 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.51 @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.15/5.51 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Maclaurin_sin_bound
% 5.15/5.51 thf(fact_9213_of__nat__id,axiom,
% 5.15/5.51 ( semiri1316708129612266289at_nat
% 5.15/5.51 = ( ^ [N3: nat] : N3 ) ) ).
% 5.15/5.51
% 5.15/5.51 % of_nat_id
% 5.15/5.51 thf(fact_9214_real__scaleR__def,axiom,
% 5.15/5.51 real_V1485227260804924795R_real = times_times_real ).
% 5.15/5.51
% 5.15/5.51 % real_scaleR_def
% 5.15/5.51 thf(fact_9215_real__sqrt__inverse,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 5.15/5.51 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_sqrt_inverse
% 5.15/5.51 thf(fact_9216_divide__real__def,axiom,
% 5.15/5.51 ( divide_divide_real
% 5.15/5.51 = ( ^ [X2: real,Y2: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divide_real_def
% 5.15/5.51 thf(fact_9217_complex__scaleR,axiom,
% 5.15/5.51 ! [R2: real,A: real,B: real] :
% 5.15/5.51 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 5.15/5.51 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_scaleR
% 5.15/5.51 thf(fact_9218_inverse__powr,axiom,
% 5.15/5.51 ! [Y: real,A: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.51 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 5.15/5.51 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % inverse_powr
% 5.15/5.51 thf(fact_9219_forall__pos__mono__1,axiom,
% 5.15/5.51 ! [P: real > $o,E: real] :
% 5.15/5.51 ( ! [D3: real,E2: real] :
% 5.15/5.51 ( ( ord_less_real @ D3 @ E2 )
% 5.15/5.51 => ( ( P @ D3 )
% 5.15/5.51 => ( P @ E2 ) ) )
% 5.15/5.51 => ( ! [N: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.15/5.51 => ( P @ E ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % forall_pos_mono_1
% 5.15/5.51 thf(fact_9220_forall__pos__mono,axiom,
% 5.15/5.51 ! [P: real > $o,E: real] :
% 5.15/5.51 ( ! [D3: real,E2: real] :
% 5.15/5.51 ( ( ord_less_real @ D3 @ E2 )
% 5.15/5.51 => ( ( P @ D3 )
% 5.15/5.51 => ( P @ E2 ) ) )
% 5.15/5.51 => ( ! [N: nat] :
% 5.15/5.51 ( ( N != zero_zero_nat )
% 5.15/5.51 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) ) )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.15/5.51 => ( P @ E ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % forall_pos_mono
% 5.15/5.51 thf(fact_9221_real__arch__inverse,axiom,
% 5.15/5.51 ! [E: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ E )
% 5.15/5.51 = ( ? [N3: nat] :
% 5.15/5.51 ( ( N3 != zero_zero_nat )
% 5.15/5.51 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.15/5.51 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ E ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_arch_inverse
% 5.15/5.51 thf(fact_9222_sqrt__divide__self__eq,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 5.15/5.51 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sqrt_divide_self_eq
% 5.15/5.51 thf(fact_9223_ln__inverse,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 5.15/5.51 = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % ln_inverse
% 5.15/5.51 thf(fact_9224_log__inverse,axiom,
% 5.15/5.51 ! [A: real,X: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.51 => ( ( A != one_one_real )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 5.15/5.51 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % log_inverse
% 5.15/5.51 thf(fact_9225_exp__plus__inverse__exp,axiom,
% 5.15/5.51 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % exp_plus_inverse_exp
% 5.15/5.51 thf(fact_9226_plus__inverse__ge__2,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % plus_inverse_ge_2
% 5.15/5.51 thf(fact_9227_real__inv__sqrt__pow2,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.51 = ( inverse_inverse_real @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_inv_sqrt_pow2
% 5.15/5.51 thf(fact_9228_tan__cot,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.15/5.51 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % tan_cot
% 5.15/5.51 thf(fact_9229_real__le__x__sinh,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_le_x_sinh
% 5.15/5.51 thf(fact_9230_real__le__abs__sinh,axiom,
% 5.15/5.51 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_le_abs_sinh
% 5.15/5.51 thf(fact_9231_bij__betw__nth__root__unity,axiom,
% 5.15/5.51 ! [C: complex,N2: nat] :
% 5.15/5.51 ( ( C != zero_zero_complex )
% 5.15/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 5.15/5.51 @ ( collect_complex
% 5.15/5.51 @ ^ [Z3: complex] :
% 5.15/5.51 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.51 = one_one_complex ) )
% 5.15/5.51 @ ( collect_complex
% 5.15/5.51 @ ^ [Z3: complex] :
% 5.15/5.51 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.51 = C ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bij_betw_nth_root_unity
% 5.15/5.51 thf(fact_9232_cot__less__zero,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.15/5.51 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.51 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cot_less_zero
% 5.15/5.51 thf(fact_9233_sinh__real__less__iff,axiom,
% 5.15/5.51 ! [X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 5.15/5.51 = ( ord_less_real @ X @ Y ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_real_less_iff
% 5.15/5.51 thf(fact_9234_sinh__real__le__iff,axiom,
% 5.15/5.51 ! [X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 5.15/5.51 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_real_le_iff
% 5.15/5.51 thf(fact_9235_sinh__real__pos__iff,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.15/5.51 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_real_pos_iff
% 5.15/5.51 thf(fact_9236_sinh__real__neg__iff,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_real_neg_iff
% 5.15/5.51 thf(fact_9237_sinh__real__nonpos__iff,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_real_nonpos_iff
% 5.15/5.51 thf(fact_9238_sinh__real__nonneg__iff,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.15/5.51 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_real_nonneg_iff
% 5.15/5.51 thf(fact_9239_real__root__zero,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( root @ N2 @ zero_zero_real )
% 5.15/5.51 = zero_zero_real ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_zero
% 5.15/5.51 thf(fact_9240_real__root__Suc__0,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.15/5.51 = X ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_Suc_0
% 5.15/5.51 thf(fact_9241_real__root__eq__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ( root @ N2 @ X )
% 5.15/5.51 = ( root @ N2 @ Y ) )
% 5.15/5.51 = ( X = Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_eq_iff
% 5.15/5.51 thf(fact_9242_root__0,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( root @ zero_zero_nat @ X )
% 5.15/5.51 = zero_zero_real ) ).
% 5.15/5.51
% 5.15/5.51 % root_0
% 5.15/5.51 thf(fact_9243_real__root__eq__0__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ( root @ N2 @ X )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 = ( X = zero_zero_real ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_eq_0_iff
% 5.15/5.51 thf(fact_9244_real__root__less__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) )
% 5.15/5.51 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_less_iff
% 5.15/5.51 thf(fact_9245_real__root__le__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) )
% 5.15/5.51 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_le_iff
% 5.15/5.51 thf(fact_9246_real__root__one,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( root @ N2 @ one_one_real )
% 5.15/5.51 = one_one_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_one
% 5.15/5.51 thf(fact_9247_real__root__eq__1__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ( root @ N2 @ X )
% 5.15/5.51 = one_one_real )
% 5.15/5.51 = ( X = one_one_real ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_eq_1_iff
% 5.15/5.51 thf(fact_9248_real__root__gt__0__iff,axiom,
% 5.15/5.51 ! [N2: nat,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.15/5.51 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_gt_0_iff
% 5.15/5.51 thf(fact_9249_real__root__lt__0__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ ( root @ N2 @ X ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_lt_0_iff
% 5.15/5.51 thf(fact_9250_real__root__le__0__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_le_0_iff
% 5.15/5.51 thf(fact_9251_real__root__ge__0__iff,axiom,
% 5.15/5.51 ! [N2: nat,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.15/5.51 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_ge_0_iff
% 5.15/5.51 thf(fact_9252_real__root__gt__1__iff,axiom,
% 5.15/5.51 ! [N2: nat,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.15/5.51 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_gt_1_iff
% 5.15/5.51 thf(fact_9253_real__root__lt__1__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ ( root @ N2 @ X ) @ one_one_real )
% 5.15/5.51 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_lt_1_iff
% 5.15/5.51 thf(fact_9254_real__root__le__1__iff,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ one_one_real )
% 5.15/5.51 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_le_1_iff
% 5.15/5.51 thf(fact_9255_real__root__ge__1__iff,axiom,
% 5.15/5.51 ! [N2: nat,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.15/5.51 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_ge_1_iff
% 5.15/5.51 thf(fact_9256_cot__npi,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.15/5.51 = zero_zero_real ) ).
% 5.15/5.51
% 5.15/5.51 % cot_npi
% 5.15/5.51 thf(fact_9257_real__root__pow__pos2,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.15/5.51 = X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_pow_pos2
% 5.15/5.51 thf(fact_9258_cot__periodic,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.15/5.51 = ( cot_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % cot_periodic
% 5.15/5.51 thf(fact_9259_real__root__inverse,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( root @ N2 @ ( inverse_inverse_real @ X ) )
% 5.15/5.51 = ( inverse_inverse_real @ ( root @ N2 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_inverse
% 5.15/5.51 thf(fact_9260_real__root__commute,axiom,
% 5.15/5.51 ! [M: nat,N2: nat,X: real] :
% 5.15/5.51 ( ( root @ M @ ( root @ N2 @ X ) )
% 5.15/5.51 = ( root @ N2 @ ( root @ M @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_commute
% 5.15/5.51 thf(fact_9261_sinh__le__cosh__real,axiom,
% 5.15/5.51 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_le_cosh_real
% 5.15/5.51 thf(fact_9262_sinh__less__cosh__real,axiom,
% 5.15/5.51 ! [X: real] : ( ord_less_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_less_cosh_real
% 5.15/5.51 thf(fact_9263_real__root__mult,axiom,
% 5.15/5.51 ! [N2: nat,X: real,Y: real] :
% 5.15/5.51 ( ( root @ N2 @ ( times_times_real @ X @ Y ) )
% 5.15/5.51 = ( times_times_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_mult
% 5.15/5.51 thf(fact_9264_real__root__mult__exp,axiom,
% 5.15/5.51 ! [M: nat,N2: nat,X: real] :
% 5.15/5.51 ( ( root @ ( times_times_nat @ M @ N2 ) @ X )
% 5.15/5.51 = ( root @ M @ ( root @ N2 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_mult_exp
% 5.15/5.51 thf(fact_9265_real__root__minus,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( root @ N2 @ ( uminus_uminus_real @ X ) )
% 5.15/5.51 = ( uminus_uminus_real @ ( root @ N2 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_minus
% 5.15/5.51 thf(fact_9266_real__root__divide,axiom,
% 5.15/5.51 ! [N2: nat,X: real,Y: real] :
% 5.15/5.51 ( ( root @ N2 @ ( divide_divide_real @ X @ Y ) )
% 5.15/5.51 = ( divide_divide_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_divide
% 5.15/5.51 thf(fact_9267_real__root__pos__pos__le,axiom,
% 5.15/5.51 ! [X: real,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_pos_pos_le
% 5.15/5.51 thf(fact_9268_cosh__real__pos,axiom,
% 5.15/5.51 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_real_pos
% 5.15/5.51 thf(fact_9269_cosh__real__nonpos__le__iff,axiom,
% 5.15/5.51 ! [X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.51 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.15/5.51 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.15/5.51 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_real_nonpos_le_iff
% 5.15/5.51 thf(fact_9270_cosh__real__nonneg__le__iff,axiom,
% 5.15/5.51 ! [X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.51 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.15/5.51 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_real_nonneg_le_iff
% 5.15/5.51 thf(fact_9271_cosh__real__nonneg,axiom,
% 5.15/5.51 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_real_nonneg
% 5.15/5.51 thf(fact_9272_cosh__real__ge__1,axiom,
% 5.15/5.51 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_real_ge_1
% 5.15/5.51 thf(fact_9273_divide__complex__def,axiom,
% 5.15/5.51 ( divide1717551699836669952omplex
% 5.15/5.51 = ( ^ [X2: complex,Y2: complex] : ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ Y2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divide_complex_def
% 5.15/5.51 thf(fact_9274_real__root__less__mono,axiom,
% 5.15/5.51 ! [N2: nat,X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ X @ Y )
% 5.15/5.51 => ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_less_mono
% 5.15/5.51 thf(fact_9275_real__root__le__mono,axiom,
% 5.15/5.51 ! [N2: nat,X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ X @ Y )
% 5.15/5.51 => ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_le_mono
% 5.15/5.51 thf(fact_9276_real__root__power,axiom,
% 5.15/5.51 ! [N2: nat,X: real,K: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( root @ N2 @ ( power_power_real @ X @ K ) )
% 5.15/5.51 = ( power_power_real @ ( root @ N2 @ X ) @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_power
% 5.15/5.51 thf(fact_9277_real__root__abs,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( root @ N2 @ ( abs_abs_real @ X ) )
% 5.15/5.51 = ( abs_abs_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_abs
% 5.15/5.51 thf(fact_9278_cosh__real__strict__mono,axiom,
% 5.15/5.51 ! [X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ord_less_real @ X @ Y )
% 5.15/5.51 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_real_strict_mono
% 5.15/5.51 thf(fact_9279_cosh__real__nonneg__less__iff,axiom,
% 5.15/5.51 ! [X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.51 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.15/5.51 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_real_nonneg_less_iff
% 5.15/5.51 thf(fact_9280_cosh__real__nonpos__less__iff,axiom,
% 5.15/5.51 ! [X: real,Y: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.51 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.15/5.51 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.15/5.51 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_real_nonpos_less_iff
% 5.15/5.51 thf(fact_9281_arcosh__cosh__real,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 5.15/5.51 = X ) ) ).
% 5.15/5.51
% 5.15/5.51 % arcosh_cosh_real
% 5.15/5.51 thf(fact_9282_real__root__gt__zero,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_gt_zero
% 5.15/5.51 thf(fact_9283_real__root__strict__decreasing,axiom,
% 5.15/5.51 ! [N2: nat,N5: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.51 => ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.51 => ( ord_less_real @ ( root @ N5 @ X ) @ ( root @ N2 @ X ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_strict_decreasing
% 5.15/5.51 thf(fact_9284_sqrt__def,axiom,
% 5.15/5.51 ( sqrt
% 5.15/5.51 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sqrt_def
% 5.15/5.51 thf(fact_9285_root__abs__power,axiom,
% 5.15/5.51 ! [N2: nat,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 5.15/5.51 = ( abs_abs_real @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % root_abs_power
% 5.15/5.51 thf(fact_9286_real__root__pos__pos,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_pos_pos
% 5.15/5.51 thf(fact_9287_real__root__strict__increasing,axiom,
% 5.15/5.51 ! [N2: nat,N5: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_nat @ N2 @ N5 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.51 => ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_strict_increasing
% 5.15/5.51 thf(fact_9288_real__root__decreasing,axiom,
% 5.15/5.51 ! [N2: nat,N5: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.51 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.15/5.51 => ( ord_less_eq_real @ ( root @ N5 @ X ) @ ( root @ N2 @ X ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_decreasing
% 5.15/5.51 thf(fact_9289_real__root__pow__pos,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.15/5.51 = X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_pow_pos
% 5.15/5.51 thf(fact_9290_real__root__power__cancel,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( root @ N2 @ ( power_power_real @ X @ N2 ) )
% 5.15/5.51 = X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_power_cancel
% 5.15/5.51 thf(fact_9291_real__root__pos__unique,axiom,
% 5.15/5.51 ! [N2: nat,Y: real,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.15/5.51 => ( ( ( power_power_real @ Y @ N2 )
% 5.15/5.51 = X )
% 5.15/5.51 => ( ( root @ N2 @ X )
% 5.15/5.51 = Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_pos_unique
% 5.15/5.51 thf(fact_9292_odd__real__root__pow,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.51 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.15/5.51 = X ) ) ).
% 5.15/5.51
% 5.15/5.51 % odd_real_root_pow
% 5.15/5.51 thf(fact_9293_odd__real__root__unique,axiom,
% 5.15/5.51 ! [N2: nat,Y: real,X: real] :
% 5.15/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.51 => ( ( ( power_power_real @ Y @ N2 )
% 5.15/5.51 = X )
% 5.15/5.51 => ( ( root @ N2 @ X )
% 5.15/5.51 = Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % odd_real_root_unique
% 5.15/5.51 thf(fact_9294_odd__real__root__power__cancel,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.51 => ( ( root @ N2 @ ( power_power_real @ X @ N2 ) )
% 5.15/5.51 = X ) ) ).
% 5.15/5.51
% 5.15/5.51 % odd_real_root_power_cancel
% 5.15/5.51 thf(fact_9295_real__root__increasing,axiom,
% 5.15/5.51 ! [N2: nat,N5: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.51 => ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_root_increasing
% 5.15/5.51 thf(fact_9296_log__root,axiom,
% 5.15/5.51 ! [N2: nat,A: real,B: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.15/5.51 => ( ( log @ B @ ( root @ N2 @ A ) )
% 5.15/5.51 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % log_root
% 5.15/5.51 thf(fact_9297_log__base__root,axiom,
% 5.15/5.51 ! [N2: nat,B: real,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.51 => ( ( log @ ( root @ N2 @ B ) @ X )
% 5.15/5.51 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % log_base_root
% 5.15/5.51 thf(fact_9298_ln__root,axiom,
% 5.15/5.51 ! [N2: nat,B: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.15/5.51 => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 5.15/5.51 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % ln_root
% 5.15/5.51 thf(fact_9299_root__powr__inverse,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( root @ N2 @ X )
% 5.15/5.51 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % root_powr_inverse
% 5.15/5.51 thf(fact_9300_complex__inverse,axiom,
% 5.15/5.51 ! [A: real,B: real] :
% 5.15/5.51 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.15/5.51 = ( 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 ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_inverse
% 5.15/5.51 thf(fact_9301_cosh__ln__real,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 5.15/5.51 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cosh_ln_real
% 5.15/5.51 thf(fact_9302_cot__gt__zero,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.51 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cot_gt_zero
% 5.15/5.51 thf(fact_9303_sinh__ln__real,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 5.15/5.51 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sinh_ln_real
% 5.15/5.51 thf(fact_9304_tan__cot_H,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.15/5.51 = ( cot_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % tan_cot'
% 5.15/5.51 thf(fact_9305_arctan__def,axiom,
% 5.15/5.51 ( arctan
% 5.15/5.51 = ( ^ [Y2: real] :
% 5.15/5.51 ( the_real
% 5.15/5.51 @ ^ [X2: real] :
% 5.15/5.51 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.15/5.51 & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.51 & ( ( tan_real @ X2 )
% 5.15/5.51 = Y2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % arctan_def
% 5.15/5.51 thf(fact_9306_arcsin__def,axiom,
% 5.15/5.51 ( arcsin
% 5.15/5.51 = ( ^ [Y2: real] :
% 5.15/5.51 ( the_real
% 5.15/5.51 @ ^ [X2: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.15/5.51 & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.51 & ( ( sin_real @ X2 )
% 5.15/5.51 = Y2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % arcsin_def
% 5.15/5.51 thf(fact_9307_signed__take__bit__eq__take__bit__minus,axiom,
% 5.15/5.51 ( bit_ri631733984087533419it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % signed_take_bit_eq_take_bit_minus
% 5.15/5.51 thf(fact_9308_modulo__int__unfold,axiom,
% 5.15/5.51 ! [L: int,K: int,N2: nat,M: nat] :
% 5.15/5.51 ( ( ( ( ( sgn_sgn_int @ L )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 | ( ( sgn_sgn_int @ K )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 | ( N2 = zero_zero_nat ) )
% 5.15/5.51 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.15/5.51 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.15/5.51 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 | ( ( sgn_sgn_int @ K )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 | ( N2 = zero_zero_nat ) )
% 5.15/5.51 => ( ( ( ( sgn_sgn_int @ K )
% 5.15/5.51 = ( sgn_sgn_int @ L ) )
% 5.15/5.51 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.15/5.51 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 5.15/5.51 & ( ( ( sgn_sgn_int @ K )
% 5.15/5.51 != ( sgn_sgn_int @ L ) )
% 5.15/5.51 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.15/5.51 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.15/5.51 @ ( minus_minus_int
% 5.15/5.51 @ ( semiri1314217659103216013at_int
% 5.15/5.51 @ ( times_times_nat @ N2
% 5.15/5.51 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.51 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 5.15/5.51 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % modulo_int_unfold
% 5.15/5.51 thf(fact_9309_dvd__mult__sgn__iff,axiom,
% 5.15/5.51 ! [L: int,K: int,R2: int] :
% 5.15/5.51 ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.15/5.51 = ( ( dvd_dvd_int @ L @ K )
% 5.15/5.51 | ( R2 = zero_zero_int ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % dvd_mult_sgn_iff
% 5.15/5.51 thf(fact_9310_dvd__sgn__mult__iff,axiom,
% 5.15/5.51 ! [L: int,R2: int,K: int] :
% 5.15/5.51 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.15/5.51 = ( ( dvd_dvd_int @ L @ K )
% 5.15/5.51 | ( R2 = zero_zero_int ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % dvd_sgn_mult_iff
% 5.15/5.51 thf(fact_9311_mult__sgn__dvd__iff,axiom,
% 5.15/5.51 ! [L: int,R2: int,K: int] :
% 5.15/5.51 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.15/5.51 = ( ( dvd_dvd_int @ L @ K )
% 5.15/5.51 & ( ( R2 = zero_zero_int )
% 5.15/5.51 => ( K = zero_zero_int ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % mult_sgn_dvd_iff
% 5.15/5.51 thf(fact_9312_sgn__mult__dvd__iff,axiom,
% 5.15/5.51 ! [R2: int,L: int,K: int] :
% 5.15/5.51 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 5.15/5.51 = ( ( dvd_dvd_int @ L @ K )
% 5.15/5.51 & ( ( R2 = zero_zero_int )
% 5.15/5.51 => ( K = zero_zero_int ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sgn_mult_dvd_iff
% 5.15/5.51 thf(fact_9313_signed__take__bit__nonnegative__iff,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.15/5.51 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % signed_take_bit_nonnegative_iff
% 5.15/5.51 thf(fact_9314_signed__take__bit__negative__iff,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 5.15/5.51 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % signed_take_bit_negative_iff
% 5.15/5.51 thf(fact_9315_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.15/5.51 ! [W: num,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N2 ) )
% 5.15/5.51 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_minus_numeral_Bit0_Suc_iff
% 5.15/5.51 thf(fact_9316_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.15/5.51 ! [W: num,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N2 ) )
% 5.15/5.51 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_minus_numeral_Bit1_Suc_iff
% 5.15/5.51 thf(fact_9317_bit__minus__numeral__int_I1_J,axiom,
% 5.15/5.51 ! [W: num,N2: num] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.51 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_minus_numeral_int(1)
% 5.15/5.51 thf(fact_9318_bit__minus__numeral__int_I2_J,axiom,
% 5.15/5.51 ! [W: num,N2: num] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.15/5.51 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_minus_numeral_int(2)
% 5.15/5.51 thf(fact_9319_bit__and__int__iff,axiom,
% 5.15/5.51 ! [K: int,L: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N2 )
% 5.15/5.51 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.15/5.51 & ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_and_int_iff
% 5.15/5.51 thf(fact_9320_bit__or__int__iff,axiom,
% 5.15/5.51 ! [K: int,L: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N2 )
% 5.15/5.51 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.15/5.51 | ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_or_int_iff
% 5.15/5.51 thf(fact_9321_int__sgnE,axiom,
% 5.15/5.51 ! [K: int] :
% 5.15/5.51 ~ ! [N: nat,L4: int] :
% 5.15/5.51 ( K
% 5.15/5.51 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % int_sgnE
% 5.15/5.51 thf(fact_9322_div__eq__sgn__abs,axiom,
% 5.15/5.51 ! [K: int,L: int] :
% 5.15/5.51 ( ( ( sgn_sgn_int @ K )
% 5.15/5.51 = ( sgn_sgn_int @ L ) )
% 5.15/5.51 => ( ( divide_divide_int @ K @ L )
% 5.15/5.51 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % div_eq_sgn_abs
% 5.15/5.51 thf(fact_9323_ln__real__def,axiom,
% 5.15/5.51 ( ln_ln_real
% 5.15/5.51 = ( ^ [X2: real] :
% 5.15/5.51 ( the_real
% 5.15/5.51 @ ^ [U2: real] :
% 5.15/5.51 ( ( exp_real @ U2 )
% 5.15/5.51 = X2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % ln_real_def
% 5.15/5.51 thf(fact_9324_bit__not__int__iff_H,axiom,
% 5.15/5.51 ! [K: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N2 )
% 5.15/5.51 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_not_int_iff'
% 5.15/5.51 thf(fact_9325_sgn__mod,axiom,
% 5.15/5.51 ! [L: int,K: int] :
% 5.15/5.51 ( ( L != zero_zero_int )
% 5.15/5.51 => ( ~ ( dvd_dvd_int @ L @ K )
% 5.15/5.51 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 5.15/5.51 = ( sgn_sgn_int @ L ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sgn_mod
% 5.15/5.51 thf(fact_9326_ln__neg__is__const,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.51 => ( ( ln_ln_real @ X )
% 5.15/5.51 = ( the_real
% 5.15/5.51 @ ^ [X2: real] : $false ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % ln_neg_is_const
% 5.15/5.51 thf(fact_9327_div__sgn__abs__cancel,axiom,
% 5.15/5.51 ! [V: int,K: int,L: int] :
% 5.15/5.51 ( ( V != zero_zero_int )
% 5.15/5.51 => ( ( 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 ) ) )
% 5.15/5.51 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % div_sgn_abs_cancel
% 5.15/5.51 thf(fact_9328_bit__imp__take__bit__positive,axiom,
% 5.15/5.51 ! [N2: nat,M: nat,K: int] :
% 5.15/5.51 ( ( ord_less_nat @ N2 @ M )
% 5.15/5.51 => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.15/5.51 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_imp_take_bit_positive
% 5.15/5.51 thf(fact_9329_div__dvd__sgn__abs,axiom,
% 5.15/5.51 ! [L: int,K: int] :
% 5.15/5.51 ( ( dvd_dvd_int @ L @ K )
% 5.15/5.51 => ( ( divide_divide_int @ K @ L )
% 5.15/5.51 = ( 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 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % div_dvd_sgn_abs
% 5.15/5.51 thf(fact_9330_bit__concat__bit__iff,axiom,
% 5.15/5.51 ! [M: nat,K: int,L: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N2 )
% 5.15/5.51 = ( ( ( ord_less_nat @ N2 @ M )
% 5.15/5.51 & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 5.15/5.51 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.51 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_concat_bit_iff
% 5.15/5.51 thf(fact_9331_signed__take__bit__eq__concat__bit,axiom,
% 5.15/5.51 ( bit_ri631733984087533419it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] : ( bit_concat_bit @ N3 @ K2 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % signed_take_bit_eq_concat_bit
% 5.15/5.51 thf(fact_9332_int__bit__bound,axiom,
% 5.15/5.51 ! [K: int] :
% 5.15/5.51 ~ ! [N: nat] :
% 5.15/5.51 ( ! [M4: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ N @ M4 )
% 5.15/5.51 => ( ( bit_se1146084159140164899it_int @ K @ M4 )
% 5.15/5.51 = ( bit_se1146084159140164899it_int @ K @ N ) ) )
% 5.15/5.51 => ~ ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.15/5.51 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.15/5.51 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % int_bit_bound
% 5.15/5.51 thf(fact_9333_bit__int__def,axiom,
% 5.15/5.51 ( bit_se1146084159140164899it_int
% 5.15/5.51 = ( ^ [K2: int,N3: nat] :
% 5.15/5.51 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_int_def
% 5.15/5.51 thf(fact_9334_arccos__def,axiom,
% 5.15/5.51 ( arccos
% 5.15/5.51 = ( ^ [Y2: real] :
% 5.15/5.51 ( the_real
% 5.15/5.51 @ ^ [X2: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.15/5.51 & ( ord_less_eq_real @ X2 @ pi )
% 5.15/5.51 & ( ( cos_real @ X2 )
% 5.15/5.51 = Y2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % arccos_def
% 5.15/5.51 thf(fact_9335_eucl__rel__int__remainderI,axiom,
% 5.15/5.51 ! [R2: int,L: int,K: int,Q3: int] :
% 5.15/5.51 ( ( ( sgn_sgn_int @ R2 )
% 5.15/5.51 = ( sgn_sgn_int @ L ) )
% 5.15/5.51 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 5.15/5.51 => ( ( K
% 5.15/5.51 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 5.15/5.51 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % eucl_rel_int_remainderI
% 5.15/5.51 thf(fact_9336_eucl__rel__int_Osimps,axiom,
% 5.15/5.51 ( eucl_rel_int
% 5.15/5.51 = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 5.15/5.51 ( ? [K2: int] :
% 5.15/5.51 ( ( A12 = K2 )
% 5.15/5.51 & ( A23 = zero_zero_int )
% 5.15/5.51 & ( A32
% 5.15/5.51 = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 5.15/5.51 | ? [L2: int,K2: int,Q4: int] :
% 5.15/5.51 ( ( A12 = K2 )
% 5.15/5.51 & ( A23 = L2 )
% 5.15/5.51 & ( A32
% 5.15/5.51 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.15/5.51 & ( L2 != zero_zero_int )
% 5.15/5.51 & ( K2
% 5.15/5.51 = ( times_times_int @ Q4 @ L2 ) ) )
% 5.15/5.51 | ? [R5: int,L2: int,K2: int,Q4: int] :
% 5.15/5.51 ( ( A12 = K2 )
% 5.15/5.51 & ( A23 = L2 )
% 5.15/5.51 & ( A32
% 5.15/5.51 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.15/5.51 & ( ( sgn_sgn_int @ R5 )
% 5.15/5.51 = ( sgn_sgn_int @ L2 ) )
% 5.15/5.51 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 5.15/5.51 & ( K2
% 5.15/5.51 = ( plus_plus_int @ ( times_times_int @ Q4 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % eucl_rel_int.simps
% 5.15/5.51 thf(fact_9337_eucl__rel__int_Ocases,axiom,
% 5.15/5.51 ! [A1: int,A22: int,A33: product_prod_int_int] :
% 5.15/5.51 ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 5.15/5.51 => ( ( ( A22 = zero_zero_int )
% 5.15/5.51 => ( A33
% 5.15/5.51 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 5.15/5.51 => ( ! [Q2: int] :
% 5.15/5.51 ( ( A33
% 5.15/5.51 = ( product_Pair_int_int @ Q2 @ zero_zero_int ) )
% 5.15/5.51 => ( ( A22 != zero_zero_int )
% 5.15/5.51 => ( A1
% 5.15/5.51 != ( times_times_int @ Q2 @ A22 ) ) ) )
% 5.15/5.51 => ~ ! [R3: int,Q2: int] :
% 5.15/5.51 ( ( A33
% 5.15/5.51 = ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.15/5.51 => ( ( ( sgn_sgn_int @ R3 )
% 5.15/5.51 = ( sgn_sgn_int @ A22 ) )
% 5.15/5.51 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 5.15/5.51 => ( A1
% 5.15/5.51 != ( plus_plus_int @ ( times_times_int @ Q2 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % eucl_rel_int.cases
% 5.15/5.51 thf(fact_9338_div__noneq__sgn__abs,axiom,
% 5.15/5.51 ! [L: int,K: int] :
% 5.15/5.51 ( ( L != zero_zero_int )
% 5.15/5.51 => ( ( ( sgn_sgn_int @ K )
% 5.15/5.51 != ( sgn_sgn_int @ L ) )
% 5.15/5.51 => ( ( divide_divide_int @ K @ L )
% 5.15/5.51 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.15/5.51 @ ( zero_n2684676970156552555ol_int
% 5.15/5.51 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % div_noneq_sgn_abs
% 5.15/5.51 thf(fact_9339_set__bit__eq,axiom,
% 5.15/5.51 ( bit_se7879613467334960850it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] :
% 5.15/5.51 ( plus_plus_int @ K2
% 5.15/5.51 @ ( times_times_int
% 5.15/5.51 @ ( zero_n2684676970156552555ol_int
% 5.15/5.51 @ ~ ( bit_se1146084159140164899it_int @ K2 @ N3 ) )
% 5.15/5.51 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % set_bit_eq
% 5.15/5.51 thf(fact_9340_unset__bit__eq,axiom,
% 5.15/5.51 ( bit_se4203085406695923979it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] : ( minus_minus_int @ K2 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % unset_bit_eq
% 5.15/5.51 thf(fact_9341_pi__half,axiom,
% 5.15/5.51 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.51 = ( the_real
% 5.15/5.51 @ ^ [X2: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.15/5.51 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.51 & ( ( cos_real @ X2 )
% 5.15/5.51 = zero_zero_real ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % pi_half
% 5.15/5.51 thf(fact_9342_pi__def,axiom,
% 5.15/5.51 ( pi
% 5.15/5.51 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.15/5.51 @ ( the_real
% 5.15/5.51 @ ^ [X2: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.15/5.51 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.15/5.51 & ( ( cos_real @ X2 )
% 5.15/5.51 = zero_zero_real ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % pi_def
% 5.15/5.51 thf(fact_9343_take__bit__Suc__from__most,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 5.15/5.51 = ( 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 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % take_bit_Suc_from_most
% 5.15/5.51 thf(fact_9344_divide__int__unfold,axiom,
% 5.15/5.51 ! [L: int,K: int,N2: nat,M: nat] :
% 5.15/5.51 ( ( ( ( ( sgn_sgn_int @ L )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 | ( ( sgn_sgn_int @ K )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 | ( N2 = zero_zero_nat ) )
% 5.15/5.51 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.15/5.51 = zero_zero_int ) )
% 5.15/5.51 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 | ( ( sgn_sgn_int @ K )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 | ( N2 = zero_zero_nat ) )
% 5.15/5.51 => ( ( ( ( sgn_sgn_int @ K )
% 5.15/5.51 = ( sgn_sgn_int @ L ) )
% 5.15/5.51 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.15/5.51 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 5.15/5.51 & ( ( ( sgn_sgn_int @ K )
% 5.15/5.51 != ( sgn_sgn_int @ L ) )
% 5.15/5.51 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.15/5.51 = ( uminus_uminus_int
% 5.15/5.51 @ ( semiri1314217659103216013at_int
% 5.15/5.51 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 5.15/5.51 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.51 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divide_int_unfold
% 5.15/5.51 thf(fact_9345_zero__le__sgn__iff,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 5.15/5.51 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % zero_le_sgn_iff
% 5.15/5.51 thf(fact_9346_sgn__le__0__iff,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % sgn_le_0_iff
% 5.15/5.51 thf(fact_9347_not__bit__Suc__0__Suc,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % not_bit_Suc_0_Suc
% 5.15/5.51 thf(fact_9348_bit__Suc__0__iff,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.51 = ( N2 = zero_zero_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_Suc_0_iff
% 5.15/5.51 thf(fact_9349_real__sgn__eq,axiom,
% 5.15/5.51 ( sgn_sgn_real
% 5.15/5.51 = ( ^ [X2: real] : ( divide_divide_real @ X2 @ ( abs_abs_real @ X2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_sgn_eq
% 5.15/5.51 thf(fact_9350_not__bit__Suc__0__numeral,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % not_bit_Suc_0_numeral
% 5.15/5.51 thf(fact_9351_sgn__root,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( sgn_sgn_real @ ( root @ N2 @ X ) )
% 5.15/5.51 = ( sgn_sgn_real @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sgn_root
% 5.15/5.51 thf(fact_9352_sgn__real__def,axiom,
% 5.15/5.51 ( sgn_sgn_real
% 5.15/5.51 = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sgn_real_def
% 5.15/5.51 thf(fact_9353_sgn__power__injE,axiom,
% 5.15/5.51 ! [A: real,N2: nat,X: real,B: real] :
% 5.15/5.51 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.15/5.51 = X )
% 5.15/5.51 => ( ( X
% 5.15/5.51 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 5.15/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( A = B ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sgn_power_injE
% 5.15/5.51 thf(fact_9354_bit__nat__def,axiom,
% 5.15/5.51 ( bit_se1148574629649215175it_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.51 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_nat_def
% 5.15/5.51 thf(fact_9355_sgn__power__root,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X ) ) @ N2 ) )
% 5.15/5.51 = X ) ) ).
% 5.15/5.51
% 5.15/5.51 % sgn_power_root
% 5.15/5.51 thf(fact_9356_root__sgn__power,axiom,
% 5.15/5.51 ! [N2: nat,Y: real] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 5.15/5.51 = Y ) ) ).
% 5.15/5.51
% 5.15/5.51 % root_sgn_power
% 5.15/5.51 thf(fact_9357_cis__Arg__unique,axiom,
% 5.15/5.51 ! [Z: complex,X: real] :
% 5.15/5.51 ( ( ( sgn_sgn_complex @ Z )
% 5.15/5.51 = ( cis @ X ) )
% 5.15/5.51 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.15/5.51 => ( ( ord_less_eq_real @ X @ pi )
% 5.15/5.51 => ( ( arg @ Z )
% 5.15/5.51 = X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cis_Arg_unique
% 5.15/5.51 thf(fact_9358_split__root,axiom,
% 5.15/5.51 ! [P: real > $o,N2: nat,X: real] :
% 5.15/5.51 ( ( P @ ( root @ N2 @ X ) )
% 5.15/5.51 = ( ( ( N2 = zero_zero_nat )
% 5.15/5.51 => ( P @ zero_zero_real ) )
% 5.15/5.51 & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ! [Y2: real] :
% 5.15/5.51 ( ( ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N2 ) )
% 5.15/5.51 = X )
% 5.15/5.51 => ( P @ Y2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % split_root
% 5.15/5.51 thf(fact_9359_floor__real__def,axiom,
% 5.15/5.51 ( archim6058952711729229775r_real
% 5.15/5.51 = ( ^ [X2: real] :
% 5.15/5.51 ( the_int
% 5.15/5.51 @ ^ [Z3: int] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X2 )
% 5.15/5.51 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % floor_real_def
% 5.15/5.51 thf(fact_9360_Arg__correct,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( Z != zero_zero_complex )
% 5.15/5.51 => ( ( ( sgn_sgn_complex @ Z )
% 5.15/5.51 = ( cis @ ( arg @ Z ) ) )
% 5.15/5.51 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.15/5.51 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Arg_correct
% 5.15/5.51 thf(fact_9361_arctan__inverse,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( X != zero_zero_real )
% 5.15/5.51 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.15/5.51 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % arctan_inverse
% 5.15/5.51 thf(fact_9362_modulo__int__def,axiom,
% 5.15/5.51 ( modulo_modulo_int
% 5.15/5.51 = ( ^ [K2: int,L2: int] :
% 5.15/5.51 ( if_int @ ( L2 = zero_zero_int ) @ K2
% 5.15/5.51 @ ( if_int
% 5.15/5.51 @ ( ( sgn_sgn_int @ K2 )
% 5.15/5.51 = ( sgn_sgn_int @ L2 ) )
% 5.15/5.51 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 5.15/5.51 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.15/5.51 @ ( minus_minus_int
% 5.15/5.51 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 5.15/5.51 @ ( zero_n2684676970156552555ol_int
% 5.15/5.51 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) )
% 5.15/5.51 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % modulo_int_def
% 5.15/5.51 thf(fact_9363_divide__int__def,axiom,
% 5.15/5.51 ( divide_divide_int
% 5.15/5.51 = ( ^ [K2: int,L2: int] :
% 5.15/5.51 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 5.15/5.51 @ ( if_int
% 5.15/5.51 @ ( ( sgn_sgn_int @ K2 )
% 5.15/5.51 = ( sgn_sgn_int @ L2 ) )
% 5.15/5.51 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 5.15/5.51 @ ( uminus_uminus_int
% 5.15/5.51 @ ( semiri1314217659103216013at_int
% 5.15/5.51 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 5.15/5.51 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.51 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divide_int_def
% 5.15/5.51 thf(fact_9364_powr__int,axiom,
% 5.15/5.51 ! [X: real,I: int] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.15/5.51 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 5.15/5.51 = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 5.15/5.51 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.15/5.51 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 5.15/5.51 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % powr_int
% 5.15/5.51 thf(fact_9365_nat__numeral,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.15/5.51 = ( numeral_numeral_nat @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_numeral
% 5.15/5.51 thf(fact_9366_nat__1,axiom,
% 5.15/5.51 ( ( nat2 @ one_one_int )
% 5.15/5.51 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_1
% 5.15/5.51 thf(fact_9367_zless__nat__conj,axiom,
% 5.15/5.51 ! [W: int,Z: int] :
% 5.15/5.51 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.15/5.51 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.15/5.51 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % zless_nat_conj
% 5.15/5.51 thf(fact_9368_nat__neg__numeral,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.51 = zero_zero_nat ) ).
% 5.15/5.51
% 5.15/5.51 % nat_neg_numeral
% 5.15/5.51 thf(fact_9369_zero__less__nat__eq,axiom,
% 5.15/5.51 ! [Z: int] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.15/5.51 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.15/5.51
% 5.15/5.51 % zero_less_nat_eq
% 5.15/5.51 thf(fact_9370_diff__nat__numeral,axiom,
% 5.15/5.51 ! [V: num,V3: num] :
% 5.15/5.51 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.15/5.51 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % diff_nat_numeral
% 5.15/5.51 thf(fact_9371_nat__eq__numeral__power__cancel__iff,axiom,
% 5.15/5.51 ! [Y: int,X: num,N2: nat] :
% 5.15/5.51 ( ( ( nat2 @ Y )
% 5.15/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.15/5.51 = ( Y
% 5.15/5.51 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_eq_numeral_power_cancel_iff
% 5.15/5.51 thf(fact_9372_numeral__power__eq__nat__cancel__iff,axiom,
% 5.15/5.51 ! [X: num,N2: nat,Y: int] :
% 5.15/5.51 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.15/5.51 = ( nat2 @ Y ) )
% 5.15/5.51 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.15/5.51 = Y ) ) ).
% 5.15/5.51
% 5.15/5.51 % numeral_power_eq_nat_cancel_iff
% 5.15/5.51 thf(fact_9373_nat__ceiling__le__eq,axiom,
% 5.15/5.51 ! [X: real,A: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.15/5.51 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_ceiling_le_eq
% 5.15/5.51 thf(fact_9374_one__less__nat__eq,axiom,
% 5.15/5.51 ! [Z: int] :
% 5.15/5.51 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.15/5.51 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.15/5.51
% 5.15/5.51 % one_less_nat_eq
% 5.15/5.51 thf(fact_9375_nat__numeral__diff__1,axiom,
% 5.15/5.51 ! [V: num] :
% 5.15/5.51 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.15/5.51 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_numeral_diff_1
% 5.15/5.51 thf(fact_9376_nat__less__numeral__power__cancel__iff,axiom,
% 5.15/5.51 ! [A: int,X: num,N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.15/5.51 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_less_numeral_power_cancel_iff
% 5.15/5.51 thf(fact_9377_numeral__power__less__nat__cancel__iff,axiom,
% 5.15/5.51 ! [X: num,N2: nat,A: int] :
% 5.15/5.51 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 5.15/5.51 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.15/5.51
% 5.15/5.51 % numeral_power_less_nat_cancel_iff
% 5.15/5.51 thf(fact_9378_nat__le__numeral__power__cancel__iff,axiom,
% 5.15/5.51 ! [A: int,X: num,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.15/5.51 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_le_numeral_power_cancel_iff
% 5.15/5.51 thf(fact_9379_numeral__power__le__nat__cancel__iff,axiom,
% 5.15/5.51 ! [X: num,N2: nat,A: int] :
% 5.15/5.51 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 5.15/5.51 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.15/5.51
% 5.15/5.51 % numeral_power_le_nat_cancel_iff
% 5.15/5.51 thf(fact_9380_nat__numeral__as__int,axiom,
% 5.15/5.51 ( numeral_numeral_nat
% 5.15/5.51 = ( ^ [I3: num] : ( nat2 @ ( numeral_numeral_int @ I3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_numeral_as_int
% 5.15/5.51 thf(fact_9381_nat__mono,axiom,
% 5.15/5.51 ! [X: int,Y: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ X @ Y )
% 5.15/5.51 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_mono
% 5.15/5.51 thf(fact_9382_nat__one__as__int,axiom,
% 5.15/5.51 ( one_one_nat
% 5.15/5.51 = ( nat2 @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_one_as_int
% 5.15/5.51 thf(fact_9383_unset__bit__nat__def,axiom,
% 5.15/5.51 ( bit_se4205575877204974255it_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M5 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % unset_bit_nat_def
% 5.15/5.51 thf(fact_9384_nat__mask__eq,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.15/5.51 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_mask_eq
% 5.15/5.51 thf(fact_9385_nat__mono__iff,axiom,
% 5.15/5.51 ! [Z: int,W: int] :
% 5.15/5.51 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.15/5.51 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.15/5.51 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_mono_iff
% 5.15/5.51 thf(fact_9386_zless__nat__eq__int__zless,axiom,
% 5.15/5.51 ! [M: nat,Z: int] :
% 5.15/5.51 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.15/5.51 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.15/5.51
% 5.15/5.51 % zless_nat_eq_int_zless
% 5.15/5.51 thf(fact_9387_nat__le__iff,axiom,
% 5.15/5.51 ! [X: int,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N2 )
% 5.15/5.51 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_le_iff
% 5.15/5.51 thf(fact_9388_nat__int__add,axiom,
% 5.15/5.51 ! [A: nat,B: nat] :
% 5.15/5.51 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.15/5.51 = ( plus_plus_nat @ A @ B ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_int_add
% 5.15/5.51 thf(fact_9389_int__minus,axiom,
% 5.15/5.51 ! [N2: nat,M: nat] :
% 5.15/5.51 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ M ) )
% 5.15/5.51 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % int_minus
% 5.15/5.51 thf(fact_9390_nat__abs__mult__distrib,axiom,
% 5.15/5.51 ! [W: int,Z: int] :
% 5.15/5.51 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.15/5.51 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_abs_mult_distrib
% 5.15/5.51 thf(fact_9391_real__nat__ceiling__ge,axiom,
% 5.15/5.51 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_nat_ceiling_ge
% 5.15/5.51 thf(fact_9392_and__nat__def,axiom,
% 5.15/5.51 ( bit_se727722235901077358nd_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % and_nat_def
% 5.15/5.51 thf(fact_9393_nat__plus__as__int,axiom,
% 5.15/5.51 ( plus_plus_nat
% 5.15/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_plus_as_int
% 5.15/5.51 thf(fact_9394_or__nat__def,axiom,
% 5.15/5.51 ( bit_se1412395901928357646or_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_nat_def
% 5.15/5.51 thf(fact_9395_nat__times__as__int,axiom,
% 5.15/5.51 ( times_times_nat
% 5.15/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_times_as_int
% 5.15/5.51 thf(fact_9396_nat__minus__as__int,axiom,
% 5.15/5.51 ( minus_minus_nat
% 5.15/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_minus_as_int
% 5.15/5.51 thf(fact_9397_nat__div__as__int,axiom,
% 5.15/5.51 ( divide_divide_nat
% 5.15/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_div_as_int
% 5.15/5.51 thf(fact_9398_nat__mod__as__int,axiom,
% 5.15/5.51 ( modulo_modulo_nat
% 5.15/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_mod_as_int
% 5.15/5.51 thf(fact_9399_nat__less__eq__zless,axiom,
% 5.15/5.51 ! [W: int,Z: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.15/5.51 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.15/5.51 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_less_eq_zless
% 5.15/5.51 thf(fact_9400_nat__le__eq__zle,axiom,
% 5.15/5.51 ! [W: int,Z: int] :
% 5.15/5.51 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.15/5.51 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.15/5.51 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.15/5.51 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_le_eq_zle
% 5.15/5.51 thf(fact_9401_le__nat__iff,axiom,
% 5.15/5.51 ! [K: int,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.51 => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 5.15/5.51 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % le_nat_iff
% 5.15/5.51 thf(fact_9402_nat__add__distrib,axiom,
% 5.15/5.51 ! [Z: int,Z7: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.15/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.15/5.51 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.15/5.51 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_add_distrib
% 5.15/5.51 thf(fact_9403_Suc__as__int,axiom,
% 5.15/5.51 ( suc
% 5.15/5.51 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_as_int
% 5.15/5.51 thf(fact_9404_nat__mult__distrib,axiom,
% 5.15/5.51 ! [Z: int,Z7: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.15/5.51 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.15/5.51 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_mult_distrib
% 5.15/5.51 thf(fact_9405_nat__diff__distrib_H,axiom,
% 5.15/5.51 ! [X: int,Y: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.51 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 5.15/5.51 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_diff_distrib'
% 5.15/5.51 thf(fact_9406_nat__diff__distrib,axiom,
% 5.15/5.51 ! [Z7: int,Z: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.15/5.51 => ( ( ord_less_eq_int @ Z7 @ Z )
% 5.15/5.51 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 5.15/5.51 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_diff_distrib
% 5.15/5.51 thf(fact_9407_nat__abs__triangle__ineq,axiom,
% 5.15/5.51 ! [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 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_abs_triangle_ineq
% 5.15/5.51 thf(fact_9408_nat__div__distrib_H,axiom,
% 5.15/5.51 ! [Y: int,X: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.51 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.15/5.51 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_div_distrib'
% 5.15/5.51 thf(fact_9409_nat__div__distrib,axiom,
% 5.15/5.51 ! [X: int,Y: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.51 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.15/5.51 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_div_distrib
% 5.15/5.51 thf(fact_9410_nat__power__eq,axiom,
% 5.15/5.51 ! [Z: int,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.15/5.51 => ( ( nat2 @ ( power_power_int @ Z @ N2 ) )
% 5.15/5.51 = ( power_power_nat @ ( nat2 @ Z ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_power_eq
% 5.15/5.51 thf(fact_9411_nat__floor__neg,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.15/5.51 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.51 = zero_zero_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_floor_neg
% 5.15/5.51 thf(fact_9412_nat__mod__distrib,axiom,
% 5.15/5.51 ! [X: int,Y: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.51 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 5.15/5.51 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_mod_distrib
% 5.15/5.51 thf(fact_9413_div__abs__eq__div__nat,axiom,
% 5.15/5.51 ! [K: int,L: int] :
% 5.15/5.51 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.15/5.51 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % div_abs_eq_div_nat
% 5.15/5.51 thf(fact_9414_floor__eq3,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X )
% 5.15/5.51 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.15/5.51 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.51 = N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % floor_eq3
% 5.15/5.51 thf(fact_9415_le__nat__floor,axiom,
% 5.15/5.51 ! [X: nat,A: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.15/5.51 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % le_nat_floor
% 5.15/5.51 thf(fact_9416_mod__abs__eq__div__nat,axiom,
% 5.15/5.51 ! [K: int,L: int] :
% 5.15/5.51 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.15/5.51 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % mod_abs_eq_div_nat
% 5.15/5.51 thf(fact_9417_take__bit__nat__eq,axiom,
% 5.15/5.51 ! [K: int,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.51 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) )
% 5.15/5.51 = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % take_bit_nat_eq
% 5.15/5.51 thf(fact_9418_nat__take__bit__eq,axiom,
% 5.15/5.51 ! [K: int,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.51 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.15/5.51 = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_take_bit_eq
% 5.15/5.51 thf(fact_9419_bit__nat__iff,axiom,
% 5.15/5.51 ! [K: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N2 )
% 5.15/5.51 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.51 & ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_nat_iff
% 5.15/5.51 thf(fact_9420_nat__2,axiom,
% 5.15/5.51 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.51 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_2
% 5.15/5.51 thf(fact_9421_Suc__nat__eq__nat__zadd1,axiom,
% 5.15/5.51 ! [Z: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.15/5.51 => ( ( suc @ ( nat2 @ Z ) )
% 5.15/5.51 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_nat_eq_nat_zadd1
% 5.15/5.51 thf(fact_9422_nat__less__iff,axiom,
% 5.15/5.51 ! [W: int,M: nat] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.15/5.51 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.15/5.51 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_less_iff
% 5.15/5.51 thf(fact_9423_nat__mult__distrib__neg,axiom,
% 5.15/5.51 ! [Z: int,Z7: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.15/5.51 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.15/5.51 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_mult_distrib_neg
% 5.15/5.51 thf(fact_9424_nat__abs__int__diff,axiom,
% 5.15/5.51 ! [A: nat,B: nat] :
% 5.15/5.51 ( ( ( ord_less_eq_nat @ A @ B )
% 5.15/5.51 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.15/5.51 = ( minus_minus_nat @ B @ A ) ) )
% 5.15/5.51 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.15/5.51 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.15/5.51 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_abs_int_diff
% 5.15/5.51 thf(fact_9425_floor__eq4,axiom,
% 5.15/5.51 ! [N2: nat,X: real] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X )
% 5.15/5.51 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.15/5.51 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.15/5.51 = N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % floor_eq4
% 5.15/5.51 thf(fact_9426_diff__nat__eq__if,axiom,
% 5.15/5.51 ! [Z7: int,Z: int] :
% 5.15/5.51 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.15/5.51 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.15/5.51 = ( nat2 @ Z ) ) )
% 5.15/5.51 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.15/5.51 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.15/5.51 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % diff_nat_eq_if
% 5.15/5.51 thf(fact_9427_even__nat__iff,axiom,
% 5.15/5.51 ! [K: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.51 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.15/5.51 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % even_nat_iff
% 5.15/5.51 thf(fact_9428_powr__real__of__int,axiom,
% 5.15/5.51 ! [X: real,N2: int] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.51 => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.15/5.51 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N2 ) )
% 5.15/5.51 = ( power_power_real @ X @ ( nat2 @ N2 ) ) ) )
% 5.15/5.51 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.15/5.51 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N2 ) )
% 5.15/5.51 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % powr_real_of_int
% 5.15/5.51 thf(fact_9429_floor__rat__def,axiom,
% 5.15/5.51 ( archim3151403230148437115or_rat
% 5.15/5.51 = ( ^ [X2: rat] :
% 5.15/5.51 ( the_int
% 5.15/5.51 @ ^ [Z3: int] :
% 5.15/5.51 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 )
% 5.15/5.51 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % floor_rat_def
% 5.15/5.51 thf(fact_9430_Arg__def,axiom,
% 5.15/5.51 ( arg
% 5.15/5.51 = ( ^ [Z3: complex] :
% 5.15/5.51 ( if_real @ ( Z3 = zero_zero_complex ) @ zero_zero_real
% 5.15/5.51 @ ( fChoice_real
% 5.15/5.51 @ ^ [A3: real] :
% 5.15/5.51 ( ( ( sgn_sgn_complex @ Z3 )
% 5.15/5.51 = ( cis @ A3 ) )
% 5.15/5.51 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 5.15/5.51 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Arg_def
% 5.15/5.51 thf(fact_9431_cis__multiple__2pi,axiom,
% 5.15/5.51 ! [N2: real] :
% 5.15/5.51 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.15/5.51 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.15/5.51 = one_one_complex ) ) ).
% 5.15/5.51
% 5.15/5.51 % cis_multiple_2pi
% 5.15/5.51 thf(fact_9432_setceilmax,axiom,
% 5.15/5.51 ! [S: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N2: nat] :
% 5.15/5.51 ( ( vEBT_invar_vebt @ S @ M )
% 5.15/5.51 => ( ! [X3: vEBT_VEBT] :
% 5.15/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.15/5.51 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.15/5.51 => ( ( M
% 5.15/5.51 = ( suc @ N2 ) )
% 5.15/5.51 => ( ! [X3: vEBT_VEBT] :
% 5.15/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.15/5.51 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X3 ) )
% 5.15/5.51 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 5.15/5.51 => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S ) )
% 5.15/5.51 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 5.15/5.51 => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 5.15/5.51 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % setceilmax
% 5.15/5.51 thf(fact_9433_height__compose__list,axiom,
% 5.15/5.51 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.51 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.51 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % height_compose_list
% 5.15/5.51 thf(fact_9434_max__ins__scaled,axiom,
% 5.15/5.51 ! [N2: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % max_ins_scaled
% 5.15/5.51 thf(fact_9435_height__i__max,axiom,
% 5.15/5.51 ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 5.15/5.51 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.15/5.51 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % height_i_max
% 5.15/5.51 thf(fact_9436_max__idx__list,axiom,
% 5.15/5.51 ! [I: nat,X13: list_VEBT_VEBT,N2: nat,X14: vEBT_VEBT] :
% 5.15/5.51 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.15/5.51 => ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N2 @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % max_idx_list
% 5.15/5.51 thf(fact_9437_Max__divisors__self__nat,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( N2 != zero_zero_nat )
% 5.15/5.51 => ( ( lattic8265883725875713057ax_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ N2 ) ) )
% 5.15/5.51 = N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % Max_divisors_self_nat
% 5.15/5.51 thf(fact_9438_obtain__pos__sum,axiom,
% 5.15/5.51 ! [R2: rat] :
% 5.15/5.51 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.15/5.51 => ~ ! [S2: rat] :
% 5.15/5.51 ( ( ord_less_rat @ zero_zero_rat @ S2 )
% 5.15/5.51 => ! [T3: rat] :
% 5.15/5.51 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 5.15/5.51 => ( R2
% 5.15/5.51 != ( plus_plus_rat @ S2 @ T3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % obtain_pos_sum
% 5.15/5.51 thf(fact_9439_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 5.15/5.51 ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.15/5.51 ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu @ Deg @ TreeList @ Summary ) )
% 5.15/5.51 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT_internal.height.simps(2)
% 5.15/5.51 thf(fact_9440_VEBT__internal_Oheight_Oelims,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT,Y: nat] :
% 5.15/5.51 ( ( ( vEBT_VEBT_height @ X )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( ? [A5: $o,B6: $o] :
% 5.15/5.51 ( X
% 5.15/5.51 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.51 => ( Y != zero_zero_nat ) )
% 5.15/5.51 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.51 => ( Y
% 5.15/5.51 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT_internal.height.elims
% 5.15/5.51 thf(fact_9441_sin__times__pi__eq__0,axiom,
% 5.15/5.51 ! [X: real] :
% 5.15/5.51 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % sin_times_pi_eq_0
% 5.15/5.51 thf(fact_9442_divide__nat__def,axiom,
% 5.15/5.51 ( divide_divide_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.51 ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 5.15/5.51 @ ( lattic8265883725875713057ax_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N3 ) @ M5 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divide_nat_def
% 5.15/5.51 thf(fact_9443_sin__integer__2pi,axiom,
% 5.15/5.51 ! [N2: real] :
% 5.15/5.51 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.15/5.51 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.15/5.51 = zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % sin_integer_2pi
% 5.15/5.51 thf(fact_9444_cos__integer__2pi,axiom,
% 5.15/5.51 ! [N2: real] :
% 5.15/5.51 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.15/5.51 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.15/5.51 = one_one_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % cos_integer_2pi
% 5.15/5.51 thf(fact_9445_bij__betw__Suc,axiom,
% 5.15/5.51 ! [M7: set_nat,N5: set_nat] :
% 5.15/5.51 ( ( bij_betw_nat_nat @ suc @ M7 @ N5 )
% 5.15/5.51 = ( ( image_nat_nat @ suc @ M7 )
% 5.15/5.51 = N5 ) ) ).
% 5.15/5.51
% 5.15/5.51 % bij_betw_Suc
% 5.15/5.51 thf(fact_9446_image__Suc__atLeastAtMost,axiom,
% 5.15/5.51 ! [I: nat,J: nat] :
% 5.15/5.51 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.15/5.51 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % image_Suc_atLeastAtMost
% 5.15/5.51 thf(fact_9447_Max__divisors__self__int,axiom,
% 5.15/5.51 ! [N2: int] :
% 5.15/5.51 ( ( N2 != zero_zero_int )
% 5.15/5.51 => ( ( lattic8263393255366662781ax_int
% 5.15/5.51 @ ( collect_int
% 5.15/5.51 @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ N2 ) ) )
% 5.15/5.51 = ( abs_abs_int @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Max_divisors_self_int
% 5.15/5.51 thf(fact_9448_zero__notin__Suc__image,axiom,
% 5.15/5.51 ! [A2: set_nat] :
% 5.15/5.51 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % zero_notin_Suc_image
% 5.15/5.51 thf(fact_9449_image__Suc__lessThan,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.51 = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % image_Suc_lessThan
% 5.15/5.51 thf(fact_9450_image__Suc__atMost,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 5.15/5.51 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % image_Suc_atMost
% 5.15/5.51 thf(fact_9451_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.15/5.51 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeast0_atMost_Suc_eq_insert_0
% 5.15/5.51 thf(fact_9452_lessThan__Suc__eq__insert__0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 5.15/5.51 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % lessThan_Suc_eq_insert_0
% 5.15/5.51 thf(fact_9453_atMost__Suc__eq__insert__0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 5.15/5.51 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atMost_Suc_eq_insert_0
% 5.15/5.51 thf(fact_9454_rat__inverse__code,axiom,
% 5.15/5.51 ! [P2: rat] :
% 5.15/5.51 ( ( quotient_of @ ( inverse_inverse_rat @ P2 ) )
% 5.15/5.51 = ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B2 ) @ ( abs_abs_int @ A3 ) ) )
% 5.15/5.51 @ ( quotient_of @ P2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_inverse_code
% 5.15/5.51 thf(fact_9455_normalize__negative,axiom,
% 5.15/5.51 ! [Q3: int,P2: int] :
% 5.15/5.51 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 5.15/5.51 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.15/5.51 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P2 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % normalize_negative
% 5.15/5.51 thf(fact_9456_rat__one__code,axiom,
% 5.15/5.51 ( ( quotient_of @ one_one_rat )
% 5.15/5.51 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_one_code
% 5.15/5.51 thf(fact_9457_quotient__of__number_I3_J,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.15/5.51 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % quotient_of_number(3)
% 5.15/5.51 thf(fact_9458_quotient__of__number_I4_J,axiom,
% 5.15/5.51 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.15/5.51 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % quotient_of_number(4)
% 5.15/5.51 thf(fact_9459_normalize__denom__zero,axiom,
% 5.15/5.51 ! [P2: int] :
% 5.15/5.51 ( ( normalize @ ( product_Pair_int_int @ P2 @ zero_zero_int ) )
% 5.15/5.51 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % normalize_denom_zero
% 5.15/5.51 thf(fact_9460_quotient__of__number_I5_J,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.15/5.51 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % quotient_of_number(5)
% 5.15/5.51 thf(fact_9461_rat__zero__code,axiom,
% 5.15/5.51 ( ( quotient_of @ zero_zero_rat )
% 5.15/5.51 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_zero_code
% 5.15/5.51 thf(fact_9462_divide__rat__def,axiom,
% 5.15/5.51 ( divide_divide_rat
% 5.15/5.51 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divide_rat_def
% 5.15/5.51 thf(fact_9463_rat__times__code,axiom,
% 5.15/5.51 ! [P2: rat,Q3: rat] :
% 5.15/5.51 ( ( quotient_of @ ( times_times_rat @ P2 @ Q3 ) )
% 5.15/5.51 = ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [A3: int,C3: int] :
% 5.15/5.51 ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B2 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.15/5.51 @ ( quotient_of @ Q3 ) )
% 5.15/5.51 @ ( quotient_of @ P2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_times_code
% 5.15/5.51 thf(fact_9464_rat__divide__code,axiom,
% 5.15/5.51 ! [P2: rat,Q3: rat] :
% 5.15/5.51 ( ( quotient_of @ ( divide_divide_rat @ P2 @ Q3 ) )
% 5.15/5.51 = ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [A3: int,C3: int] :
% 5.15/5.51 ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) ) )
% 5.15/5.51 @ ( quotient_of @ Q3 ) )
% 5.15/5.51 @ ( quotient_of @ P2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_divide_code
% 5.15/5.51 thf(fact_9465_quotient__of__div,axiom,
% 5.15/5.51 ! [R2: rat,N2: int,D: int] :
% 5.15/5.51 ( ( ( quotient_of @ R2 )
% 5.15/5.51 = ( product_Pair_int_int @ N2 @ D ) )
% 5.15/5.51 => ( R2
% 5.15/5.51 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N2 ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % quotient_of_div
% 5.15/5.51 thf(fact_9466_rat__minus__code,axiom,
% 5.15/5.51 ! [P2: rat,Q3: rat] :
% 5.15/5.51 ( ( quotient_of @ ( minus_minus_rat @ P2 @ Q3 ) )
% 5.15/5.51 = ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [A3: int,C3: int] :
% 5.15/5.51 ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.15/5.51 @ ( quotient_of @ Q3 ) )
% 5.15/5.51 @ ( quotient_of @ P2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_minus_code
% 5.15/5.51 thf(fact_9467_quotient__of__denom__pos,axiom,
% 5.15/5.51 ! [R2: rat,P2: int,Q3: int] :
% 5.15/5.51 ( ( ( quotient_of @ R2 )
% 5.15/5.51 = ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.15/5.51 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 5.15/5.51
% 5.15/5.51 % quotient_of_denom_pos
% 5.15/5.51 thf(fact_9468_rat__plus__code,axiom,
% 5.15/5.51 ! [P2: rat,Q3: rat] :
% 5.15/5.51 ( ( quotient_of @ ( plus_plus_rat @ P2 @ Q3 ) )
% 5.15/5.51 = ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [A3: int,C3: int] :
% 5.15/5.51 ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.15/5.51 @ ( quotient_of @ Q3 ) )
% 5.15/5.51 @ ( quotient_of @ P2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_plus_code
% 5.15/5.51 thf(fact_9469_rat__uminus__code,axiom,
% 5.15/5.51 ! [P2: rat] :
% 5.15/5.51 ( ( quotient_of @ ( uminus_uminus_rat @ P2 ) )
% 5.15/5.51 = ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [A3: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A3 ) )
% 5.15/5.51 @ ( quotient_of @ P2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_uminus_code
% 5.15/5.51 thf(fact_9470_rat__abs__code,axiom,
% 5.15/5.51 ! [P2: rat] :
% 5.15/5.51 ( ( quotient_of @ ( abs_abs_rat @ P2 ) )
% 5.15/5.51 = ( produc4245557441103728435nt_int
% 5.15/5.51 @ ^ [A3: int] : ( product_Pair_int_int @ ( abs_abs_int @ A3 ) )
% 5.15/5.51 @ ( quotient_of @ P2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_abs_code
% 5.15/5.51 thf(fact_9471_normalize__denom__pos,axiom,
% 5.15/5.51 ! [R2: product_prod_int_int,P2: int,Q3: int] :
% 5.15/5.51 ( ( ( normalize @ R2 )
% 5.15/5.51 = ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.15/5.51 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 5.15/5.51
% 5.15/5.51 % normalize_denom_pos
% 5.15/5.51 thf(fact_9472_normalize__crossproduct,axiom,
% 5.15/5.51 ! [Q3: int,S: int,P2: int,R2: int] :
% 5.15/5.51 ( ( Q3 != zero_zero_int )
% 5.15/5.51 => ( ( S != zero_zero_int )
% 5.15/5.51 => ( ( ( normalize @ ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.15/5.51 = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 5.15/5.51 => ( ( times_times_int @ P2 @ S )
% 5.15/5.51 = ( times_times_int @ R2 @ Q3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % normalize_crossproduct
% 5.15/5.51 thf(fact_9473_rat__less__code,axiom,
% 5.15/5.51 ( ord_less_rat
% 5.15/5.51 = ( ^ [P5: rat,Q4: rat] :
% 5.15/5.51 ( produc4947309494688390418_int_o
% 5.15/5.51 @ ^ [A3: int,C3: int] :
% 5.15/5.51 ( produc4947309494688390418_int_o
% 5.15/5.51 @ ^ [B2: int,D2: int] : ( ord_less_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) )
% 5.15/5.51 @ ( quotient_of @ Q4 ) )
% 5.15/5.51 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_less_code
% 5.15/5.51 thf(fact_9474_rat__floor__code,axiom,
% 5.15/5.51 ( archim3151403230148437115or_rat
% 5.15/5.51 = ( ^ [P5: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P5 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_floor_code
% 5.15/5.51 thf(fact_9475_rat__less__eq__code,axiom,
% 5.15/5.51 ( ord_less_eq_rat
% 5.15/5.51 = ( ^ [P5: rat,Q4: rat] :
% 5.15/5.51 ( produc4947309494688390418_int_o
% 5.15/5.51 @ ^ [A3: int,C3: int] :
% 5.15/5.51 ( produc4947309494688390418_int_o
% 5.15/5.51 @ ^ [B2: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) )
% 5.15/5.51 @ ( quotient_of @ Q4 ) )
% 5.15/5.51 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_less_eq_code
% 5.15/5.51 thf(fact_9476_quotient__of__int,axiom,
% 5.15/5.51 ! [A: int] :
% 5.15/5.51 ( ( quotient_of @ ( of_int @ A ) )
% 5.15/5.51 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % quotient_of_int
% 5.15/5.51 thf(fact_9477_Suc__0__xor__eq,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.51 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.51 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_0_xor_eq
% 5.15/5.51 thf(fact_9478_xor__nat__numerals_I1_J,axiom,
% 5.15/5.51 ! [Y: num] :
% 5.15/5.51 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.15/5.51 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_nat_numerals(1)
% 5.15/5.51 thf(fact_9479_xor__nat__numerals_I2_J,axiom,
% 5.15/5.51 ! [Y: num] :
% 5.15/5.51 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.15/5.51 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_nat_numerals(2)
% 5.15/5.51 thf(fact_9480_xor__nat__numerals_I3_J,axiom,
% 5.15/5.51 ! [X: num] :
% 5.15/5.51 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.51 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_nat_numerals(3)
% 5.15/5.51 thf(fact_9481_xor__nat__numerals_I4_J,axiom,
% 5.15/5.51 ! [X: num] :
% 5.15/5.51 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.15/5.51 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_nat_numerals(4)
% 5.15/5.51 thf(fact_9482_xor__nat__unfold,axiom,
% 5.15/5.51 ( bit_se6528837805403552850or_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ 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 @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_nat_unfold
% 5.15/5.51 thf(fact_9483_xor__nat__rec,axiom,
% 5.15/5.51 ( bit_se6528837805403552850or_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] :
% 5.15/5.51 ( plus_plus_nat
% 5.15/5.51 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.51 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.15/5.51 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.15/5.51 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_nat_rec
% 5.15/5.51 thf(fact_9484_xor__Suc__0__eq,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.15/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.51 @ ( zero_n2687167440665602831ol_nat
% 5.15/5.51 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_Suc_0_eq
% 5.15/5.51 thf(fact_9485_Frct__code__post_I5_J,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.15/5.51 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Frct_code_post(5)
% 5.15/5.51 thf(fact_9486_horner__sum__of__bool__2__less,axiom,
% 5.15/5.51 ! [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 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % horner_sum_of_bool_2_less
% 5.15/5.51 thf(fact_9487_push__bit__nonnegative__int__iff,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.15/5.51 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % push_bit_nonnegative_int_iff
% 5.15/5.51 thf(fact_9488_push__bit__negative__int__iff,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 5.15/5.51 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % push_bit_negative_int_iff
% 5.15/5.51 thf(fact_9489_concat__bit__of__zero__1,axiom,
% 5.15/5.51 ! [N2: nat,L: int] :
% 5.15/5.51 ( ( bit_concat_bit @ N2 @ zero_zero_int @ L )
% 5.15/5.51 = ( bit_se545348938243370406it_int @ N2 @ L ) ) ).
% 5.15/5.51
% 5.15/5.51 % concat_bit_of_zero_1
% 5.15/5.51 thf(fact_9490_xor__nonnegative__int__iff,axiom,
% 5.15/5.51 ! [K: int,L: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.15/5.51 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.15/5.51 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_nonnegative_int_iff
% 5.15/5.51 thf(fact_9491_xor__negative__int__iff,axiom,
% 5.15/5.51 ! [K: int,L: int] :
% 5.15/5.51 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.15/5.51 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.15/5.51 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_negative_int_iff
% 5.15/5.51 thf(fact_9492_push__bit__of__Suc__0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.15/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % push_bit_of_Suc_0
% 5.15/5.51 thf(fact_9493_bit__xor__int__iff,axiom,
% 5.15/5.51 ! [K: int,L: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N2 )
% 5.15/5.51 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.15/5.51 != ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_xor_int_iff
% 5.15/5.51 thf(fact_9494_flip__bit__int__def,axiom,
% 5.15/5.51 ( bit_se2159334234014336723it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % flip_bit_int_def
% 5.15/5.51 thf(fact_9495_push__bit__nat__eq,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( bit_se547839408752420682it_nat @ N2 @ ( nat2 @ K ) )
% 5.15/5.51 = ( nat2 @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % push_bit_nat_eq
% 5.15/5.51 thf(fact_9496_XOR__lower,axiom,
% 5.15/5.51 ! [X: int,Y: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.15/5.51 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % XOR_lower
% 5.15/5.51 thf(fact_9497_set__bit__nat__def,axiom,
% 5.15/5.51 ( bit_se7882103937844011126it_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M5 @ one_one_nat ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % set_bit_nat_def
% 5.15/5.51 thf(fact_9498_flip__bit__nat__def,axiom,
% 5.15/5.51 ( bit_se2161824704523386999it_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M5 @ one_one_nat ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % flip_bit_nat_def
% 5.15/5.51 thf(fact_9499_bit__push__bit__iff__int,axiom,
% 5.15/5.51 ! [M: nat,K: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 5.15/5.51 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.51 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_push_bit_iff_int
% 5.15/5.51 thf(fact_9500_xor__nat__def,axiom,
% 5.15/5.51 ( bit_se6528837805403552850or_nat
% 5.15/5.51 = ( ^ [M5: nat,N3: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_nat_def
% 5.15/5.51 thf(fact_9501_bit__push__bit__iff__nat,axiom,
% 5.15/5.51 ! [M: nat,Q3: nat,N2: nat] :
% 5.15/5.51 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N2 )
% 5.15/5.51 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.51 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_push_bit_iff_nat
% 5.15/5.51 thf(fact_9502_concat__bit__eq,axiom,
% 5.15/5.51 ( bit_concat_bit
% 5.15/5.51 = ( ^ [N3: nat,K2: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N3 @ K2 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % concat_bit_eq
% 5.15/5.51 thf(fact_9503_concat__bit__def,axiom,
% 5.15/5.51 ( bit_concat_bit
% 5.15/5.51 = ( ^ [N3: nat,K2: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N3 @ K2 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % concat_bit_def
% 5.15/5.51 thf(fact_9504_set__bit__int__def,axiom,
% 5.15/5.51 ( bit_se7879613467334960850it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % set_bit_int_def
% 5.15/5.51 thf(fact_9505_push__bit__int__def,axiom,
% 5.15/5.51 ( bit_se545348938243370406it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] : ( times_times_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % push_bit_int_def
% 5.15/5.51 thf(fact_9506_push__bit__nat__def,axiom,
% 5.15/5.51 ( bit_se547839408752420682it_nat
% 5.15/5.51 = ( ^ [N3: nat,M5: nat] : ( times_times_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % push_bit_nat_def
% 5.15/5.51 thf(fact_9507_Frct__code__post_I1_J,axiom,
% 5.15/5.51 ! [A: int] :
% 5.15/5.51 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.15/5.51 = zero_zero_rat ) ).
% 5.15/5.51
% 5.15/5.51 % Frct_code_post(1)
% 5.15/5.51 thf(fact_9508_Frct__code__post_I2_J,axiom,
% 5.15/5.51 ! [A: int] :
% 5.15/5.51 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.15/5.51 = zero_zero_rat ) ).
% 5.15/5.51
% 5.15/5.51 % Frct_code_post(2)
% 5.15/5.51 thf(fact_9509_Frct__code__post_I8_J,axiom,
% 5.15/5.51 ! [A: int,B: int] :
% 5.15/5.51 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 5.15/5.51 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Frct_code_post(8)
% 5.15/5.51 thf(fact_9510_Frct__code__post_I7_J,axiom,
% 5.15/5.51 ! [A: int,B: int] :
% 5.15/5.51 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.15/5.51 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Frct_code_post(7)
% 5.15/5.51 thf(fact_9511_Frct__code__post_I3_J,axiom,
% 5.15/5.51 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.15/5.51 = one_one_rat ) ).
% 5.15/5.51
% 5.15/5.51 % Frct_code_post(3)
% 5.15/5.51 thf(fact_9512_push__bit__minus__one,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.51 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % push_bit_minus_one
% 5.15/5.51 thf(fact_9513_XOR__upper,axiom,
% 5.15/5.51 ! [X: int,N2: nat,Y: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.15/5.51 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.51 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.15/5.51 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % XOR_upper
% 5.15/5.51 thf(fact_9514_Frct__code__post_I4_J,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.15/5.51 = ( numeral_numeral_rat @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % Frct_code_post(4)
% 5.15/5.51 thf(fact_9515_xor__int__rec,axiom,
% 5.15/5.51 ( bit_se6526347334894502574or_int
% 5.15/5.51 = ( ^ [K2: int,L2: int] :
% 5.15/5.51 ( plus_plus_int
% 5.15/5.51 @ ( zero_n2684676970156552555ol_int
% 5.15/5.51 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 5.15/5.51 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.15/5.51 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_int_rec
% 5.15/5.51 thf(fact_9516_Frct__code__post_I6_J,axiom,
% 5.15/5.51 ! [K: num,L: num] :
% 5.15/5.51 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 5.15/5.51 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Frct_code_post(6)
% 5.15/5.51 thf(fact_9517_xor__int__unfold,axiom,
% 5.15/5.51 ( bit_se6526347334894502574or_int
% 5.15/5.51 = ( ^ [K2: int,L2: int] :
% 5.15/5.51 ( if_int
% 5.15/5.51 @ ( K2
% 5.15/5.51 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.51 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 5.15/5.51 @ ( if_int
% 5.15/5.51 @ ( L2
% 5.15/5.51 = ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.51 @ ( bit_ri7919022796975470100ot_int @ K2 )
% 5.15/5.51 @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_int_unfold
% 5.15/5.51 thf(fact_9518_VEBT__internal_Oheight_Opelims,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT,Y: nat] :
% 5.15/5.51 ( ( ( vEBT_VEBT_height @ X )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X )
% 5.15/5.51 => ( ! [A5: $o,B6: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.51 => ( ( Y = zero_zero_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A5 @ B6 ) ) ) )
% 5.15/5.51 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.51 => ( ( Y
% 5.15/5.51 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList3 ) ) ) ) ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu2 @ Deg2 @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT_internal.height.pelims
% 5.15/5.51 thf(fact_9519_not__nonnegative__int__iff,axiom,
% 5.15/5.51 ! [K: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.15/5.51 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % not_nonnegative_int_iff
% 5.15/5.51 thf(fact_9520_not__negative__int__iff,axiom,
% 5.15/5.51 ! [K: int] :
% 5.15/5.51 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.15/5.51 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % not_negative_int_iff
% 5.15/5.51 thf(fact_9521_or__minus__minus__numerals,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.51 = ( 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 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_minus_minus_numerals
% 5.15/5.51 thf(fact_9522_and__minus__minus__numerals,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.51 = ( 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 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % and_minus_minus_numerals
% 5.15/5.51 thf(fact_9523_bit__not__int__iff,axiom,
% 5.15/5.51 ! [K: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N2 )
% 5.15/5.51 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_not_int_iff
% 5.15/5.51 thf(fact_9524_or__int__def,axiom,
% 5.15/5.51 ( bit_se1409905431419307370or_int
% 5.15/5.51 = ( ^ [K2: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_int_def
% 5.15/5.51 thf(fact_9525_not__int__def,axiom,
% 5.15/5.51 ( bit_ri7919022796975470100ot_int
% 5.15/5.51 = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % not_int_def
% 5.15/5.51 thf(fact_9526_and__not__numerals_I1_J,axiom,
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.15/5.51 = zero_zero_int ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(1)
% 5.15/5.51 thf(fact_9527_or__not__numerals_I1_J,axiom,
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.15/5.51 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(1)
% 5.15/5.51 thf(fact_9528_unset__bit__int__def,axiom,
% 5.15/5.51 ( bit_se4203085406695923979it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % unset_bit_int_def
% 5.15/5.51 thf(fact_9529_xor__int__def,axiom,
% 5.15/5.51 ( bit_se6526347334894502574or_int
% 5.15/5.51 = ( ^ [K2: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ L2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_int_def
% 5.15/5.51 thf(fact_9530_not__int__div__2,axiom,
% 5.15/5.51 ! [K: int] :
% 5.15/5.51 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.51 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % not_int_div_2
% 5.15/5.51 thf(fact_9531_even__not__iff__int,axiom,
% 5.15/5.51 ! [K: int] :
% 5.15/5.51 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.15/5.51 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % even_not_iff_int
% 5.15/5.51 thf(fact_9532_and__not__numerals_I4_J,axiom,
% 5.15/5.51 ! [M: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.15/5.51 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(4)
% 5.15/5.51 thf(fact_9533_and__not__numerals_I2_J,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.51 = one_one_int ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(2)
% 5.15/5.51 thf(fact_9534_or__not__numerals_I4_J,axiom,
% 5.15/5.51 ! [M: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.15/5.51 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(4)
% 5.15/5.51 thf(fact_9535_or__not__numerals_I2_J,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.51 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(2)
% 5.15/5.51 thf(fact_9536_bit__minus__int__iff,axiom,
% 5.15/5.51 ! [K: int,N2: nat] :
% 5.15/5.51 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N2 )
% 5.15/5.51 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_minus_int_iff
% 5.15/5.51 thf(fact_9537_int__numeral__or__not__num__neg,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % int_numeral_or_not_num_neg
% 5.15/5.51 thf(fact_9538_int__numeral__not__or__num__neg,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % int_numeral_not_or_num_neg
% 5.15/5.51 thf(fact_9539_numeral__or__not__num__eq,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) )
% 5.15/5.51 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % numeral_or_not_num_eq
% 5.15/5.51 thf(fact_9540_and__not__numerals_I5_J,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(5)
% 5.15/5.51 thf(fact_9541_and__not__numerals_I7_J,axiom,
% 5.15/5.51 ! [M: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.15/5.51 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(7)
% 5.15/5.51 thf(fact_9542_or__not__numerals_I3_J,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.51 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(3)
% 5.15/5.51 thf(fact_9543_and__not__numerals_I3_J,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.51 = zero_zero_int ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(3)
% 5.15/5.51 thf(fact_9544_or__not__numerals_I7_J,axiom,
% 5.15/5.51 ! [M: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.15/5.51 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(7)
% 5.15/5.51 thf(fact_9545_and__not__numerals_I6_J,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(6)
% 5.15/5.51 thf(fact_9546_and__not__numerals_I9_J,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(9)
% 5.15/5.51 thf(fact_9547_or__not__numerals_I6_J,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(6)
% 5.15/5.51 thf(fact_9548_or__not__numerals_I5_J,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(5)
% 5.15/5.51 thf(fact_9549_and__not__numerals_I8_J,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % and_not_numerals(8)
% 5.15/5.51 thf(fact_9550_or__not__numerals_I9_J,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(9)
% 5.15/5.51 thf(fact_9551_or__not__numerals_I8_J,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % or_not_numerals(8)
% 5.15/5.51 thf(fact_9552_not__int__rec,axiom,
% 5.15/5.51 ( bit_ri7919022796975470100ot_int
% 5.15/5.51 = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % not_int_rec
% 5.15/5.51 thf(fact_9553_vebt__maxt_Opelims,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.15/5.51 ( ( ( vEBT_vebt_maxt @ X )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 5.15/5.51 => ( ! [A5: $o,B6: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.51 => ( ( ( B6
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.51 & ( ~ B6
% 5.15/5.51 => ( ( A5
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.51 & ( ~ A5
% 5.15/5.51 => ( Y = none_nat ) ) ) ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B6 ) ) ) )
% 5.15/5.51 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.51 => ( ( Y = none_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.15/5.51 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.51 => ( ( Y
% 5.15/5.51 = ( some_nat @ Ma2 ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % vebt_maxt.pelims
% 5.15/5.51 thf(fact_9554_vebt__mint_Opelims,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.15/5.51 ( ( ( vEBT_vebt_mint @ X )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 5.15/5.51 => ( ! [A5: $o,B6: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.51 => ( ( ( A5
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( some_nat @ zero_zero_nat ) ) )
% 5.15/5.51 & ( ~ A5
% 5.15/5.51 => ( ( B6
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( some_nat @ one_one_nat ) ) )
% 5.15/5.51 & ( ~ B6
% 5.15/5.51 => ( Y = none_nat ) ) ) ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B6 ) ) ) )
% 5.15/5.51 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.51 => ( ( Y = none_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.15/5.51 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.51 => ( ( Y
% 5.15/5.51 = ( some_nat @ Mi2 ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % vebt_mint.pelims
% 5.15/5.51 thf(fact_9555_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT,Y: nat] :
% 5.15/5.51 ( ( ( vEBT_T_m_i_n_t @ X )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X )
% 5.15/5.51 => ( ! [A5: $o,B6: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.51 => ( ( Y
% 5.15/5.51 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A5 @ B6 ) ) ) )
% 5.15/5.51 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.15/5.51 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.pelims
% 5.15/5.51 thf(fact_9556_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT,Y: nat] :
% 5.15/5.51 ( ( ( vEBT_T_m_a_x_t @ X )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X )
% 5.15/5.51 => ( ! [A5: $o,B6: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ A5 @ B6 ) )
% 5.15/5.51 => ( ( Y
% 5.15/5.51 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B6 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A5 @ B6 ) ) ) )
% 5.15/5.51 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.15/5.51 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.pelims
% 5.15/5.51 thf(fact_9557_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Opelims,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT,Y: nat] :
% 5.15/5.51 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X )
% 5.15/5.51 => ( ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.15/5.51 => ( ! [Uv2: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.15/5.51 => ( ! [Uu2: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.15/5.51 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.15/5.51 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.15/5.51 => ( ( Y = one_one_nat )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.pelims
% 5.15/5.51 thf(fact_9558_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT,Y: $o] :
% 5.15/5.51 ( ( ( vEBT_VEBT_minNull @ X )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.15/5.51 => ( ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.51 => ( Y
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.15/5.51 => ( ! [Uv2: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.15/5.51 => ( ~ Y
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.15/5.51 => ( ! [Uu2: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.15/5.51 => ( ~ Y
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.15/5.51 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.15/5.51 => ( Y
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.15/5.51 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.15/5.51 => ( ~ Y
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT_internal.minNull.pelims(1)
% 5.15/5.51 thf(fact_9559_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT] :
% 5.15/5.51 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.15/5.51 => ( ! [Uv2: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.15/5.51 => ( ! [Uu2: $o] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.15/5.51 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT_internal.minNull.pelims(3)
% 5.15/5.51 thf(fact_9560_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.15/5.51 ! [X: vEBT_VEBT] :
% 5.15/5.51 ( ( vEBT_VEBT_minNull @ X )
% 5.15/5.51 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.15/5.51 => ( ( ( X
% 5.15/5.51 = ( vEBT_Leaf @ $false @ $false ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.15/5.51 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.15/5.51 ( ( X
% 5.15/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.15/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT_internal.minNull.pelims(2)
% 5.15/5.51 thf(fact_9561_Cauchy__iff2,axiom,
% 5.15/5.51 ( topolo4055970368930404560y_real
% 5.15/5.51 = ( ^ [X4: nat > real] :
% 5.15/5.51 ! [J3: nat] :
% 5.15/5.51 ? [M8: nat] :
% 5.15/5.51 ! [M5: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ M8 @ M5 )
% 5.15/5.51 => ! [N3: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ M8 @ N3 )
% 5.15/5.51 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X4 @ M5 ) @ ( X4 @ N3 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Cauchy_iff2
% 5.15/5.51 thf(fact_9562_Sum__Ico__nat,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [X2: nat] : X2
% 5.15/5.51 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.15/5.51 = ( 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 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Sum_Ico_nat
% 5.15/5.51 thf(fact_9563_image__Suc__atLeastLessThan,axiom,
% 5.15/5.51 ! [I: nat,J: nat] :
% 5.15/5.51 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.15/5.51 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % image_Suc_atLeastLessThan
% 5.15/5.51 thf(fact_9564_atLeastLessThan__singleton,axiom,
% 5.15/5.51 ! [M: nat] :
% 5.15/5.51 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.15/5.51 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeastLessThan_singleton
% 5.15/5.51 thf(fact_9565_ex__nat__less__eq,axiom,
% 5.15/5.51 ! [N2: nat,P: nat > $o] :
% 5.15/5.51 ( ( ? [M5: nat] :
% 5.15/5.51 ( ( ord_less_nat @ M5 @ N2 )
% 5.15/5.51 & ( P @ M5 ) ) )
% 5.15/5.51 = ( ? [X2: nat] :
% 5.15/5.51 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.51 & ( P @ X2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % ex_nat_less_eq
% 5.15/5.51 thf(fact_9566_all__nat__less__eq,axiom,
% 5.15/5.51 ! [N2: nat,P: nat > $o] :
% 5.15/5.51 ( ( ! [M5: nat] :
% 5.15/5.51 ( ( ord_less_nat @ M5 @ N2 )
% 5.15/5.51 => ( P @ M5 ) ) )
% 5.15/5.51 = ( ! [X2: nat] :
% 5.15/5.51 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.51 => ( P @ X2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % all_nat_less_eq
% 5.15/5.51 thf(fact_9567_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.15/5.51 ! [L: nat,U: nat] :
% 5.15/5.51 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.15/5.51 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeastLessThanSuc_atLeastAtMost
% 5.15/5.51 thf(fact_9568_atLeast0__lessThan__Suc,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.15/5.51 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeast0_lessThan_Suc
% 5.15/5.51 thf(fact_9569_atLeastLessThanSuc,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.51 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.15/5.51 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 5.15/5.51 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.51 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.15/5.51 = bot_bot_set_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeastLessThanSuc
% 5.15/5.51 thf(fact_9570_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.15/5.51 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeast0_lessThan_Suc_eq_insert_0
% 5.15/5.51 thf(fact_9571_prod__Suc__Suc__fact,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.15/5.51 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_Suc_Suc_fact
% 5.15/5.51 thf(fact_9572_prod__Suc__fact,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.51 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_Suc_fact
% 5.15/5.51 thf(fact_9573_atLeastLessThan__nat__numeral,axiom,
% 5.15/5.51 ! [M: nat,K: num] :
% 5.15/5.51 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.15/5.51 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.15/5.51 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.15/5.51 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.15/5.51 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.15/5.51 = bot_bot_set_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeastLessThan_nat_numeral
% 5.15/5.51 thf(fact_9574_image__minus__const__atLeastLessThan__nat,axiom,
% 5.15/5.51 ! [C: nat,Y: nat,X: nat] :
% 5.15/5.51 ( ( ( ord_less_nat @ C @ Y )
% 5.15/5.51 => ( ( image_nat_nat
% 5.15/5.51 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.15/5.51 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.15/5.51 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.15/5.51 & ( ~ ( ord_less_nat @ C @ Y )
% 5.15/5.51 => ( ( ( ord_less_nat @ X @ Y )
% 5.15/5.51 => ( ( image_nat_nat
% 5.15/5.51 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.15/5.51 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.15/5.51 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.15/5.51 & ( ~ ( ord_less_nat @ X @ Y )
% 5.15/5.51 => ( ( image_nat_nat
% 5.15/5.51 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.15/5.51 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.15/5.51 = bot_bot_set_nat ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % image_minus_const_atLeastLessThan_nat
% 5.15/5.51 thf(fact_9575_atLeast1__lessThan__eq__remove0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.15/5.51 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % atLeast1_lessThan_eq_remove0
% 5.15/5.51 thf(fact_9576_sum__power2,axiom,
% 5.15/5.51 ! [K: nat] :
% 5.15/5.51 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.15/5.51 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % sum_power2
% 5.15/5.51 thf(fact_9577_Chebyshev__sum__upper__nat,axiom,
% 5.15/5.51 ! [N2: nat,A: nat > nat,B: nat > nat] :
% 5.15/5.51 ( ! [I2: nat,J2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.15/5.51 => ( ( ord_less_nat @ J2 @ N2 )
% 5.15/5.51 => ( ord_less_eq_nat @ ( A @ I2 ) @ ( A @ J2 ) ) ) )
% 5.15/5.51 => ( ! [I2: nat,J2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.15/5.51 => ( ( ord_less_nat @ J2 @ N2 )
% 5.15/5.51 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I2 ) ) ) )
% 5.15/5.51 => ( ord_less_eq_nat
% 5.15/5.51 @ ( times_times_nat @ N2
% 5.15/5.51 @ ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 5.15/5.51 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 5.15/5.51 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Chebyshev_sum_upper_nat
% 5.15/5.51 thf(fact_9578_image__add__int__atLeastLessThan,axiom,
% 5.15/5.51 ! [L: int,U: int] :
% 5.15/5.51 ( ( image_int_int
% 5.15/5.51 @ ^ [X2: int] : ( plus_plus_int @ X2 @ L )
% 5.15/5.51 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.15/5.51 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.15/5.51
% 5.15/5.51 % image_add_int_atLeastLessThan
% 5.15/5.51 thf(fact_9579_VEBT_Osize_I3_J,axiom,
% 5.15/5.51 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.15/5.51 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.15/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT.size(3)
% 5.15/5.51 thf(fact_9580_VEBT_Osize__gen_I1_J,axiom,
% 5.15/5.51 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.15/5.51 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.15/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT.size_gen(1)
% 5.15/5.51 thf(fact_9581_valid__eq2,axiom,
% 5.15/5.51 ! [T: vEBT_VEBT,D: nat] :
% 5.15/5.51 ( ( vEBT_VEBT_valid @ T @ D )
% 5.15/5.51 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.15/5.51
% 5.15/5.51 % valid_eq2
% 5.15/5.51 thf(fact_9582_valid__eq1,axiom,
% 5.15/5.51 ! [T: vEBT_VEBT,D: nat] :
% 5.15/5.51 ( ( vEBT_invar_vebt @ T @ D )
% 5.15/5.51 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.15/5.51
% 5.15/5.51 % valid_eq1
% 5.15/5.51 thf(fact_9583_valid__eq,axiom,
% 5.15/5.51 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.15/5.51
% 5.15/5.51 % valid_eq
% 5.15/5.51 thf(fact_9584_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.15/5.51 ! [Uu: $o,Uv: $o,D: nat] :
% 5.15/5.51 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.15/5.51 = ( D = one_one_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT_internal.valid'.simps(1)
% 5.15/5.51 thf(fact_9585_VEBT_Osize__gen_I2_J,axiom,
% 5.15/5.51 ! [X21: $o,X222: $o] :
% 5.15/5.51 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.15/5.51 = zero_zero_nat ) ).
% 5.15/5.51
% 5.15/5.51 % VEBT.size_gen(2)
% 5.15/5.51 thf(fact_9586_Code__Target__Int_Opositive__def,axiom,
% 5.15/5.51 code_Target_positive = numeral_numeral_int ).
% 5.15/5.51
% 5.15/5.51 % Code_Target_Int.positive_def
% 5.15/5.51 thf(fact_9587_csqrt_Osimps_I1_J,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( re @ ( csqrt @ Z ) )
% 5.15/5.51 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt.simps(1)
% 5.15/5.51 thf(fact_9588_divmod__step__integer__def,axiom,
% 5.15/5.51 ( unique4921790084139445826nteger
% 5.15/5.51 = ( ^ [L2: num] :
% 5.15/5.51 ( produc6916734918728496179nteger
% 5.15/5.51 @ ^ [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 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divmod_step_integer_def
% 5.15/5.51 thf(fact_9589_complex__Re__numeral,axiom,
% 5.15/5.51 ! [V: num] :
% 5.15/5.51 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.15/5.51 = ( numeral_numeral_real @ V ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_Re_numeral
% 5.15/5.51 thf(fact_9590_Re__divide__of__nat,axiom,
% 5.15/5.51 ! [Z: complex,N2: nat] :
% 5.15/5.51 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.15/5.51 = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_divide_of_nat
% 5.15/5.51 thf(fact_9591_Re__divide__of__real,axiom,
% 5.15/5.51 ! [Z: complex,R2: real] :
% 5.15/5.51 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 5.15/5.51 = ( divide_divide_real @ ( re @ Z ) @ R2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_divide_of_real
% 5.15/5.51 thf(fact_9592_Re__sgn,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( re @ ( sgn_sgn_complex @ Z ) )
% 5.15/5.51 = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_sgn
% 5.15/5.51 thf(fact_9593_Re__divide__numeral,axiom,
% 5.15/5.51 ! [Z: complex,W: num] :
% 5.15/5.51 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.51 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_divide_numeral
% 5.15/5.51 thf(fact_9594_times__integer__code_I1_J,axiom,
% 5.15/5.51 ! [K: code_integer] :
% 5.15/5.51 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.15/5.51 = zero_z3403309356797280102nteger ) ).
% 5.15/5.51
% 5.15/5.51 % times_integer_code(1)
% 5.15/5.51 thf(fact_9595_times__integer__code_I2_J,axiom,
% 5.15/5.51 ! [L: code_integer] :
% 5.15/5.51 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 5.15/5.51 = zero_z3403309356797280102nteger ) ).
% 5.15/5.51
% 5.15/5.51 % times_integer_code(2)
% 5.15/5.51 thf(fact_9596_divmod__integer_H__def,axiom,
% 5.15/5.51 ( unique3479559517661332726nteger
% 5.15/5.51 = ( ^ [M5: num,N3: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N3 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divmod_integer'_def
% 5.15/5.51 thf(fact_9597_sums__Re,axiom,
% 5.15/5.51 ! [X8: nat > complex,A: complex] :
% 5.15/5.51 ( ( sums_complex @ X8 @ A )
% 5.15/5.51 => ( sums_real
% 5.15/5.51 @ ^ [N3: nat] : ( re @ ( X8 @ N3 ) )
% 5.15/5.51 @ ( re @ A ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sums_Re
% 5.15/5.51 thf(fact_9598_Cauchy__Re,axiom,
% 5.15/5.51 ! [X8: nat > complex] :
% 5.15/5.51 ( ( topolo6517432010174082258omplex @ X8 )
% 5.15/5.51 => ( topolo4055970368930404560y_real
% 5.15/5.51 @ ^ [N3: nat] : ( re @ ( X8 @ N3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Cauchy_Re
% 5.15/5.51 thf(fact_9599_complex__Re__le__cmod,axiom,
% 5.15/5.51 ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_Re_le_cmod
% 5.15/5.51 thf(fact_9600_one__complex_Osimps_I1_J,axiom,
% 5.15/5.51 ( ( re @ one_one_complex )
% 5.15/5.51 = one_one_real ) ).
% 5.15/5.51
% 5.15/5.51 % one_complex.simps(1)
% 5.15/5.51 thf(fact_9601_plus__complex_Osimps_I1_J,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( re @ ( plus_plus_complex @ X @ Y ) )
% 5.15/5.51 = ( plus_plus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % plus_complex.simps(1)
% 5.15/5.51 thf(fact_9602_scaleR__complex_Osimps_I1_J,axiom,
% 5.15/5.51 ! [R2: real,X: complex] :
% 5.15/5.51 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.15/5.51 = ( times_times_real @ R2 @ ( re @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % scaleR_complex.simps(1)
% 5.15/5.51 thf(fact_9603_minus__complex_Osimps_I1_J,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( re @ ( minus_minus_complex @ X @ Y ) )
% 5.15/5.51 = ( minus_minus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % minus_complex.simps(1)
% 5.15/5.51 thf(fact_9604_summable__Re,axiom,
% 5.15/5.51 ! [F: nat > complex] :
% 5.15/5.51 ( ( summable_complex @ F )
% 5.15/5.51 => ( summable_real
% 5.15/5.51 @ ^ [X2: nat] : ( re @ ( F @ X2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % summable_Re
% 5.15/5.51 thf(fact_9605_abs__Re__le__cmod,axiom,
% 5.15/5.51 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % abs_Re_le_cmod
% 5.15/5.51 thf(fact_9606_Re__csqrt,axiom,
% 5.15/5.51 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_csqrt
% 5.15/5.51 thf(fact_9607_one__natural_Orsp,axiom,
% 5.15/5.51 one_one_nat = one_one_nat ).
% 5.15/5.51
% 5.15/5.51 % one_natural.rsp
% 5.15/5.51 thf(fact_9608_cmod__plus__Re__le__0__iff,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.15/5.51 = ( ( re @ Z )
% 5.15/5.51 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cmod_plus_Re_le_0_iff
% 5.15/5.51 thf(fact_9609_cos__n__Re__cis__pow__n,axiom,
% 5.15/5.51 ! [N2: nat,A: real] :
% 5.15/5.51 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) )
% 5.15/5.51 = ( re @ ( power_power_complex @ ( cis @ A ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cos_n_Re_cis_pow_n
% 5.15/5.51 thf(fact_9610_csqrt_Ocode,axiom,
% 5.15/5.51 ( csqrt
% 5.15/5.51 = ( ^ [Z3: complex] :
% 5.15/5.51 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.51 @ ( times_times_real
% 5.15/5.51 @ ( if_real
% 5.15/5.51 @ ( ( im @ Z3 )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 @ one_one_real
% 5.15/5.51 @ ( sgn_sgn_real @ ( im @ Z3 ) ) )
% 5.15/5.51 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt.code
% 5.15/5.51 thf(fact_9611_csqrt_Osimps_I2_J,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( im @ ( csqrt @ Z ) )
% 5.15/5.51 = ( times_times_real
% 5.15/5.51 @ ( if_real
% 5.15/5.51 @ ( ( im @ Z )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 @ one_one_real
% 5.15/5.51 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.15/5.51 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt.simps(2)
% 5.15/5.51 thf(fact_9612_integer__of__int__code,axiom,
% 5.15/5.51 ( code_integer_of_int
% 5.15/5.51 = ( ^ [K2: int] :
% 5.15/5.51 ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.15/5.51 @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.15/5.51 @ ( if_Code_integer
% 5.15/5.51 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.15/5.51 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % integer_of_int_code
% 5.15/5.51 thf(fact_9613_Im__i__times,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.15/5.51 = ( re @ Z ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_i_times
% 5.15/5.51 thf(fact_9614_Im__divide__of__real,axiom,
% 5.15/5.51 ! [Z: complex,R2: real] :
% 5.15/5.51 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 5.15/5.51 = ( divide_divide_real @ ( im @ Z ) @ R2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_divide_of_real
% 5.15/5.51 thf(fact_9615_Im__sgn,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( im @ ( sgn_sgn_complex @ Z ) )
% 5.15/5.51 = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_sgn
% 5.15/5.51 thf(fact_9616_Re__power__real,axiom,
% 5.15/5.51 ! [X: complex,N2: nat] :
% 5.15/5.51 ( ( ( im @ X )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 => ( ( re @ ( power_power_complex @ X @ N2 ) )
% 5.15/5.51 = ( power_power_real @ ( re @ X ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_power_real
% 5.15/5.51 thf(fact_9617_Re__i__times,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.15/5.51 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_i_times
% 5.15/5.51 thf(fact_9618_Im__divide__numeral,axiom,
% 5.15/5.51 ! [Z: complex,W: num] :
% 5.15/5.51 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.15/5.51 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_divide_numeral
% 5.15/5.51 thf(fact_9619_Im__divide__of__nat,axiom,
% 5.15/5.51 ! [Z: complex,N2: nat] :
% 5.15/5.51 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.15/5.51 = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_divide_of_nat
% 5.15/5.51 thf(fact_9620_csqrt__of__real__nonneg,axiom,
% 5.15/5.51 ! [X: complex] :
% 5.15/5.51 ( ( ( im @ X )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 5.15/5.51 => ( ( csqrt @ X )
% 5.15/5.51 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt_of_real_nonneg
% 5.15/5.51 thf(fact_9621_csqrt__minus,axiom,
% 5.15/5.51 ! [X: complex] :
% 5.15/5.51 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.15/5.51 | ( ( ( im @ X )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.15/5.51 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.15/5.51 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt_minus
% 5.15/5.51 thf(fact_9622_csqrt__of__real__nonpos,axiom,
% 5.15/5.51 ! [X: complex] :
% 5.15/5.51 ( ( ( im @ X )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 5.15/5.51 => ( ( csqrt @ X )
% 5.15/5.51 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt_of_real_nonpos
% 5.15/5.51 thf(fact_9623_divide__integer_Oabs__eq,axiom,
% 5.15/5.51 ! [Xa2: int,X: int] :
% 5.15/5.51 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.15/5.51 = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divide_integer.abs_eq
% 5.15/5.51 thf(fact_9624_sums__Im,axiom,
% 5.15/5.51 ! [X8: nat > complex,A: complex] :
% 5.15/5.51 ( ( sums_complex @ X8 @ A )
% 5.15/5.51 => ( sums_real
% 5.15/5.51 @ ^ [N3: nat] : ( im @ ( X8 @ N3 ) )
% 5.15/5.51 @ ( im @ A ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sums_Im
% 5.15/5.51 thf(fact_9625_Cauchy__Im,axiom,
% 5.15/5.51 ! [X8: nat > complex] :
% 5.15/5.51 ( ( topolo6517432010174082258omplex @ X8 )
% 5.15/5.51 => ( topolo4055970368930404560y_real
% 5.15/5.51 @ ^ [N3: nat] : ( im @ ( X8 @ N3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Cauchy_Im
% 5.15/5.51 thf(fact_9626_imaginary__unit_Osimps_I2_J,axiom,
% 5.15/5.51 ( ( im @ imaginary_unit )
% 5.15/5.51 = one_one_real ) ).
% 5.15/5.51
% 5.15/5.51 % imaginary_unit.simps(2)
% 5.15/5.51 thf(fact_9627_times__integer_Oabs__eq,axiom,
% 5.15/5.51 ! [Xa2: int,X: int] :
% 5.15/5.51 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.15/5.51 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % times_integer.abs_eq
% 5.15/5.51 thf(fact_9628_plus__complex_Osimps_I2_J,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( im @ ( plus_plus_complex @ X @ Y ) )
% 5.15/5.51 = ( plus_plus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % plus_complex.simps(2)
% 5.15/5.51 thf(fact_9629_scaleR__complex_Osimps_I2_J,axiom,
% 5.15/5.51 ! [R2: real,X: complex] :
% 5.15/5.51 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.15/5.51 = ( times_times_real @ R2 @ ( im @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % scaleR_complex.simps(2)
% 5.15/5.51 thf(fact_9630_minus__complex_Osimps_I2_J,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( im @ ( minus_minus_complex @ X @ Y ) )
% 5.15/5.51 = ( minus_minus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % minus_complex.simps(2)
% 5.15/5.51 thf(fact_9631_sums__complex__iff,axiom,
% 5.15/5.51 ( sums_complex
% 5.15/5.51 = ( ^ [F3: nat > complex,X2: complex] :
% 5.15/5.51 ( ( sums_real
% 5.15/5.51 @ ^ [Y2: nat] : ( re @ ( F3 @ Y2 ) )
% 5.15/5.51 @ ( re @ X2 ) )
% 5.15/5.51 & ( sums_real
% 5.15/5.51 @ ^ [Y2: nat] : ( im @ ( F3 @ Y2 ) )
% 5.15/5.51 @ ( im @ X2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sums_complex_iff
% 5.15/5.51 thf(fact_9632_summable__Im,axiom,
% 5.15/5.51 ! [F: nat > complex] :
% 5.15/5.51 ( ( summable_complex @ F )
% 5.15/5.51 => ( summable_real
% 5.15/5.51 @ ^ [X2: nat] : ( im @ ( F @ X2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % summable_Im
% 5.15/5.51 thf(fact_9633_abs__Im__le__cmod,axiom,
% 5.15/5.51 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % abs_Im_le_cmod
% 5.15/5.51 thf(fact_9634_summable__complex__iff,axiom,
% 5.15/5.51 ( summable_complex
% 5.15/5.51 = ( ^ [F3: nat > complex] :
% 5.15/5.51 ( ( summable_real
% 5.15/5.51 @ ^ [X2: nat] : ( re @ ( F3 @ X2 ) ) )
% 5.15/5.51 & ( summable_real
% 5.15/5.51 @ ^ [X2: nat] : ( im @ ( F3 @ X2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % summable_complex_iff
% 5.15/5.51 thf(fact_9635_times__complex_Osimps_I2_J,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( im @ ( times_times_complex @ X @ Y ) )
% 5.15/5.51 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % times_complex.simps(2)
% 5.15/5.51 thf(fact_9636_cmod__Re__le__iff,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( ( im @ X )
% 5.15/5.51 = ( im @ Y ) )
% 5.15/5.51 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.15/5.51 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cmod_Re_le_iff
% 5.15/5.51 thf(fact_9637_cmod__Im__le__iff,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( ( re @ X )
% 5.15/5.51 = ( re @ Y ) )
% 5.15/5.51 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.15/5.51 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cmod_Im_le_iff
% 5.15/5.51 thf(fact_9638_times__complex_Osimps_I1_J,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( re @ ( times_times_complex @ X @ Y ) )
% 5.15/5.51 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % times_complex.simps(1)
% 5.15/5.51 thf(fact_9639_plus__complex_Ocode,axiom,
% 5.15/5.51 ( plus_plus_complex
% 5.15/5.51 = ( ^ [X2: complex,Y2: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % plus_complex.code
% 5.15/5.51 thf(fact_9640_scaleR__complex_Ocode,axiom,
% 5.15/5.51 ( real_V2046097035970521341omplex
% 5.15/5.51 = ( ^ [R5: real,X2: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X2 ) ) @ ( times_times_real @ R5 @ ( im @ X2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % scaleR_complex.code
% 5.15/5.51 thf(fact_9641_minus__complex_Ocode,axiom,
% 5.15/5.51 ( minus_minus_complex
% 5.15/5.51 = ( ^ [X2: complex,Y2: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( minus_minus_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % minus_complex.code
% 5.15/5.51 thf(fact_9642_csqrt__principal,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.15/5.51 | ( ( ( re @ ( csqrt @ Z ) )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt_principal
% 5.15/5.51 thf(fact_9643_cmod__le,axiom,
% 5.15/5.51 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cmod_le
% 5.15/5.51 thf(fact_9644_sin__n__Im__cis__pow__n,axiom,
% 5.15/5.51 ! [N2: nat,A: real] :
% 5.15/5.51 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) )
% 5.15/5.51 = ( im @ ( power_power_complex @ ( cis @ A ) @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sin_n_Im_cis_pow_n
% 5.15/5.51 thf(fact_9645_Re__exp,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( re @ ( exp_complex @ Z ) )
% 5.15/5.51 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_exp
% 5.15/5.51 thf(fact_9646_Im__exp,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( im @ ( exp_complex @ Z ) )
% 5.15/5.51 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_exp
% 5.15/5.51 thf(fact_9647_complex__eq,axiom,
% 5.15/5.51 ! [A: complex] :
% 5.15/5.51 ( A
% 5.15/5.51 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_eq
% 5.15/5.51 thf(fact_9648_times__complex_Ocode,axiom,
% 5.15/5.51 ( times_times_complex
% 5.15/5.51 = ( ^ [X2: complex,Y2: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % times_complex.code
% 5.15/5.51 thf(fact_9649_exp__eq__polar,axiom,
% 5.15/5.51 ( exp_complex
% 5.15/5.51 = ( ^ [Z3: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z3 ) ) ) @ ( cis @ ( im @ Z3 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % exp_eq_polar
% 5.15/5.51 thf(fact_9650_cmod__power2,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.51 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cmod_power2
% 5.15/5.51 thf(fact_9651_Im__power2,axiom,
% 5.15/5.51 ! [X: complex] :
% 5.15/5.51 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.51 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_power2
% 5.15/5.51 thf(fact_9652_Re__power2,axiom,
% 5.15/5.51 ! [X: complex] :
% 5.15/5.51 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.51 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_power2
% 5.15/5.51 thf(fact_9653_complex__eq__0,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( Z = zero_zero_complex )
% 5.15/5.51 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.51 = zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_eq_0
% 5.15/5.51 thf(fact_9654_norm__complex__def,axiom,
% 5.15/5.51 ( real_V1022390504157884413omplex
% 5.15/5.51 = ( ^ [Z3: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % norm_complex_def
% 5.15/5.51 thf(fact_9655_inverse__complex_Osimps_I1_J,axiom,
% 5.15/5.51 ! [X: complex] :
% 5.15/5.51 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 5.15/5.51 = ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % inverse_complex.simps(1)
% 5.15/5.51 thf(fact_9656_complex__neq__0,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( Z != zero_zero_complex )
% 5.15/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_neq_0
% 5.15/5.51 thf(fact_9657_Re__divide,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.15/5.51 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_divide
% 5.15/5.51 thf(fact_9658_csqrt__square,axiom,
% 5.15/5.51 ! [B: complex] :
% 5.15/5.51 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.15/5.51 | ( ( ( re @ B )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.15/5.51 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.51 = B ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt_square
% 5.15/5.51 thf(fact_9659_csqrt__unique,axiom,
% 5.15/5.51 ! [W: complex,Z: complex] :
% 5.15/5.51 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.15/5.51 = Z )
% 5.15/5.51 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.15/5.51 | ( ( ( re @ W )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.15/5.51 => ( ( csqrt @ Z )
% 5.15/5.51 = W ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % csqrt_unique
% 5.15/5.51 thf(fact_9660_inverse__complex_Osimps_I2_J,axiom,
% 5.15/5.51 ! [X: complex] :
% 5.15/5.51 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 5.15/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % inverse_complex.simps(2)
% 5.15/5.51 thf(fact_9661_Im__divide,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.15/5.51 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_divide
% 5.15/5.51 thf(fact_9662_complex__abs__le__norm,axiom,
% 5.15/5.51 ! [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 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_abs_le_norm
% 5.15/5.51 thf(fact_9663_complex__unit__circle,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( Z != zero_zero_complex )
% 5.15/5.51 => ( ( 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 ) ) ) )
% 5.15/5.51 = one_one_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_unit_circle
% 5.15/5.51 thf(fact_9664_inverse__complex_Ocode,axiom,
% 5.15/5.51 ( invers8013647133539491842omplex
% 5.15/5.51 = ( ^ [X2: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % inverse_complex.code
% 5.15/5.51 thf(fact_9665_Complex__divide,axiom,
% 5.15/5.51 ( divide1717551699836669952omplex
% 5.15/5.51 = ( ^ [X2: complex,Y2: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Complex_divide
% 5.15/5.51 thf(fact_9666_Im__Reals__divide,axiom,
% 5.15/5.51 ! [R2: complex,Z: complex] :
% 5.15/5.51 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.15/5.51 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.15/5.51 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_Reals_divide
% 5.15/5.51 thf(fact_9667_Re__Reals__divide,axiom,
% 5.15/5.51 ! [R2: complex,Z: complex] :
% 5.15/5.51 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.15/5.51 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.15/5.51 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_Reals_divide
% 5.15/5.51 thf(fact_9668_Re__divide__Reals,axiom,
% 5.15/5.51 ! [R2: complex,Z: complex] :
% 5.15/5.51 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.15/5.51 => ( ( re @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 5.15/5.51 = ( divide_divide_real @ ( re @ Z ) @ ( re @ R2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_divide_Reals
% 5.15/5.51 thf(fact_9669_imaginary__eq__real__iff,axiom,
% 5.15/5.51 ! [Y: complex,X: complex] :
% 5.15/5.51 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.15/5.51 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.15/5.51 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 5.15/5.51 = X )
% 5.15/5.51 = ( ( X = zero_zero_complex )
% 5.15/5.51 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % imaginary_eq_real_iff
% 5.15/5.51 thf(fact_9670_real__eq__imaginary__iff,axiom,
% 5.15/5.51 ! [Y: complex,X: complex] :
% 5.15/5.51 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.15/5.51 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.15/5.51 => ( ( X
% 5.15/5.51 = ( times_times_complex @ imaginary_unit @ Y ) )
% 5.15/5.51 = ( ( X = zero_zero_complex )
% 5.15/5.51 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % real_eq_imaginary_iff
% 5.15/5.51 thf(fact_9671_Im__divide__Reals,axiom,
% 5.15/5.51 ! [R2: complex,Z: complex] :
% 5.15/5.51 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.15/5.51 => ( ( im @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 5.15/5.51 = ( divide_divide_real @ ( im @ Z ) @ ( re @ R2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_divide_Reals
% 5.15/5.51 thf(fact_9672_complex__diff__cnj,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.15/5.51 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_diff_cnj
% 5.15/5.51 thf(fact_9673_complex__mult__cnj,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.15/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_mult_cnj
% 5.15/5.51 thf(fact_9674_complex__cnj__mult,axiom,
% 5.15/5.51 ! [X: complex,Y: complex] :
% 5.15/5.51 ( ( cnj @ ( times_times_complex @ X @ Y ) )
% 5.15/5.51 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_cnj_mult
% 5.15/5.51 thf(fact_9675_complex__In__mult__cnj__zero,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.15/5.51 = zero_zero_real ) ).
% 5.15/5.51
% 5.15/5.51 % complex_In_mult_cnj_zero
% 5.15/5.51 thf(fact_9676_sums__cnj,axiom,
% 5.15/5.51 ! [F: nat > complex,L: complex] :
% 5.15/5.51 ( ( sums_complex
% 5.15/5.51 @ ^ [X2: nat] : ( cnj @ ( F @ X2 ) )
% 5.15/5.51 @ ( cnj @ L ) )
% 5.15/5.51 = ( sums_complex @ F @ L ) ) ).
% 5.15/5.51
% 5.15/5.51 % sums_cnj
% 5.15/5.51 thf(fact_9677_Re__complex__div__eq__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.15/5.51 = zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_complex_div_eq_0
% 5.15/5.51 thf(fact_9678_Im__complex__div__eq__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.15/5.51 = zero_zero_real )
% 5.15/5.51 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.15/5.51 = zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_complex_div_eq_0
% 5.15/5.51 thf(fact_9679_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.15/5.51 ( real_V1022390504157884413omplex
% 5.15/5.51 = ( ^ [Z3: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_mod_sqrt_Re_mult_cnj
% 5.15/5.51 thf(fact_9680_Re__complex__div__gt__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.15/5.51 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_complex_div_gt_0
% 5.15/5.51 thf(fact_9681_Re__complex__div__lt__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_complex_div_lt_0
% 5.15/5.51 thf(fact_9682_Re__complex__div__ge__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.15/5.51 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_complex_div_ge_0
% 5.15/5.51 thf(fact_9683_Re__complex__div__le__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % Re_complex_div_le_0
% 5.15/5.51 thf(fact_9684_Im__complex__div__gt__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.15/5.51 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_complex_div_gt_0
% 5.15/5.51 thf(fact_9685_Im__complex__div__lt__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_complex_div_lt_0
% 5.15/5.51 thf(fact_9686_Im__complex__div__ge__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.15/5.51 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_complex_div_ge_0
% 5.15/5.51 thf(fact_9687_Im__complex__div__le__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.15/5.51 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.15/5.51
% 5.15/5.51 % Im_complex_div_le_0
% 5.15/5.51 thf(fact_9688_complex__mod__mult__cnj,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.15/5.51 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_mod_mult_cnj
% 5.15/5.51 thf(fact_9689_complex__div__gt__0,axiom,
% 5.15/5.51 ! [A: complex,B: complex] :
% 5.15/5.51 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.15/5.51 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.15/5.51 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.15/5.51 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_div_gt_0
% 5.15/5.51 thf(fact_9690_complex__norm__square,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.15/5.51 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_norm_square
% 5.15/5.51 thf(fact_9691_complex__add__cnj,axiom,
% 5.15/5.51 ! [Z: complex] :
% 5.15/5.51 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.15/5.51 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_add_cnj
% 5.15/5.51 thf(fact_9692_complex__div__cnj,axiom,
% 5.15/5.51 ( divide1717551699836669952omplex
% 5.15/5.51 = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % complex_div_cnj
% 5.15/5.51 thf(fact_9693_cnj__add__mult__eq__Re,axiom,
% 5.15/5.51 ! [Z: complex,W: complex] :
% 5.15/5.51 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.15/5.51 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % cnj_add_mult_eq_Re
% 5.15/5.51 thf(fact_9694_integer__of__num_I3_J,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( code_integer_of_num @ ( bit1 @ N2 ) )
% 5.15/5.51 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.15/5.51
% 5.15/5.51 % integer_of_num(3)
% 5.15/5.51 thf(fact_9695_bit__cut__integer__def,axiom,
% 5.15/5.51 ( code_bit_cut_integer
% 5.15/5.51 = ( ^ [K2: code_integer] :
% 5.15/5.51 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.15/5.51 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_cut_integer_def
% 5.15/5.51 thf(fact_9696_num__of__integer__code,axiom,
% 5.15/5.51 ( code_num_of_integer
% 5.15/5.51 = ( ^ [K2: code_integer] :
% 5.15/5.51 ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 5.15/5.51 @ ( produc7336495610019696514er_num
% 5.15/5.51 @ ^ [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 ) )
% 5.15/5.51 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % num_of_integer_code
% 5.15/5.51 thf(fact_9697_integer__of__num__triv_I1_J,axiom,
% 5.15/5.51 ( ( code_integer_of_num @ one )
% 5.15/5.51 = one_one_Code_integer ) ).
% 5.15/5.51
% 5.15/5.51 % integer_of_num_triv(1)
% 5.15/5.51 thf(fact_9698_integer__of__num_I2_J,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 5.15/5.51 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % integer_of_num(2)
% 5.15/5.51 thf(fact_9699_integer__of__num__triv_I2_J,axiom,
% 5.15/5.51 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.15/5.51 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % integer_of_num_triv(2)
% 5.15/5.51 thf(fact_9700_divmod__integer__def,axiom,
% 5.15/5.51 ( code_divmod_integer
% 5.15/5.51 = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L2 ) @ ( modulo364778990260209775nteger @ K2 @ L2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divmod_integer_def
% 5.15/5.51 thf(fact_9701_bit__cut__integer__code,axiom,
% 5.15/5.51 ( code_bit_cut_integer
% 5.15/5.51 = ( ^ [K2: code_integer] :
% 5.15/5.51 ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.15/5.51 @ ( produc9125791028180074456eger_o
% 5.15/5.51 @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 5.15/5.51 @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bit_cut_integer_code
% 5.15/5.51 thf(fact_9702_nat__of__integer__code,axiom,
% 5.15/5.51 ( code_nat_of_integer
% 5.15/5.51 = ( ^ [K2: code_integer] :
% 5.15/5.51 ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.15/5.51 @ ( produc1555791787009142072er_nat
% 5.15/5.51 @ ^ [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 ) )
% 5.15/5.51 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_of_integer_code
% 5.15/5.51 thf(fact_9703_int__of__integer__code,axiom,
% 5.15/5.51 ( code_int_of_integer
% 5.15/5.51 = ( ^ [K2: code_integer] :
% 5.15/5.51 ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 5.15/5.51 @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.15/5.51 @ ( produc1553301316500091796er_int
% 5.15/5.51 @ ^ [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 ) )
% 5.15/5.51 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % int_of_integer_code
% 5.15/5.51 thf(fact_9704_int__of__integer__numeral,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.15/5.51 = ( numeral_numeral_int @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % int_of_integer_numeral
% 5.15/5.51 thf(fact_9705_times__integer_Orep__eq,axiom,
% 5.15/5.51 ! [X: code_integer,Xa2: code_integer] :
% 5.15/5.51 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 5.15/5.51 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % times_integer.rep_eq
% 5.15/5.51 thf(fact_9706_divide__integer_Orep__eq,axiom,
% 5.15/5.51 ! [X: code_integer,Xa2: code_integer] :
% 5.15/5.51 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa2 ) )
% 5.15/5.51 = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divide_integer.rep_eq
% 5.15/5.51 thf(fact_9707_nat__of__integer__code__post_I3_J,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.15/5.51 = ( numeral_numeral_nat @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_of_integer_code_post(3)
% 5.15/5.51 thf(fact_9708_divmod__abs__code_I5_J,axiom,
% 5.15/5.51 ! [J: code_integer] :
% 5.15/5.51 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 5.15/5.51 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divmod_abs_code(5)
% 5.15/5.51 thf(fact_9709_divmod__abs__code_I6_J,axiom,
% 5.15/5.51 ! [J: code_integer] :
% 5.15/5.51 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 5.15/5.51 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 5.15/5.51
% 5.15/5.51 % divmod_abs_code(6)
% 5.15/5.51 thf(fact_9710_nat__of__integer__code__post_I2_J,axiom,
% 5.15/5.51 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.15/5.51 = one_one_nat ) ).
% 5.15/5.51
% 5.15/5.51 % nat_of_integer_code_post(2)
% 5.15/5.51 thf(fact_9711_divmod__abs__def,axiom,
% 5.15/5.51 ( code_divmod_abs
% 5.15/5.51 = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divmod_abs_def
% 5.15/5.51 thf(fact_9712_divmod__integer__code,axiom,
% 5.15/5.51 ( code_divmod_integer
% 5.15/5.51 = ( ^ [K2: code_integer,L2: code_integer] :
% 5.15/5.51 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.15/5.51 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.15/5.51 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L2 )
% 5.15/5.51 @ ( produc6916734918728496179nteger
% 5.15/5.51 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S6 ) ) )
% 5.15/5.51 @ ( code_divmod_abs @ K2 @ L2 ) ) )
% 5.15/5.51 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.15/5.51 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.15/5.51 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L2 )
% 5.15/5.51 @ ( produc6916734918728496179nteger
% 5.15/5.51 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S6 ) ) )
% 5.15/5.51 @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divmod_integer_code
% 5.15/5.51 thf(fact_9713_card__Collect__less__nat,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( finite_card_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N2 ) ) )
% 5.15/5.51 = N2 ) ).
% 5.15/5.51
% 5.15/5.51 % card_Collect_less_nat
% 5.15/5.51 thf(fact_9714_card__atMost,axiom,
% 5.15/5.51 ! [U: nat] :
% 5.15/5.51 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.15/5.51 = ( suc @ U ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_atMost
% 5.15/5.51 thf(fact_9715_card__atLeastLessThan,axiom,
% 5.15/5.51 ! [L: nat,U: nat] :
% 5.15/5.51 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.15/5.51 = ( minus_minus_nat @ U @ L ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_atLeastLessThan
% 5.15/5.51 thf(fact_9716_card__Collect__le__nat,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( finite_card_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N2 ) ) )
% 5.15/5.51 = ( suc @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_Collect_le_nat
% 5.15/5.51 thf(fact_9717_card__atLeastAtMost,axiom,
% 5.15/5.51 ! [L: nat,U: nat] :
% 5.15/5.51 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.15/5.51 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_atLeastAtMost
% 5.15/5.51 thf(fact_9718_nat_Odisc__eq__case_I1_J,axiom,
% 5.15/5.51 ! [Nat: nat] :
% 5.15/5.51 ( ( Nat = zero_zero_nat )
% 5.15/5.51 = ( case_nat_o @ $true
% 5.15/5.51 @ ^ [Uu3: nat] : $false
% 5.15/5.51 @ Nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat.disc_eq_case(1)
% 5.15/5.51 thf(fact_9719_nat_Odisc__eq__case_I2_J,axiom,
% 5.15/5.51 ! [Nat: nat] :
% 5.15/5.51 ( ( Nat != zero_zero_nat )
% 5.15/5.51 = ( case_nat_o @ $false
% 5.15/5.51 @ ^ [Uu3: nat] : $true
% 5.15/5.51 @ Nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat.disc_eq_case(2)
% 5.15/5.51 thf(fact_9720_card__less,axiom,
% 5.15/5.51 ! [M7: set_nat,I: nat] :
% 5.15/5.51 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.15/5.51 => ( ( finite_card_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [K2: nat] :
% 5.15/5.51 ( ( member_nat @ K2 @ M7 )
% 5.15/5.51 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 5.15/5.51 != zero_zero_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_less
% 5.15/5.51 thf(fact_9721_card__less__Suc,axiom,
% 5.15/5.51 ! [M7: set_nat,I: nat] :
% 5.15/5.51 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.15/5.51 => ( ( suc
% 5.15/5.51 @ ( finite_card_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [K2: nat] :
% 5.15/5.51 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.15/5.51 & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 5.15/5.51 = ( finite_card_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [K2: nat] :
% 5.15/5.51 ( ( member_nat @ K2 @ M7 )
% 5.15/5.51 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_less_Suc
% 5.15/5.51 thf(fact_9722_card__less__Suc2,axiom,
% 5.15/5.51 ! [M7: set_nat,I: nat] :
% 5.15/5.51 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.15/5.51 => ( ( finite_card_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [K2: nat] :
% 5.15/5.51 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.15/5.51 & ( ord_less_nat @ K2 @ I ) ) ) )
% 5.15/5.51 = ( finite_card_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [K2: nat] :
% 5.15/5.51 ( ( member_nat @ K2 @ M7 )
% 5.15/5.51 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_less_Suc2
% 5.15/5.51 thf(fact_9723_subset__card__intvl__is__intvl,axiom,
% 5.15/5.51 ! [A2: set_nat,K: nat] :
% 5.15/5.51 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.15/5.51 => ( A2
% 5.15/5.51 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % subset_card_intvl_is_intvl
% 5.15/5.51 thf(fact_9724_less__eq__nat_Osimps_I2_J,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.15/5.51 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % less_eq_nat.simps(2)
% 5.15/5.51 thf(fact_9725_max__Suc1,axiom,
% 5.15/5.51 ! [N2: nat,M: nat] :
% 5.15/5.51 ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 5.15/5.51 = ( case_nat_nat @ ( suc @ N2 )
% 5.15/5.51 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N2 @ M6 ) )
% 5.15/5.51 @ M ) ) ).
% 5.15/5.51
% 5.15/5.51 % max_Suc1
% 5.15/5.51 thf(fact_9726_max__Suc2,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 5.15/5.51 = ( case_nat_nat @ ( suc @ N2 )
% 5.15/5.51 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N2 ) )
% 5.15/5.51 @ M ) ) ).
% 5.15/5.51
% 5.15/5.51 % max_Suc2
% 5.15/5.51 thf(fact_9727_card__le__Suc__Max,axiom,
% 5.15/5.51 ! [S3: set_nat] :
% 5.15/5.51 ( ( finite_finite_nat @ S3 )
% 5.15/5.51 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_le_Suc_Max
% 5.15/5.51 thf(fact_9728_subset__eq__atLeast0__lessThan__card,axiom,
% 5.15/5.51 ! [N5: set_nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.15/5.51 => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % subset_eq_atLeast0_lessThan_card
% 5.15/5.51 thf(fact_9729_card__sum__le__nat__sum,axiom,
% 5.15/5.51 ! [S3: set_nat] :
% 5.15/5.51 ( ord_less_eq_nat
% 5.15/5.51 @ ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [X2: nat] : X2
% 5.15/5.51 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.15/5.51 @ ( groups3542108847815614940at_nat
% 5.15/5.51 @ ^ [X2: nat] : X2
% 5.15/5.51 @ S3 ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_sum_le_nat_sum
% 5.15/5.51 thf(fact_9730_card__nth__roots,axiom,
% 5.15/5.51 ! [C: complex,N2: nat] :
% 5.15/5.51 ( ( C != zero_zero_complex )
% 5.15/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( finite_card_complex
% 5.15/5.51 @ ( collect_complex
% 5.15/5.51 @ ^ [Z3: complex] :
% 5.15/5.51 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.51 = C ) ) )
% 5.15/5.51 = N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_nth_roots
% 5.15/5.51 thf(fact_9731_card__roots__unity__eq,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( finite_card_complex
% 5.15/5.51 @ ( collect_complex
% 5.15/5.51 @ ^ [Z3: complex] :
% 5.15/5.51 ( ( power_power_complex @ Z3 @ N2 )
% 5.15/5.51 = one_one_complex ) ) )
% 5.15/5.51 = N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % card_roots_unity_eq
% 5.15/5.51 thf(fact_9732_diff__Suc,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.15/5.51 = ( case_nat_nat @ zero_zero_nat
% 5.15/5.51 @ ^ [K2: nat] : K2
% 5.15/5.51 @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % diff_Suc
% 5.15/5.51 thf(fact_9733_pred__def,axiom,
% 5.15/5.51 ( pred
% 5.15/5.51 = ( case_nat_nat @ zero_zero_nat
% 5.15/5.51 @ ^ [X24: nat] : X24 ) ) ).
% 5.15/5.51
% 5.15/5.51 % pred_def
% 5.15/5.51 thf(fact_9734_binomial__def,axiom,
% 5.15/5.51 ( binomial
% 5.15/5.51 = ( ^ [N3: nat,K2: nat] :
% 5.15/5.51 ( finite_card_set_nat
% 5.15/5.51 @ ( collect_set_nat
% 5.15/5.51 @ ^ [K7: set_nat] :
% 5.15/5.51 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) )
% 5.15/5.51 & ( ( finite_card_nat @ K7 )
% 5.15/5.51 = K2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % binomial_def
% 5.15/5.51 thf(fact_9735_bezw__0,axiom,
% 5.15/5.51 ! [X: nat] :
% 5.15/5.51 ( ( bezw @ X @ zero_zero_nat )
% 5.15/5.51 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezw_0
% 5.15/5.51 thf(fact_9736_drop__bit__numeral__minus__bit1,axiom,
% 5.15/5.51 ! [L: num,K: num] :
% 5.15/5.51 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.15/5.51 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_numeral_minus_bit1
% 5.15/5.51 thf(fact_9737_prod__decode__aux_Oelims,axiom,
% 5.15/5.51 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.15/5.51 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.15/5.51 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_decode_aux.elims
% 5.15/5.51 thf(fact_9738_drop__bit__nonnegative__int__iff,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) )
% 5.15/5.51 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_nonnegative_int_iff
% 5.15/5.51 thf(fact_9739_drop__bit__negative__int__iff,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 5.15/5.51 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_negative_int_iff
% 5.15/5.51 thf(fact_9740_drop__bit__minus__one,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.15/5.51 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_minus_one
% 5.15/5.51 thf(fact_9741_drop__bit__Suc__minus__bit0,axiom,
% 5.15/5.51 ! [N2: nat,K: num] :
% 5.15/5.51 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.15/5.51 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_Suc_minus_bit0
% 5.15/5.51 thf(fact_9742_drop__bit__numeral__minus__bit0,axiom,
% 5.15/5.51 ! [L: num,K: num] :
% 5.15/5.51 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.15/5.51 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_numeral_minus_bit0
% 5.15/5.51 thf(fact_9743_drop__bit__Suc__minus__bit1,axiom,
% 5.15/5.51 ! [N2: nat,K: num] :
% 5.15/5.51 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.15/5.51 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_Suc_minus_bit1
% 5.15/5.51 thf(fact_9744_drop__bit__push__bit__int,axiom,
% 5.15/5.51 ! [M: nat,N2: nat,K: int] :
% 5.15/5.51 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.15/5.51 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N2 @ M ) @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_push_bit_int
% 5.15/5.51 thf(fact_9745_drop__bit__int__def,axiom,
% 5.15/5.51 ( bit_se8568078237143864401it_int
% 5.15/5.51 = ( ^ [N3: nat,K2: int] : ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_int_def
% 5.15/5.51 thf(fact_9746_prod__decode__aux_Osimps,axiom,
% 5.15/5.51 ( nat_prod_decode_aux
% 5.15/5.51 = ( ^ [K2: nat,M5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M5 @ K2 ) @ ( product_Pair_nat_nat @ M5 @ ( minus_minus_nat @ K2 @ M5 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M5 @ ( suc @ K2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_decode_aux.simps
% 5.15/5.51 thf(fact_9747_Suc__0__mod__numeral,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.15/5.51 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_0_mod_numeral
% 5.15/5.51 thf(fact_9748_Suc__0__div__numeral,axiom,
% 5.15/5.51 ! [K: num] :
% 5.15/5.51 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.15/5.51 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_0_div_numeral
% 5.15/5.51 thf(fact_9749_drop__bit__of__Suc__0,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.15/5.51 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_of_Suc_0
% 5.15/5.51 thf(fact_9750_fst__divmod__nat,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 5.15/5.51 = ( divide_divide_nat @ M @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % fst_divmod_nat
% 5.15/5.51 thf(fact_9751_snd__divmod__nat,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 5.15/5.51 = ( modulo_modulo_nat @ M @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % snd_divmod_nat
% 5.15/5.51 thf(fact_9752_drop__bit__nat__eq,axiom,
% 5.15/5.51 ! [N2: nat,K: int] :
% 5.15/5.51 ( ( bit_se8570568707652914677it_nat @ N2 @ ( nat2 @ K ) )
% 5.15/5.51 = ( nat2 @ ( bit_se8568078237143864401it_int @ N2 @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_nat_eq
% 5.15/5.51 thf(fact_9753_drop__bit__nat__def,axiom,
% 5.15/5.51 ( bit_se8570568707652914677it_nat
% 5.15/5.51 = ( ^ [N3: nat,M5: nat] : ( divide_divide_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % drop_bit_nat_def
% 5.15/5.51 thf(fact_9754_rat__sgn__code,axiom,
% 5.15/5.51 ! [P2: rat] :
% 5.15/5.51 ( ( quotient_of @ ( sgn_sgn_rat @ P2 ) )
% 5.15/5.51 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P2 ) ) ) @ one_one_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % rat_sgn_code
% 5.15/5.51 thf(fact_9755_bezw__non__0,axiom,
% 5.15/5.51 ! [Y: nat,X: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.15/5.51 => ( ( bezw @ X @ Y )
% 5.15/5.51 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezw_non_0
% 5.15/5.51 thf(fact_9756_bezw_Osimps,axiom,
% 5.15/5.51 ( bezw
% 5.15/5.51 = ( ^ [X2: nat,Y2: nat] : ( if_Pro3027730157355071871nt_int @ ( Y2 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezw.simps
% 5.15/5.51 thf(fact_9757_bezw_Oelims,axiom,
% 5.15/5.51 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.15/5.51 ( ( ( bezw @ X @ Xa2 )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.15/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezw.elims
% 5.15/5.51 thf(fact_9758_one__mod__minus__numeral,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.51 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % one_mod_minus_numeral
% 5.15/5.51 thf(fact_9759_minus__one__mod__numeral,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.51 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % minus_one_mod_numeral
% 5.15/5.51 thf(fact_9760_numeral__mod__minus__numeral,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.51 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % numeral_mod_minus_numeral
% 5.15/5.51 thf(fact_9761_minus__numeral__mod__numeral,axiom,
% 5.15/5.51 ! [M: num,N2: num] :
% 5.15/5.51 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.51 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % minus_numeral_mod_numeral
% 5.15/5.51 thf(fact_9762_Divides_Oadjust__mod__def,axiom,
% 5.15/5.51 ( adjust_mod
% 5.15/5.51 = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % Divides.adjust_mod_def
% 5.15/5.51 thf(fact_9763_bezw_Opelims,axiom,
% 5.15/5.51 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.15/5.51 ( ( ( bezw @ X @ Xa2 )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.15/5.51 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.15/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 5.15/5.51 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezw.pelims
% 5.15/5.51 thf(fact_9764_normalize__def,axiom,
% 5.15/5.51 ( normalize
% 5.15/5.51 = ( ^ [P5: product_prod_int_int] :
% 5.15/5.51 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 5.15/5.51 @ ( if_Pro3027730157355071871nt_int
% 5.15/5.51 @ ( ( product_snd_int_int @ P5 )
% 5.15/5.51 = zero_zero_int )
% 5.15/5.51 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.15/5.51 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % normalize_def
% 5.15/5.51 thf(fact_9765_gcd__neg__numeral__2__int,axiom,
% 5.15/5.51 ! [X: int,N2: num] :
% 5.15/5.51 ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.51 = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_neg_numeral_2_int
% 5.15/5.51 thf(fact_9766_gcd__neg__numeral__1__int,axiom,
% 5.15/5.51 ! [N2: num,X: int] :
% 5.15/5.51 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ X )
% 5.15/5.51 = ( gcd_gcd_int @ ( numeral_numeral_int @ N2 ) @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_neg_numeral_1_int
% 5.15/5.51 thf(fact_9767_bezout__int,axiom,
% 5.15/5.51 ! [X: int,Y: int] :
% 5.15/5.51 ? [U3: int,V2: int] :
% 5.15/5.51 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V2 @ Y ) )
% 5.15/5.51 = ( gcd_gcd_int @ X @ Y ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezout_int
% 5.15/5.51 thf(fact_9768_gcd__mult__distrib__int,axiom,
% 5.15/5.51 ! [K: int,M: int,N2: int] :
% 5.15/5.51 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N2 ) )
% 5.15/5.51 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_mult_distrib_int
% 5.15/5.51 thf(fact_9769_gcd__is__Max__divisors__int,axiom,
% 5.15/5.51 ! [N2: int,M: int] :
% 5.15/5.51 ( ( N2 != zero_zero_int )
% 5.15/5.51 => ( ( gcd_gcd_int @ M @ N2 )
% 5.15/5.51 = ( lattic8263393255366662781ax_int
% 5.15/5.51 @ ( collect_int
% 5.15/5.51 @ ^ [D2: int] :
% 5.15/5.51 ( ( dvd_dvd_int @ D2 @ M )
% 5.15/5.51 & ( dvd_dvd_int @ D2 @ N2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_is_Max_divisors_int
% 5.15/5.51 thf(fact_9770_nat__descend__induct,axiom,
% 5.15/5.51 ! [N2: nat,P: nat > $o,M: nat] :
% 5.15/5.51 ( ! [K3: nat] :
% 5.15/5.51 ( ( ord_less_nat @ N2 @ K3 )
% 5.15/5.51 => ( P @ K3 ) )
% 5.15/5.51 => ( ! [K3: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.15/5.51 => ( ! [I4: nat] :
% 5.15/5.51 ( ( ord_less_nat @ K3 @ I4 )
% 5.15/5.51 => ( P @ I4 ) )
% 5.15/5.51 => ( P @ K3 ) ) )
% 5.15/5.51 => ( P @ M ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat_descend_induct
% 5.15/5.51 thf(fact_9771_prod__decode__aux_Opelims,axiom,
% 5.15/5.51 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.15/5.51 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.15/5.51 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.15/5.51 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 5.15/5.51 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_decode_aux.pelims
% 5.15/5.51 thf(fact_9772_infinite__nat__iff__unbounded__le,axiom,
% 5.15/5.51 ! [S3: set_nat] :
% 5.15/5.51 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.15/5.51 = ( ! [M5: nat] :
% 5.15/5.51 ? [N3: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.15/5.51 & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % infinite_nat_iff_unbounded_le
% 5.15/5.51 thf(fact_9773_gcd__1__nat,axiom,
% 5.15/5.51 ! [M: nat] :
% 5.15/5.51 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.15/5.51 = one_one_nat ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_1_nat
% 5.15/5.51 thf(fact_9774_gcd__Suc__0,axiom,
% 5.15/5.51 ! [M: nat] :
% 5.15/5.51 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.15/5.51 = ( suc @ zero_zero_nat ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_Suc_0
% 5.15/5.51 thf(fact_9775_gcd__pos__nat,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N2 ) )
% 5.15/5.51 = ( ( M != zero_zero_nat )
% 5.15/5.51 | ( N2 != zero_zero_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_pos_nat
% 5.15/5.51 thf(fact_9776_gcd__le1__nat,axiom,
% 5.15/5.51 ! [A: nat,B: nat] :
% 5.15/5.51 ( ( A != zero_zero_nat )
% 5.15/5.51 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_le1_nat
% 5.15/5.51 thf(fact_9777_gcd__le2__nat,axiom,
% 5.15/5.51 ! [B: nat,A: nat] :
% 5.15/5.51 ( ( B != zero_zero_nat )
% 5.15/5.51 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_le2_nat
% 5.15/5.51 thf(fact_9778_gcd__mult__distrib__nat,axiom,
% 5.15/5.51 ! [K: nat,M: nat,N2: nat] :
% 5.15/5.51 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N2 ) )
% 5.15/5.51 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_mult_distrib_nat
% 5.15/5.51 thf(fact_9779_gcd__diff1__nat,axiom,
% 5.15/5.51 ! [N2: nat,M: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ N2 @ M )
% 5.15/5.51 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 )
% 5.15/5.51 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_diff1_nat
% 5.15/5.51 thf(fact_9780_gcd__diff2__nat,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ M @ N2 )
% 5.15/5.51 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N2 @ M ) @ N2 )
% 5.15/5.51 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_diff2_nat
% 5.15/5.51 thf(fact_9781_bezout__nat,axiom,
% 5.15/5.51 ! [A: nat,B: nat] :
% 5.15/5.51 ( ( A != zero_zero_nat )
% 5.15/5.51 => ? [X3: nat,Y3: nat] :
% 5.15/5.51 ( ( times_times_nat @ A @ X3 )
% 5.15/5.51 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezout_nat
% 5.15/5.51 thf(fact_9782_bezout__gcd__nat_H,axiom,
% 5.15/5.51 ! [B: nat,A: nat] :
% 5.15/5.51 ? [X3: nat,Y3: nat] :
% 5.15/5.51 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 5.15/5.51 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.15/5.51 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.15/5.51 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 5.15/5.51 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.15/5.51 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezout_gcd_nat'
% 5.15/5.51 thf(fact_9783_gcd__is__Max__divisors__nat,axiom,
% 5.15/5.51 ! [N2: nat,M: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( gcd_gcd_nat @ M @ N2 )
% 5.15/5.51 = ( lattic8265883725875713057ax_nat
% 5.15/5.51 @ ( collect_nat
% 5.15/5.51 @ ^ [D2: nat] :
% 5.15/5.51 ( ( dvd_dvd_nat @ D2 @ M )
% 5.15/5.51 & ( dvd_dvd_nat @ D2 @ N2 ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_is_Max_divisors_nat
% 5.15/5.51 thf(fact_9784_bezw__aux,axiom,
% 5.15/5.51 ! [X: nat,Y: nat] :
% 5.15/5.51 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 5.15/5.51 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % bezw_aux
% 5.15/5.51 thf(fact_9785_infinite__nat__iff__unbounded,axiom,
% 5.15/5.51 ! [S3: set_nat] :
% 5.15/5.51 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.15/5.51 = ( ! [M5: nat] :
% 5.15/5.51 ? [N3: nat] :
% 5.15/5.51 ( ( ord_less_nat @ M5 @ N3 )
% 5.15/5.51 & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % infinite_nat_iff_unbounded
% 5.15/5.51 thf(fact_9786_unbounded__k__infinite,axiom,
% 5.15/5.51 ! [K: nat,S3: set_nat] :
% 5.15/5.51 ( ! [M3: nat] :
% 5.15/5.51 ( ( ord_less_nat @ K @ M3 )
% 5.15/5.51 => ? [N9: nat] :
% 5.15/5.51 ( ( ord_less_nat @ M3 @ N9 )
% 5.15/5.51 & ( member_nat @ N9 @ S3 ) ) )
% 5.15/5.51 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.15/5.51
% 5.15/5.51 % unbounded_k_infinite
% 5.15/5.51 thf(fact_9787_gcd__nat_Opelims,axiom,
% 5.15/5.51 ! [X: nat,Xa2: nat,Y: nat] :
% 5.15/5.51 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 5.15/5.51 = Y )
% 5.15/5.51 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.15/5.51 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.15/5.51 => ( Y = X ) )
% 5.15/5.51 & ( ( Xa2 != zero_zero_nat )
% 5.15/5.51 => ( Y
% 5.15/5.51 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 5.15/5.51 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_nat.pelims
% 5.15/5.51 thf(fact_9788_finite__enumerate,axiom,
% 5.15/5.51 ! [S3: set_nat] :
% 5.15/5.51 ( ( finite_finite_nat @ S3 )
% 5.15/5.51 => ? [R3: nat > nat] :
% 5.15/5.51 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.15/5.51 & ! [N9: nat] :
% 5.15/5.51 ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S3 ) )
% 5.15/5.51 => ( member_nat @ ( R3 @ N9 ) @ S3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % finite_enumerate
% 5.15/5.51 thf(fact_9789_xor__minus__numerals_I2_J,axiom,
% 5.15/5.51 ! [K: int,N2: num] :
% 5.15/5.51 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.51 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_minus_numerals(2)
% 5.15/5.51 thf(fact_9790_xor__minus__numerals_I1_J,axiom,
% 5.15/5.51 ! [N2: num,K: int] :
% 5.15/5.51 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ K )
% 5.15/5.51 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N2 @ one ) @ K ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % xor_minus_numerals(1)
% 5.15/5.51 thf(fact_9791_sub__BitM__One__eq,axiom,
% 5.15/5.51 ! [N2: num] :
% 5.15/5.51 ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 5.15/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % sub_BitM_One_eq
% 5.15/5.51 thf(fact_9792_Suc__funpow,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( compow_nat_nat @ N2 @ suc )
% 5.15/5.51 = ( plus_plus_nat @ N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % Suc_funpow
% 5.15/5.51 thf(fact_9793_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.15/5.51 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ X2 )
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] : ( ord_less_nat @ Y2 @ X2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % max_nat.semilattice_neutr_order_axioms
% 5.15/5.51 thf(fact_9794_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.15/5.51 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.15/5.51 @ ^ [M5: nat,N3: nat] :
% 5.15/5.51 ( ( dvd_dvd_nat @ M5 @ N3 )
% 5.15/5.51 & ( M5 != N3 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % gcd_nat.semilattice_neutr_order_axioms
% 5.15/5.51 thf(fact_9795_divmod__integer__eq__cases,axiom,
% 5.15/5.51 ( code_divmod_integer
% 5.15/5.51 = ( ^ [K2: code_integer,L2: code_integer] :
% 5.15/5.51 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.15/5.51 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.15/5.51 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 5.15/5.51 @ ( if_Pro6119634080678213985nteger
% 5.15/5.51 @ ( ( sgn_sgn_Code_integer @ K2 )
% 5.15/5.51 = ( sgn_sgn_Code_integer @ L2 ) )
% 5.15/5.51 @ ( code_divmod_abs @ K2 @ L2 )
% 5.15/5.51 @ ( produc6916734918728496179nteger
% 5.15/5.51 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S6 ) ) )
% 5.15/5.51 @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % divmod_integer_eq_cases
% 5.15/5.51 thf(fact_9796_times__int_Oabs__eq,axiom,
% 5.15/5.51 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.15/5.51 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.15/5.51 = ( abs_Integ
% 5.15/5.51 @ ( produc27273713700761075at_nat
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] :
% 5.15/5.51 ( produc2626176000494625587at_nat
% 5.15/5.51 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y2 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y2 @ U2 ) ) ) )
% 5.15/5.51 @ Xa2
% 5.15/5.51 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % times_int.abs_eq
% 5.15/5.51 thf(fact_9797_card_Ocomp__fun__commute__on,axiom,
% 5.15/5.51 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.15/5.51 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.15/5.51
% 5.15/5.51 % card.comp_fun_commute_on
% 5.15/5.51 thf(fact_9798_eq__Abs__Integ,axiom,
% 5.15/5.51 ! [Z: int] :
% 5.15/5.51 ~ ! [X3: nat,Y3: nat] :
% 5.15/5.51 ( Z
% 5.15/5.51 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % eq_Abs_Integ
% 5.15/5.51 thf(fact_9799_nat_Oabs__eq,axiom,
% 5.15/5.51 ! [X: product_prod_nat_nat] :
% 5.15/5.51 ( ( nat2 @ ( abs_Integ @ X ) )
% 5.15/5.51 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat.abs_eq
% 5.15/5.51 thf(fact_9800_zero__int__def,axiom,
% 5.15/5.51 ( zero_zero_int
% 5.15/5.51 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % zero_int_def
% 5.15/5.51 thf(fact_9801_int__def,axiom,
% 5.15/5.51 ( semiri1314217659103216013at_int
% 5.15/5.51 = ( ^ [N3: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N3 @ zero_zero_nat ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % int_def
% 5.15/5.51 thf(fact_9802_uminus__int_Oabs__eq,axiom,
% 5.15/5.51 ! [X: product_prod_nat_nat] :
% 5.15/5.51 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.15/5.51 = ( abs_Integ
% 5.15/5.51 @ ( produc2626176000494625587at_nat
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] : ( product_Pair_nat_nat @ Y2 @ X2 )
% 5.15/5.51 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % uminus_int.abs_eq
% 5.15/5.51 thf(fact_9803_one__int__def,axiom,
% 5.15/5.51 ( one_one_int
% 5.15/5.51 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % one_int_def
% 5.15/5.51 thf(fact_9804_less__int_Oabs__eq,axiom,
% 5.15/5.51 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.15/5.51 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.15/5.51 = ( produc8739625826339149834_nat_o
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] :
% 5.15/5.51 ( produc6081775807080527818_nat_o
% 5.15/5.51 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) )
% 5.15/5.51 @ Xa2
% 5.15/5.51 @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % less_int.abs_eq
% 5.15/5.51 thf(fact_9805_less__eq__int_Oabs__eq,axiom,
% 5.15/5.51 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.15/5.51 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.15/5.51 = ( produc8739625826339149834_nat_o
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] :
% 5.15/5.51 ( produc6081775807080527818_nat_o
% 5.15/5.51 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) )
% 5.15/5.51 @ Xa2
% 5.15/5.51 @ X ) ) ).
% 5.15/5.51
% 5.15/5.51 % less_eq_int.abs_eq
% 5.15/5.51 thf(fact_9806_plus__int_Oabs__eq,axiom,
% 5.15/5.51 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.15/5.51 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.15/5.51 = ( abs_Integ
% 5.15/5.51 @ ( produc27273713700761075at_nat
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] :
% 5.15/5.51 ( produc2626176000494625587at_nat
% 5.15/5.51 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y2 @ V4 ) ) )
% 5.15/5.51 @ Xa2
% 5.15/5.51 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % plus_int.abs_eq
% 5.15/5.51 thf(fact_9807_minus__int_Oabs__eq,axiom,
% 5.15/5.51 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.15/5.51 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.15/5.51 = ( abs_Integ
% 5.15/5.51 @ ( produc27273713700761075at_nat
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] :
% 5.15/5.51 ( produc2626176000494625587at_nat
% 5.15/5.51 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y2 @ U2 ) ) )
% 5.15/5.51 @ Xa2
% 5.15/5.51 @ X ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % minus_int.abs_eq
% 5.15/5.51 thf(fact_9808_Code__Target__Int_Onegative__def,axiom,
% 5.15/5.51 ( code_Target_negative
% 5.15/5.51 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.15/5.51
% 5.15/5.51 % Code_Target_Int.negative_def
% 5.15/5.51 thf(fact_9809_num__of__nat_Osimps_I2_J,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.15/5.51 = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 5.15/5.51 & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.15/5.51 = one ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % num_of_nat.simps(2)
% 5.15/5.51 thf(fact_9810_num__of__nat__numeral__eq,axiom,
% 5.15/5.51 ! [Q3: num] :
% 5.15/5.51 ( ( num_of_nat @ ( numeral_numeral_nat @ Q3 ) )
% 5.15/5.51 = Q3 ) ).
% 5.15/5.51
% 5.15/5.51 % num_of_nat_numeral_eq
% 5.15/5.51 thf(fact_9811_num__of__nat_Osimps_I1_J,axiom,
% 5.15/5.51 ( ( num_of_nat @ zero_zero_nat )
% 5.15/5.51 = one ) ).
% 5.15/5.51
% 5.15/5.51 % num_of_nat.simps(1)
% 5.15/5.51 thf(fact_9812_numeral__num__of__nat,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 5.15/5.51 = N2 ) ) ).
% 5.15/5.51
% 5.15/5.51 % numeral_num_of_nat
% 5.15/5.51 thf(fact_9813_num__of__nat__One,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 5.15/5.51 => ( ( num_of_nat @ N2 )
% 5.15/5.51 = one ) ) ).
% 5.15/5.51
% 5.15/5.51 % num_of_nat_One
% 5.15/5.51 thf(fact_9814_num__of__nat__double,axiom,
% 5.15/5.51 ! [N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 5.15/5.51 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % num_of_nat_double
% 5.15/5.51 thf(fact_9815_num__of__nat__plus__distrib,axiom,
% 5.15/5.51 ! [M: nat,N2: nat] :
% 5.15/5.51 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.15/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.51 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.15/5.51 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % num_of_nat_plus_distrib
% 5.15/5.51 thf(fact_9816_less__eq__int_Orep__eq,axiom,
% 5.15/5.51 ( ord_less_eq_int
% 5.15/5.51 = ( ^ [X2: int,Xa3: int] :
% 5.15/5.51 ( produc8739625826339149834_nat_o
% 5.15/5.51 @ ^ [Y2: nat,Z3: nat] :
% 5.15/5.51 ( produc6081775807080527818_nat_o
% 5.15/5.51 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y2 @ V4 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 5.15/5.51 @ ( rep_Integ @ X2 )
% 5.15/5.51 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % less_eq_int.rep_eq
% 5.15/5.51 thf(fact_9817_less__int_Orep__eq,axiom,
% 5.15/5.51 ( ord_less_int
% 5.15/5.51 = ( ^ [X2: int,Xa3: int] :
% 5.15/5.51 ( produc8739625826339149834_nat_o
% 5.15/5.51 @ ^ [Y2: nat,Z3: nat] :
% 5.15/5.51 ( produc6081775807080527818_nat_o
% 5.15/5.51 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y2 @ V4 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 5.15/5.51 @ ( rep_Integ @ X2 )
% 5.15/5.51 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % less_int.rep_eq
% 5.15/5.51 thf(fact_9818_prod__encode__def,axiom,
% 5.15/5.51 ( nat_prod_encode
% 5.15/5.51 = ( produc6842872674320459806at_nat
% 5.15/5.51 @ ^ [M5: nat,N3: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M5 @ N3 ) ) @ M5 ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_encode_def
% 5.15/5.51 thf(fact_9819_le__prod__encode__1,axiom,
% 5.15/5.51 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % le_prod_encode_1
% 5.15/5.51 thf(fact_9820_le__prod__encode__2,axiom,
% 5.15/5.51 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % le_prod_encode_2
% 5.15/5.51 thf(fact_9821_nat_Orep__eq,axiom,
% 5.15/5.51 ( nat2
% 5.15/5.51 = ( ^ [X2: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % nat.rep_eq
% 5.15/5.51 thf(fact_9822_prod__encode__prod__decode__aux,axiom,
% 5.15/5.51 ! [K: nat,M: nat] :
% 5.15/5.51 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.15/5.51 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.15/5.51
% 5.15/5.51 % prod_encode_prod_decode_aux
% 5.15/5.51 thf(fact_9823_uminus__int__def,axiom,
% 5.15/5.51 ( uminus_uminus_int
% 5.15/5.51 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.15/5.51 @ ( produc2626176000494625587at_nat
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] : ( product_Pair_nat_nat @ Y2 @ X2 ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % uminus_int_def
% 5.15/5.51 thf(fact_9824_times__int__def,axiom,
% 5.15/5.51 ( times_times_int
% 5.15/5.51 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.15/5.51 @ ( produc27273713700761075at_nat
% 5.15/5.51 @ ^ [X2: nat,Y2: nat] :
% 5.15/5.51 ( produc2626176000494625587at_nat
% 5.15/5.51 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y2 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y2 @ U2 ) ) ) ) ) ) ) ).
% 5.15/5.51
% 5.15/5.51 % times_int_def
% 5.15/5.51 thf(fact_9825_minus__int__def,axiom,
% 5.15/5.51 ( minus_minus_int
% 5.15/5.51 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.15/5.52 @ ( produc27273713700761075at_nat
% 5.15/5.52 @ ^ [X2: nat,Y2: nat] :
% 5.15/5.52 ( produc2626176000494625587at_nat
% 5.15/5.52 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y2 @ U2 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % minus_int_def
% 5.15/5.52 thf(fact_9826_plus__int__def,axiom,
% 5.15/5.52 ( plus_plus_int
% 5.15/5.52 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.15/5.52 @ ( produc27273713700761075at_nat
% 5.15/5.52 @ ^ [X2: nat,Y2: nat] :
% 5.15/5.52 ( produc2626176000494625587at_nat
% 5.15/5.52 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y2 @ V4 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % plus_int_def
% 5.15/5.52 thf(fact_9827_pow_Osimps_I3_J,axiom,
% 5.15/5.52 ! [X: num,Y: num] :
% 5.15/5.52 ( ( pow @ X @ ( bit1 @ Y ) )
% 5.15/5.52 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 5.15/5.52
% 5.15/5.52 % pow.simps(3)
% 5.15/5.52 thf(fact_9828_sqr_Osimps_I2_J,axiom,
% 5.15/5.52 ! [N2: num] :
% 5.15/5.52 ( ( sqr @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sqr.simps(2)
% 5.15/5.52 thf(fact_9829_sqr_Osimps_I1_J,axiom,
% 5.15/5.52 ( ( sqr @ one )
% 5.15/5.52 = one ) ).
% 5.15/5.52
% 5.15/5.52 % sqr.simps(1)
% 5.15/5.52 thf(fact_9830_sqr__conv__mult,axiom,
% 5.15/5.52 ( sqr
% 5.15/5.52 = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sqr_conv_mult
% 5.15/5.52 thf(fact_9831_pow_Osimps_I2_J,axiom,
% 5.15/5.52 ! [X: num,Y: num] :
% 5.15/5.52 ( ( pow @ X @ ( bit0 @ Y ) )
% 5.15/5.52 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % pow.simps(2)
% 5.15/5.52 thf(fact_9832_sqr_Osimps_I3_J,axiom,
% 5.15/5.52 ! [N2: num] :
% 5.15/5.52 ( ( sqr @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sqr.simps(3)
% 5.15/5.52 thf(fact_9833_rat__floor__lemma,axiom,
% 5.15/5.52 ! [A: int,B: int] :
% 5.15/5.52 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.15/5.52 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % rat_floor_lemma
% 5.15/5.52 thf(fact_9834_mult__rat,axiom,
% 5.15/5.52 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.52 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.15/5.52 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % mult_rat
% 5.15/5.52 thf(fact_9835_divide__rat,axiom,
% 5.15/5.52 ! [A: int,B: int,C: int,D: int] :
% 5.15/5.52 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.15/5.52 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % divide_rat
% 5.15/5.52 thf(fact_9836_floor__Fract,axiom,
% 5.15/5.52 ! [A: int,B: int] :
% 5.15/5.52 ( ( archim3151403230148437115or_rat @ ( fract @ A @ B ) )
% 5.15/5.52 = ( divide_divide_int @ A @ B ) ) ).
% 5.15/5.52
% 5.15/5.52 % floor_Fract
% 5.15/5.52 thf(fact_9837_less__rat,axiom,
% 5.15/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.15/5.52 ( ( B != zero_zero_int )
% 5.15/5.52 => ( ( D != zero_zero_int )
% 5.15/5.52 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.15/5.52 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % less_rat
% 5.15/5.52 thf(fact_9838_add__rat,axiom,
% 5.15/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.15/5.52 ( ( B != zero_zero_int )
% 5.15/5.52 => ( ( D != zero_zero_int )
% 5.15/5.52 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.15/5.52 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % add_rat
% 5.15/5.52 thf(fact_9839_le__rat,axiom,
% 5.15/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.15/5.52 ( ( B != zero_zero_int )
% 5.15/5.52 => ( ( D != zero_zero_int )
% 5.15/5.52 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.15/5.52 = ( 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 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % le_rat
% 5.15/5.52 thf(fact_9840_diff__rat,axiom,
% 5.15/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.15/5.52 ( ( B != zero_zero_int )
% 5.15/5.52 => ( ( D != zero_zero_int )
% 5.15/5.52 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.15/5.52 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % diff_rat
% 5.15/5.52 thf(fact_9841_sgn__rat,axiom,
% 5.15/5.52 ! [A: int,B: int] :
% 5.15/5.52 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.15/5.52 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sgn_rat
% 5.15/5.52 thf(fact_9842_eq__rat_I1_J,axiom,
% 5.15/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.15/5.52 ( ( B != zero_zero_int )
% 5.15/5.52 => ( ( D != zero_zero_int )
% 5.15/5.52 => ( ( ( fract @ A @ B )
% 5.15/5.52 = ( fract @ C @ D ) )
% 5.15/5.52 = ( ( times_times_int @ A @ D )
% 5.15/5.52 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eq_rat(1)
% 5.15/5.52 thf(fact_9843_mult__rat__cancel,axiom,
% 5.15/5.52 ! [C: int,A: int,B: int] :
% 5.15/5.52 ( ( C != zero_zero_int )
% 5.15/5.52 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.15/5.52 = ( fract @ A @ B ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % mult_rat_cancel
% 5.15/5.52 thf(fact_9844_Fract__coprime,axiom,
% 5.15/5.52 ! [A: int,B: int] :
% 5.15/5.52 ( ( fract @ ( divide_divide_int @ A @ ( gcd_gcd_int @ A @ B ) ) @ ( divide_divide_int @ B @ ( gcd_gcd_int @ A @ B ) ) )
% 5.15/5.52 = ( fract @ A @ B ) ) ).
% 5.15/5.52
% 5.15/5.52 % Fract_coprime
% 5.15/5.52 thf(fact_9845_quotient__of__eq,axiom,
% 5.15/5.52 ! [A: int,B: int,P2: int,Q3: int] :
% 5.15/5.52 ( ( ( quotient_of @ ( fract @ A @ B ) )
% 5.15/5.52 = ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.15/5.52 => ( ( fract @ P2 @ Q3 )
% 5.15/5.52 = ( fract @ A @ B ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % quotient_of_eq
% 5.15/5.52 thf(fact_9846_normalize__eq,axiom,
% 5.15/5.52 ! [A: int,B: int,P2: int,Q3: int] :
% 5.15/5.52 ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 5.15/5.52 = ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.15/5.52 => ( ( fract @ P2 @ Q3 )
% 5.15/5.52 = ( fract @ A @ B ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % normalize_eq
% 5.15/5.52 thf(fact_9847_rat__number__collapse_I3_J,axiom,
% 5.15/5.52 ! [W: num] :
% 5.15/5.52 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.15/5.52 = ( numeral_numeral_rat @ W ) ) ).
% 5.15/5.52
% 5.15/5.52 % rat_number_collapse(3)
% 5.15/5.52 thf(fact_9848_rat__number__expand_I3_J,axiom,
% 5.15/5.52 ( numeral_numeral_rat
% 5.15/5.52 = ( ^ [K2: num] : ( fract @ ( numeral_numeral_int @ K2 ) @ one_one_int ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % rat_number_expand(3)
% 5.15/5.52 thf(fact_9849_quotient__of__Fract,axiom,
% 5.15/5.52 ! [A: int,B: int] :
% 5.15/5.52 ( ( quotient_of @ ( fract @ A @ B ) )
% 5.15/5.52 = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % quotient_of_Fract
% 5.15/5.52 thf(fact_9850_rat__number__collapse_I4_J,axiom,
% 5.15/5.52 ! [W: num] :
% 5.15/5.52 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.15/5.52 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % rat_number_collapse(4)
% 5.15/5.52 thf(fact_9851_rat__number__expand_I5_J,axiom,
% 5.15/5.52 ! [K: num] :
% 5.15/5.52 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.15/5.52 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.15/5.52
% 5.15/5.52 % rat_number_expand(5)
% 5.15/5.52 thf(fact_9852_Inf__real__def,axiom,
% 5.15/5.52 ( comple4887499456419720421f_real
% 5.15/5.52 = ( ^ [X4: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X4 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Inf_real_def
% 5.15/5.52 thf(fact_9853_UN__atMost__UNIV,axiom,
% 5.15/5.52 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.15/5.52 = top_top_set_nat ) ).
% 5.15/5.52
% 5.15/5.52 % UN_atMost_UNIV
% 5.15/5.52 thf(fact_9854_UN__lessThan__UNIV,axiom,
% 5.15/5.52 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.15/5.52 = top_top_set_nat ) ).
% 5.15/5.52
% 5.15/5.52 % UN_lessThan_UNIV
% 5.15/5.52 thf(fact_9855_UNIV__nat__eq,axiom,
% 5.15/5.52 ( top_top_set_nat
% 5.15/5.52 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % UNIV_nat_eq
% 5.15/5.52 thf(fact_9856_range__mod,axiom,
% 5.15/5.52 ! [N2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( image_nat_nat
% 5.15/5.52 @ ^ [M5: nat] : ( modulo_modulo_nat @ M5 @ N2 )
% 5.15/5.52 @ top_top_set_nat )
% 5.15/5.52 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % range_mod
% 5.15/5.52 thf(fact_9857_suminf__eq__SUP__real,axiom,
% 5.15/5.52 ! [X8: nat > real] :
% 5.15/5.52 ( ( summable_real @ X8 )
% 5.15/5.52 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I2 ) )
% 5.15/5.52 => ( ( suminf_real @ X8 )
% 5.15/5.52 = ( comple1385675409528146559p_real
% 5.15/5.52 @ ( image_nat_real
% 5.15/5.52 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I3 ) )
% 5.15/5.52 @ top_top_set_nat ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % suminf_eq_SUP_real
% 5.15/5.52 thf(fact_9858_card__UNIV__unit,axiom,
% 5.15/5.52 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.15/5.52 = one_one_nat ) ).
% 5.15/5.52
% 5.15/5.52 % card_UNIV_unit
% 5.15/5.52 thf(fact_9859_card__UNIV__bool,axiom,
% 5.15/5.52 ( ( finite_card_o @ top_top_set_o )
% 5.15/5.52 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % card_UNIV_bool
% 5.15/5.52 thf(fact_9860_range__mult,axiom,
% 5.15/5.52 ! [A: real] :
% 5.15/5.52 ( ( ( A = zero_zero_real )
% 5.15/5.52 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.15/5.52 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.15/5.52 & ( ( A != zero_zero_real )
% 5.15/5.52 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.15/5.52 = top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % range_mult
% 5.15/5.52 thf(fact_9861_root__def,axiom,
% 5.15/5.52 ( root
% 5.15/5.52 = ( ^ [N3: nat,X2: real] :
% 5.15/5.52 ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 5.15/5.52 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.15/5.52 @ ^ [Y2: real] : ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N3 ) )
% 5.15/5.52 @ X2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % root_def
% 5.15/5.52 thf(fact_9862_card__UNIV__char,axiom,
% 5.15/5.52 ( ( finite_card_char @ top_top_set_char )
% 5.15/5.52 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % card_UNIV_char
% 5.15/5.52 thf(fact_9863_UNIV__char__of__nat,axiom,
% 5.15/5.52 ( top_top_set_char
% 5.15/5.52 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % UNIV_char_of_nat
% 5.15/5.52 thf(fact_9864_nat__of__char__less__256,axiom,
% 5.15/5.52 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % nat_of_char_less_256
% 5.15/5.52 thf(fact_9865_range__nat__of__char,axiom,
% 5.15/5.52 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.15/5.52 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % range_nat_of_char
% 5.15/5.52 thf(fact_9866_integer__of__char__code,axiom,
% 5.15/5.52 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.15/5.52 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.15/5.52 = ( 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 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % integer_of_char_code
% 5.15/5.52 thf(fact_9867_char__of__integer__code,axiom,
% 5.15/5.52 ( char_of_integer
% 5.15/5.52 = ( ^ [K2: code_integer] :
% 5.15/5.52 ( produc4188289175737317920o_char
% 5.15/5.52 @ ^ [Q0: code_integer,B02: $o] :
% 5.15/5.52 ( produc4188289175737317920o_char
% 5.15/5.52 @ ^ [Q1: code_integer,B12: $o] :
% 5.15/5.52 ( produc4188289175737317920o_char
% 5.15/5.52 @ ^ [Q22: code_integer,B23: $o] :
% 5.15/5.52 ( produc4188289175737317920o_char
% 5.15/5.52 @ ^ [Q32: code_integer,B33: $o] :
% 5.15/5.52 ( produc4188289175737317920o_char
% 5.15/5.52 @ ^ [Q42: code_integer,B43: $o] :
% 5.15/5.52 ( produc4188289175737317920o_char
% 5.15/5.52 @ ^ [Q52: code_integer,B53: $o] :
% 5.15/5.52 ( produc4188289175737317920o_char
% 5.15/5.52 @ ^ [Q62: code_integer,B63: $o] :
% 5.15/5.52 ( produc4188289175737317920o_char
% 5.15/5.52 @ ^ [Uu3: code_integer] : ( char2 @ B02 @ B12 @ B23 @ B33 @ B43 @ B53 @ B63 )
% 5.15/5.52 @ ( code_bit_cut_integer @ Q62 ) )
% 5.15/5.52 @ ( code_bit_cut_integer @ Q52 ) )
% 5.15/5.52 @ ( code_bit_cut_integer @ Q42 ) )
% 5.15/5.52 @ ( code_bit_cut_integer @ Q32 ) )
% 5.15/5.52 @ ( code_bit_cut_integer @ Q22 ) )
% 5.15/5.52 @ ( code_bit_cut_integer @ Q1 ) )
% 5.15/5.52 @ ( code_bit_cut_integer @ Q0 ) )
% 5.15/5.52 @ ( code_bit_cut_integer @ K2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % char_of_integer_code
% 5.15/5.52 thf(fact_9868_String_Ochar__of__ascii__of,axiom,
% 5.15/5.52 ! [C: char] :
% 5.15/5.52 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.15/5.52 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % String.char_of_ascii_of
% 5.15/5.52 thf(fact_9869_sorted__list__of__set__lessThan__Suc,axiom,
% 5.15/5.52 ! [K: nat] :
% 5.15/5.52 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.15/5.52 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sorted_list_of_set_lessThan_Suc
% 5.15/5.52 thf(fact_9870_sorted__list__of__set__atMost__Suc,axiom,
% 5.15/5.52 ! [K: nat] :
% 5.15/5.52 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.15/5.52 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sorted_list_of_set_atMost_Suc
% 5.15/5.52 thf(fact_9871_upto__aux__rec,axiom,
% 5.15/5.52 ( upto_aux
% 5.15/5.52 = ( ^ [I3: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_aux_rec
% 5.15/5.52 thf(fact_9872_list__encode_Oelims,axiom,
% 5.15/5.52 ! [X: list_nat,Y: nat] :
% 5.15/5.52 ( ( ( nat_list_encode @ X )
% 5.15/5.52 = Y )
% 5.15/5.52 => ( ( ( X = nil_nat )
% 5.15/5.52 => ( Y != zero_zero_nat ) )
% 5.15/5.52 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( cons_nat @ X3 @ Xs3 ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % list_encode.elims
% 5.15/5.52 thf(fact_9873_upto_Opsimps,axiom,
% 5.15/5.52 ! [I: int,J: int] :
% 5.15/5.52 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 5.15/5.52 => ( ( ( ord_less_eq_int @ I @ J )
% 5.15/5.52 => ( ( upto @ I @ J )
% 5.15/5.52 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 5.15/5.52 & ( ~ ( ord_less_eq_int @ I @ J )
% 5.15/5.52 => ( ( upto @ I @ J )
% 5.15/5.52 = nil_int ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto.psimps
% 5.15/5.52 thf(fact_9874_upto__empty,axiom,
% 5.15/5.52 ! [J: int,I: int] :
% 5.15/5.52 ( ( ord_less_int @ J @ I )
% 5.15/5.52 => ( ( upto @ I @ J )
% 5.15/5.52 = nil_int ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_empty
% 5.15/5.52 thf(fact_9875_upto__Nil2,axiom,
% 5.15/5.52 ! [I: int,J: int] :
% 5.15/5.52 ( ( nil_int
% 5.15/5.52 = ( upto @ I @ J ) )
% 5.15/5.52 = ( ord_less_int @ J @ I ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_Nil2
% 5.15/5.52 thf(fact_9876_upto__Nil,axiom,
% 5.15/5.52 ! [I: int,J: int] :
% 5.15/5.52 ( ( ( upto @ I @ J )
% 5.15/5.52 = nil_int )
% 5.15/5.52 = ( ord_less_int @ J @ I ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_Nil
% 5.15/5.52 thf(fact_9877_upto__single,axiom,
% 5.15/5.52 ! [I: int] :
% 5.15/5.52 ( ( upto @ I @ I )
% 5.15/5.52 = ( cons_int @ I @ nil_int ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_single
% 5.15/5.52 thf(fact_9878_nth__upto,axiom,
% 5.15/5.52 ! [I: int,K: nat,J: int] :
% 5.15/5.52 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.15/5.52 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 5.15/5.52 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % nth_upto
% 5.15/5.52 thf(fact_9879_length__upto,axiom,
% 5.15/5.52 ! [I: int,J: int] :
% 5.15/5.52 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 5.15/5.52 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % length_upto
% 5.15/5.52 thf(fact_9880_upto__rec__numeral_I1_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.15/5.52 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 = nil_int ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_rec_numeral(1)
% 5.15/5.52 thf(fact_9881_upto__rec__numeral_I4_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 = ( 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 ) ) ) ) ) )
% 5.15/5.52 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 = nil_int ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_rec_numeral(4)
% 5.15/5.52 thf(fact_9882_upto__rec__numeral_I3_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 = ( 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 ) ) ) ) )
% 5.15/5.52 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 = nil_int ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_rec_numeral(3)
% 5.15/5.52 thf(fact_9883_upto__rec__numeral_I2_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.15/5.52 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 = nil_int ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_rec_numeral(2)
% 5.15/5.52 thf(fact_9884_upto__aux__def,axiom,
% 5.15/5.52 ( upto_aux
% 5.15/5.52 = ( ^ [I3: int,J3: int] : ( append_int @ ( upto @ I3 @ J3 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_aux_def
% 5.15/5.52 thf(fact_9885_upto__code,axiom,
% 5.15/5.52 ( upto
% 5.15/5.52 = ( ^ [I3: int,J3: int] : ( upto_aux @ I3 @ J3 @ nil_int ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_code
% 5.15/5.52 thf(fact_9886_atLeastAtMost__upto,axiom,
% 5.15/5.52 ( set_or1266510415728281911st_int
% 5.15/5.52 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ J3 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % atLeastAtMost_upto
% 5.15/5.52 thf(fact_9887_distinct__upto,axiom,
% 5.15/5.52 ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 5.15/5.52
% 5.15/5.52 % distinct_upto
% 5.15/5.52 thf(fact_9888_upto__split2,axiom,
% 5.15/5.52 ! [I: int,J: int,K: int] :
% 5.15/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.15/5.52 => ( ( ord_less_eq_int @ J @ K )
% 5.15/5.52 => ( ( upto @ I @ K )
% 5.15/5.52 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_split2
% 5.15/5.52 thf(fact_9889_upto__split1,axiom,
% 5.15/5.52 ! [I: int,J: int,K: int] :
% 5.15/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.15/5.52 => ( ( ord_less_eq_int @ J @ K )
% 5.15/5.52 => ( ( upto @ I @ K )
% 5.15/5.52 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_split1
% 5.15/5.52 thf(fact_9890_atLeastLessThan__upto,axiom,
% 5.15/5.52 ( set_or4662586982721622107an_int
% 5.15/5.52 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % atLeastLessThan_upto
% 5.15/5.52 thf(fact_9891_upto_Oelims,axiom,
% 5.15/5.52 ! [X: int,Xa2: int,Y: list_int] :
% 5.15/5.52 ( ( ( upto @ X @ Xa2 )
% 5.15/5.52 = Y )
% 5.15/5.52 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.15/5.52 => ( Y
% 5.15/5.52 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.15/5.52 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.15/5.52 => ( Y = nil_int ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto.elims
% 5.15/5.52 thf(fact_9892_upto_Osimps,axiom,
% 5.15/5.52 ( upto
% 5.15/5.52 = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto.simps
% 5.15/5.52 thf(fact_9893_upto__rec1,axiom,
% 5.15/5.52 ! [I: int,J: int] :
% 5.15/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.15/5.52 => ( ( upto @ I @ J )
% 5.15/5.52 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_rec1
% 5.15/5.52 thf(fact_9894_upto__rec2,axiom,
% 5.15/5.52 ! [I: int,J: int] :
% 5.15/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.15/5.52 => ( ( upto @ I @ J )
% 5.15/5.52 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_rec2
% 5.15/5.52 thf(fact_9895_upto__split3,axiom,
% 5.15/5.52 ! [I: int,J: int,K: int] :
% 5.15/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.15/5.52 => ( ( ord_less_eq_int @ J @ K )
% 5.15/5.52 => ( ( upto @ I @ K )
% 5.15/5.52 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto_split3
% 5.15/5.52 thf(fact_9896_list__encode_Osimps_I2_J,axiom,
% 5.15/5.52 ! [X: nat,Xs2: list_nat] :
% 5.15/5.52 ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 5.15/5.52 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % list_encode.simps(2)
% 5.15/5.52 thf(fact_9897_upto_Opelims,axiom,
% 5.15/5.52 ! [X: int,Xa2: int,Y: list_int] :
% 5.15/5.52 ( ( ( upto @ X @ Xa2 )
% 5.15/5.52 = Y )
% 5.15/5.52 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.15/5.52 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.15/5.52 => ( Y
% 5.15/5.52 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.15/5.52 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.15/5.52 => ( Y = nil_int ) ) )
% 5.15/5.52 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % upto.pelims
% 5.15/5.52 thf(fact_9898_Gcd__eq__Max,axiom,
% 5.15/5.52 ! [M7: set_nat] :
% 5.15/5.52 ( ( finite_finite_nat @ M7 )
% 5.15/5.52 => ( ( M7 != bot_bot_set_nat )
% 5.15/5.52 => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.15/5.52 => ( ( gcd_Gcd_nat @ M7 )
% 5.15/5.52 = ( lattic8265883725875713057ax_nat
% 5.15/5.52 @ ( comple7806235888213564991et_nat
% 5.15/5.52 @ ( image_nat_set_nat
% 5.15/5.52 @ ^ [M5: nat] :
% 5.15/5.52 ( collect_nat
% 5.15/5.52 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M5 ) )
% 5.15/5.52 @ M7 ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Gcd_eq_Max
% 5.15/5.52 thf(fact_9899_Gcd__nat__eq__one,axiom,
% 5.15/5.52 ! [N5: set_nat] :
% 5.15/5.52 ( ( member_nat @ one_one_nat @ N5 )
% 5.15/5.52 => ( ( gcd_Gcd_nat @ N5 )
% 5.15/5.52 = one_one_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % Gcd_nat_eq_one
% 5.15/5.52 thf(fact_9900_DERIV__real__root__generic,axiom,
% 5.15/5.52 ! [N2: nat,X: real,D4: real] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( X != zero_zero_real )
% 5.15/5.52 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.52 => ( D4
% 5.15/5.52 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.15/5.52 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.52 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.52 => ( D4
% 5.15/5.52 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.15/5.52 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.52 => ( D4
% 5.15/5.52 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_real_root_generic
% 5.15/5.52 thf(fact_9901_Gcd__int__eq,axiom,
% 5.15/5.52 ! [N5: set_nat] :
% 5.15/5.52 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N5 ) )
% 5.15/5.52 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N5 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Gcd_int_eq
% 5.15/5.52 thf(fact_9902_Gcd__abs__eq,axiom,
% 5.15/5.52 ! [K5: set_int] :
% 5.15/5.52 ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 5.15/5.52 = ( gcd_Gcd_int @ K5 ) ) ).
% 5.15/5.52
% 5.15/5.52 % Gcd_abs_eq
% 5.15/5.52 thf(fact_9903_Gcd__nat__abs__eq,axiom,
% 5.15/5.52 ! [K5: set_int] :
% 5.15/5.52 ( ( gcd_Gcd_nat
% 5.15/5.52 @ ( image_int_nat
% 5.15/5.52 @ ^ [K2: int] : ( nat2 @ ( abs_abs_int @ K2 ) )
% 5.15/5.52 @ K5 ) )
% 5.15/5.52 = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Gcd_nat_abs_eq
% 5.15/5.52 thf(fact_9904_DERIV__ln,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_ln
% 5.15/5.52 thf(fact_9905_DERIV__neg__dec__left,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.15/5.52 => ? [D3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.52 & ! [H4: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.15/5.52 => ( ( ord_less_real @ H4 @ D3 )
% 5.15/5.52 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_neg_dec_left
% 5.15/5.52 thf(fact_9906_DERIV__pos__inc__left,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.15/5.52 => ? [D3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.52 & ! [H4: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.15/5.52 => ( ( ord_less_real @ H4 @ D3 )
% 5.15/5.52 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_pos_inc_left
% 5.15/5.52 thf(fact_9907_DERIV__pos__inc__right,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.15/5.52 => ? [D3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.52 & ! [H4: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.15/5.52 => ( ( ord_less_real @ H4 @ D3 )
% 5.15/5.52 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_pos_inc_right
% 5.15/5.52 thf(fact_9908_DERIV__neg__dec__right,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.15/5.52 => ? [D3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.52 & ! [H4: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.15/5.52 => ( ( ord_less_real @ H4 @ D3 )
% 5.15/5.52 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_neg_dec_right
% 5.15/5.52 thf(fact_9909_DERIV__const__ratio__const2,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real,K: real] :
% 5.15/5.52 ( ( A != B )
% 5.15/5.52 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.15/5.52 = K ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_const_ratio_const2
% 5.15/5.52 thf(fact_9910_DERIV__isconst__all,axiom,
% 5.15/5.52 ! [F: real > real,X: real,Y: real] :
% 5.15/5.52 ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 => ( ( F @ X )
% 5.15/5.52 = ( F @ Y ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_isconst_all
% 5.15/5.52 thf(fact_9911_DERIV__const__ratio__const,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real,K: real] :
% 5.15/5.52 ( ( A != B )
% 5.15/5.52 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.15/5.52 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_const_ratio_const
% 5.15/5.52 thf(fact_9912_DERIV__mirror,axiom,
% 5.15/5.52 ! [F: real > real,Y: real,X: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ X ) @ top_top_set_real ) )
% 5.15/5.52 = ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X2: real] : ( F @ ( uminus_uminus_real @ X2 ) )
% 5.15/5.52 @ ( uminus_uminus_real @ Y )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_mirror
% 5.15/5.52 thf(fact_9913_has__real__derivative__neg__dec__right,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real,S3: set_real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.15/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.15/5.52 => ? [D3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.52 & ! [H4: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.15/5.52 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S3 )
% 5.15/5.52 => ( ( ord_less_real @ H4 @ D3 )
% 5.15/5.52 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % has_real_derivative_neg_dec_right
% 5.15/5.52 thf(fact_9914_has__real__derivative__pos__inc__right,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real,S3: set_real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.15/5.52 => ? [D3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.52 & ! [H4: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.15/5.52 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S3 )
% 5.15/5.52 => ( ( ord_less_real @ H4 @ D3 )
% 5.15/5.52 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % has_real_derivative_pos_inc_right
% 5.15/5.52 thf(fact_9915_has__real__derivative__pos__inc__left,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real,S3: set_real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.15/5.52 => ? [D3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.52 & ! [H4: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.15/5.52 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S3 )
% 5.15/5.52 => ( ( ord_less_real @ H4 @ D3 )
% 5.15/5.52 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % has_real_derivative_pos_inc_left
% 5.15/5.52 thf(fact_9916_has__real__derivative__neg__dec__left,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real,S3: set_real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.15/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.15/5.52 => ? [D3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.15/5.52 & ! [H4: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.15/5.52 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S3 )
% 5.15/5.52 => ( ( ord_less_real @ H4 @ D3 )
% 5.15/5.52 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % has_real_derivative_neg_dec_left
% 5.15/5.52 thf(fact_9917_DERIV__local__const,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real,D: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.15/5.52 => ( ! [Y3: real] :
% 5.15/5.52 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 5.15/5.52 => ( ( F @ X )
% 5.15/5.52 = ( F @ Y3 ) ) )
% 5.15/5.52 => ( L = zero_zero_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_local_const
% 5.15/5.52 thf(fact_9918_MVT2,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_eq_real @ X3 @ B )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ? [Z2: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.15/5.52 & ( ord_less_real @ Z2 @ B )
% 5.15/5.52 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.15/5.52 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z2 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % MVT2
% 5.15/5.52 thf(fact_9919_deriv__nonneg__imp__mono,axiom,
% 5.15/5.52 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.15/5.52 ( ! [X3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.15/5.52 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.15/5.52 => ( ( ord_less_eq_real @ A @ B )
% 5.15/5.52 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % deriv_nonneg_imp_mono
% 5.15/5.52 thf(fact_9920_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_eq_real @ X3 @ B )
% 5.15/5.52 => ? [Y4: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 5.15/5.52 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_nonpos_imp_nonincreasing
% 5.15/5.52 thf(fact_9921_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_eq_real @ X3 @ B )
% 5.15/5.52 => ? [Y4: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 5.15/5.52 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_nonneg_imp_nondecreasing
% 5.15/5.52 thf(fact_9922_DERIV__neg__imp__decreasing,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_eq_real @ X3 @ B )
% 5.15/5.52 => ? [Y4: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.15/5.52 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_neg_imp_decreasing
% 5.15/5.52 thf(fact_9923_DERIV__pos__imp__increasing,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_eq_real @ X3 @ B )
% 5.15/5.52 => ? [Y4: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.15/5.52 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_pos_imp_increasing
% 5.15/5.52 thf(fact_9924_DERIV__const__average,axiom,
% 5.15/5.52 ! [A: real,B: real,V: real > real,K: real] :
% 5.15/5.52 ( ( A != B )
% 5.15/5.52 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.15/5.52 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_const_average
% 5.15/5.52 thf(fact_9925_DERIV__local__max,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real,D: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.15/5.52 => ( ! [Y3: real] :
% 5.15/5.52 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 5.15/5.52 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 5.15/5.52 => ( L = zero_zero_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_local_max
% 5.15/5.52 thf(fact_9926_DERIV__local__min,axiom,
% 5.15/5.52 ! [F: real > real,L: real,X: real,D: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.15/5.52 => ( ! [Y3: real] :
% 5.15/5.52 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 5.15/5.52 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 5.15/5.52 => ( L = zero_zero_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_local_min
% 5.15/5.52 thf(fact_9927_DERIV__ln__divide,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_ln_divide
% 5.15/5.52 thf(fact_9928_DERIV__pow,axiom,
% 5.15/5.52 ! [N2: nat,X: real,S: set_real] :
% 5.15/5.52 ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X2: real] : ( power_power_real @ X2 @ N2 )
% 5.15/5.52 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_pow
% 5.15/5.52 thf(fact_9929_DERIV__fun__pow,axiom,
% 5.15/5.52 ! [G: real > real,M: real,X: real,N2: nat] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N2 )
% 5.15/5.52 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) @ M )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_fun_pow
% 5.15/5.52 thf(fact_9930_has__real__derivative__powr,axiom,
% 5.15/5.52 ! [Z: real,R2: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.15/5.52 => ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [Z3: real] : ( powr_real @ Z3 @ R2 )
% 5.15/5.52 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % has_real_derivative_powr
% 5.15/5.52 thf(fact_9931_DERIV__log,axiom,
% 5.15/5.52 ! [X: real,B: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_log
% 5.15/5.52 thf(fact_9932_DERIV__fun__powr,axiom,
% 5.15/5.52 ! [G: real > real,M: real,X: real,R2: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R2 )
% 5.15/5.52 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_fun_powr
% 5.15/5.52 thf(fact_9933_DERIV__powr,axiom,
% 5.15/5.52 ! [G: real > real,M: real,X: real,F: real > real,R2: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.15/5.52 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 5.15/5.52 @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_powr
% 5.15/5.52 thf(fact_9934_DERIV__real__sqrt,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_real_sqrt
% 5.15/5.52 thf(fact_9935_DERIV__arctan,axiom,
% 5.15/5.52 ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_arctan
% 5.15/5.52 thf(fact_9936_arsinh__real__has__field__derivative,axiom,
% 5.15/5.52 ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 5.15/5.52
% 5.15/5.52 % arsinh_real_has_field_derivative
% 5.15/5.52 thf(fact_9937_DERIV__real__sqrt__generic,axiom,
% 5.15/5.52 ! [X: real,D4: real] :
% 5.15/5.52 ( ( X != zero_zero_real )
% 5.15/5.52 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.52 => ( D4
% 5.15/5.52 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.52 => ( D4
% 5.15/5.52 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_real_sqrt_generic
% 5.15/5.52 thf(fact_9938_arcosh__real__has__field__derivative,axiom,
% 5.15/5.52 ! [X: real,A2: set_real] :
% 5.15/5.52 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % arcosh_real_has_field_derivative
% 5.15/5.52 thf(fact_9939_artanh__real__has__field__derivative,axiom,
% 5.15/5.52 ! [X: real,A2: set_real] :
% 5.15/5.52 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % artanh_real_has_field_derivative
% 5.15/5.52 thf(fact_9940_Gcd__int__def,axiom,
% 5.15/5.52 ( gcd_Gcd_int
% 5.15/5.52 = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Gcd_int_def
% 5.15/5.52 thf(fact_9941_DERIV__real__root,axiom,
% 5.15/5.52 ! [N2: nat,X: real] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_real_root
% 5.15/5.52 thf(fact_9942_DERIV__arccos,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_arccos
% 5.15/5.52 thf(fact_9943_DERIV__arcsin,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_arcsin
% 5.15/5.52 thf(fact_9944_Maclaurin__all__le__objl,axiom,
% 5.15/5.52 ! [Diff: nat > real > real,F: real > real,X: real,N2: nat] :
% 5.15/5.52 ( ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 & ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.15/5.52 & ( ( F @ X )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Maclaurin_all_le_objl
% 5.15/5.52 thf(fact_9945_Maclaurin__all__le,axiom,
% 5.15/5.52 ! [Diff: nat > real > real,F: real > real,X: real,N2: nat] :
% 5.15/5.52 ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.15/5.52 & ( ( F @ X )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Maclaurin_all_le
% 5.15/5.52 thf(fact_9946_DERIV__odd__real__root,axiom,
% 5.15/5.52 ! [N2: nat,X: real] :
% 5.15/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.52 => ( ( X != zero_zero_real )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_odd_real_root
% 5.15/5.52 thf(fact_9947_Maclaurin,axiom,
% 5.15/5.52 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.15/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ! [M3: nat,T3: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.15/5.52 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.15/5.52 & ( ord_less_real @ T3 @ H2 )
% 5.15/5.52 & ( ( F @ H2 )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Maclaurin
% 5.15/5.52 thf(fact_9948_Maclaurin2,axiom,
% 5.15/5.52 ! [H2: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.15/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ! [M3: nat,T3: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.15/5.52 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.15/5.52 & ( ord_less_eq_real @ T3 @ H2 )
% 5.15/5.52 & ( ( F @ H2 )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Maclaurin2
% 5.15/5.52 thf(fact_9949_Maclaurin__minus,axiom,
% 5.15/5.52 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.15/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ! [M3: nat,T3: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ H2 @ T3 )
% 5.15/5.52 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_real @ H2 @ T3 )
% 5.15/5.52 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.15/5.52 & ( ( F @ H2 )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Maclaurin_minus
% 5.15/5.52 thf(fact_9950_Maclaurin__all__lt,axiom,
% 5.15/5.52 ! [Diff: nat > real > real,F: real > real,N2: nat,X: real] :
% 5.15/5.52 ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( X != zero_zero_real )
% 5.15/5.52 => ( ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.15/5.52 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.15/5.52 & ( ( F @ X )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Maclaurin_all_lt
% 5.15/5.52 thf(fact_9951_Maclaurin__bi__le,axiom,
% 5.15/5.52 ! [Diff: nat > real > real,F: real > real,N2: nat,X: real] :
% 5.15/5.52 ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ! [M3: nat,T3: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.15/5.52 & ( ( F @ X )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Maclaurin_bi_le
% 5.15/5.52 thf(fact_9952_Taylor,axiom,
% 5.15/5.52 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ! [M3: nat,T3: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ A @ T3 )
% 5.15/5.52 & ( ord_less_eq_real @ T3 @ B ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.15/5.52 => ( ( ord_less_eq_real @ A @ C )
% 5.15/5.52 => ( ( ord_less_eq_real @ C @ B )
% 5.15/5.52 => ( ( ord_less_eq_real @ A @ X )
% 5.15/5.52 => ( ( ord_less_eq_real @ X @ B )
% 5.15/5.52 => ( ( X != C )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ( ord_less_real @ X @ C )
% 5.15/5.52 => ( ( ord_less_real @ X @ T3 )
% 5.15/5.52 & ( ord_less_real @ T3 @ C ) ) )
% 5.15/5.52 & ( ~ ( ord_less_real @ X @ C )
% 5.15/5.52 => ( ( ord_less_real @ C @ T3 )
% 5.15/5.52 & ( ord_less_real @ T3 @ X ) ) )
% 5.15/5.52 & ( ( F @ X )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Taylor
% 5.15/5.52 thf(fact_9953_Taylor__up,axiom,
% 5.15/5.52 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ! [M3: nat,T3: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ A @ T3 )
% 5.15/5.52 & ( ord_less_eq_real @ T3 @ B ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.15/5.52 => ( ( ord_less_eq_real @ A @ C )
% 5.15/5.52 => ( ( ord_less_real @ C @ B )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_real @ C @ T3 )
% 5.15/5.52 & ( ord_less_real @ T3 @ B )
% 5.15/5.52 & ( ( F @ B )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Taylor_up
% 5.15/5.52 thf(fact_9954_Taylor__down,axiom,
% 5.15/5.52 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.15/5.52 = F )
% 5.15/5.52 => ( ! [M3: nat,T3: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ A @ T3 )
% 5.15/5.52 & ( ord_less_eq_real @ T3 @ B ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.15/5.52 => ( ( ord_less_real @ A @ C )
% 5.15/5.52 => ( ( ord_less_eq_real @ C @ B )
% 5.15/5.52 => ? [T3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ T3 )
% 5.15/5.52 & ( ord_less_real @ T3 @ C )
% 5.15/5.52 & ( ( F @ A )
% 5.15/5.52 = ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.15/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Taylor_down
% 5.15/5.52 thf(fact_9955_Maclaurin__lemma2,axiom,
% 5.15/5.52 ! [N2: nat,H2: real,Diff: nat > real > real,K: nat,B3: real] :
% 5.15/5.52 ( ! [M3: nat,T3: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.15/5.52 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.15/5.52 => ( ( N2
% 5.15/5.52 = ( suc @ K ) )
% 5.15/5.52 => ! [M4: nat,T4: real] :
% 5.15/5.52 ( ( ( ord_less_nat @ M4 @ N2 )
% 5.15/5.52 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.15/5.52 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [U2: real] :
% 5.15/5.52 ( minus_minus_real @ ( Diff @ M4 @ U2 )
% 5.15/5.52 @ ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M4 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M4 ) ) )
% 5.15/5.52 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M4 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M4 ) ) ) ) ) )
% 5.15/5.52 @ ( minus_minus_real @ ( Diff @ ( suc @ M4 ) @ T4 )
% 5.15/5.52 @ ( plus_plus_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M4 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T4 @ P5 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M4 ) ) ) )
% 5.15/5.52 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N2 @ ( suc @ M4 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M4 ) ) ) ) ) ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Maclaurin_lemma2
% 5.15/5.52 thf(fact_9956_DERIV__arctan__series,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.52 => ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X9: real] :
% 5.15/5.52 ( suminf_real
% 5.15/5.52 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_arctan_series
% 5.15/5.52 thf(fact_9957_DERIV__even__real__root,axiom,
% 5.15/5.52 ! [N2: nat,X: real] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.52 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_even_real_root
% 5.15/5.52 thf(fact_9958_DERIV__power__series_H,axiom,
% 5.15/5.52 ! [R: real,F: nat > real,X0: real] :
% 5.15/5.52 ( ! [X3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.15/5.52 => ( summable_real
% 5.15/5.52 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X3 @ N3 ) ) ) )
% 5.15/5.52 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.15/5.52 => ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( suminf_real
% 5.15/5.52 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X2 @ ( suc @ N3 ) ) ) )
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X0 @ N3 ) ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_power_series'
% 5.15/5.52 thf(fact_9959_tanh__real__bounds,axiom,
% 5.15/5.52 ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % tanh_real_bounds
% 5.15/5.52 thf(fact_9960_DERIV__isconst3,axiom,
% 5.15/5.52 ! [A: real,B: real,X: real,Y: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.15/5.52 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.15/5.52 => ( ( F @ X )
% 5.15/5.52 = ( F @ Y ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_isconst3
% 5.15/5.52 thf(fact_9961_DERIV__series_H,axiom,
% 5.15/5.52 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.15/5.52 ( ! [N: nat] :
% 5.15/5.52 ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X2: real] : ( F @ X2 @ N )
% 5.15/5.52 @ ( F4 @ X0 @ N )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.15/5.52 => ( summable_real @ ( F @ X3 ) ) )
% 5.15/5.52 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.15/5.52 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.15/5.52 => ( ( summable_real @ L5 )
% 5.15/5.52 => ( ! [N: nat,X3: real,Y3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.15/5.52 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.15/5.52 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N ) @ ( F @ Y3 @ N ) ) ) @ ( times_times_real @ ( L5 @ N ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 5.15/5.52 => ( has_fi5821293074295781190e_real
% 5.15/5.52 @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 5.15/5.52 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_series'
% 5.15/5.52 thf(fact_9962_take__bit__numeral__minus__numeral__int,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 = ( case_option_int_num @ zero_zero_int
% 5.15/5.52 @ ^ [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 ) ) )
% 5.15/5.52 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_numeral_minus_numeral_int
% 5.15/5.52 thf(fact_9963_and__minus__numerals_I7_J,axiom,
% 5.15/5.52 ! [N2: num,M: num] :
% 5.15/5.52 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.15/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_minus_numerals(7)
% 5.15/5.52 thf(fact_9964_take__bit__num__simps_I1_J,axiom,
% 5.15/5.52 ! [M: num] :
% 5.15/5.52 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.15/5.52 = none_num ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_num_simps(1)
% 5.15/5.52 thf(fact_9965_take__bit__num__simps_I2_J,axiom,
% 5.15/5.52 ! [N2: nat] :
% 5.15/5.52 ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 5.15/5.52 = ( some_num @ one ) ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_num_simps(2)
% 5.15/5.52 thf(fact_9966_take__bit__num__simps_I5_J,axiom,
% 5.15/5.52 ! [R2: num] :
% 5.15/5.52 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.15/5.52 = ( some_num @ one ) ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_num_simps(5)
% 5.15/5.52 thf(fact_9967_card__greaterThanLessThan,axiom,
% 5.15/5.52 ! [L: nat,U: nat] :
% 5.15/5.52 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.15/5.52 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % card_greaterThanLessThan
% 5.15/5.52 thf(fact_9968_take__bit__num__simps_I3_J,axiom,
% 5.15/5.52 ! [N2: nat,M: num] :
% 5.15/5.52 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 5.15/5.52 = ( case_o6005452278849405969um_num @ none_num
% 5.15/5.52 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.15/5.52 @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_num_simps(3)
% 5.15/5.52 thf(fact_9969_take__bit__num__simps_I4_J,axiom,
% 5.15/5.52 ! [N2: nat,M: num] :
% 5.15/5.52 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 5.15/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_num_simps(4)
% 5.15/5.52 thf(fact_9970_take__bit__num__simps_I6_J,axiom,
% 5.15/5.52 ! [R2: num,M: num] :
% 5.15/5.52 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.15/5.52 = ( case_o6005452278849405969um_num @ none_num
% 5.15/5.52 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.15/5.52 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_num_simps(6)
% 5.15/5.52 thf(fact_9971_take__bit__num__simps_I7_J,axiom,
% 5.15/5.52 ! [R2: num,M: num] :
% 5.15/5.52 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.15/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_num_simps(7)
% 5.15/5.52 thf(fact_9972_and__minus__numerals_I4_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.15/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_minus_numerals(4)
% 5.15/5.52 thf(fact_9973_and__minus__numerals_I8_J,axiom,
% 5.15/5.52 ! [N2: num,M: num] :
% 5.15/5.52 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.15/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_minus_numerals(8)
% 5.15/5.52 thf(fact_9974_and__minus__numerals_I3_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.15/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_minus_numerals(3)
% 5.15/5.52 thf(fact_9975_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.15/5.52 ! [N2: nat,M: num] :
% 5.15/5.52 ( ( bit_take_bit_num @ N2 @ ( bit0 @ M ) )
% 5.15/5.52 = ( case_nat_option_num @ none_num
% 5.15/5.52 @ ^ [N3: nat] :
% 5.15/5.52 ( case_o6005452278849405969um_num @ none_num
% 5.15/5.52 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.15/5.52 @ ( bit_take_bit_num @ N3 @ M ) )
% 5.15/5.52 @ N2 ) ) ).
% 5.15/5.52
% 5.15/5.52 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.15/5.52 thf(fact_9976_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.15/5.52 ! [L: nat,U: nat] :
% 5.15/5.52 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.15/5.52 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.15/5.52
% 5.15/5.52 % atLeastSucLessThan_greaterThanLessThan
% 5.15/5.52 thf(fact_9977_and__not__num_Osimps_I2_J,axiom,
% 5.15/5.52 ! [N2: num] :
% 5.15/5.52 ( ( bit_and_not_num @ one @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( some_num @ one ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(2)
% 5.15/5.52 thf(fact_9978_and__not__num_Osimps_I4_J,axiom,
% 5.15/5.52 ! [M: num] :
% 5.15/5.52 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.15/5.52 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(4)
% 5.15/5.52 thf(fact_9979_and__not__num_Osimps_I1_J,axiom,
% 5.15/5.52 ( ( bit_and_not_num @ one @ one )
% 5.15/5.52 = none_num ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(1)
% 5.15/5.52 thf(fact_9980_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.15/5.52 ! [N2: nat] :
% 5.15/5.52 ( ( bit_take_bit_num @ N2 @ one )
% 5.15/5.52 = ( case_nat_option_num @ none_num
% 5.15/5.52 @ ^ [N3: nat] : ( some_num @ one )
% 5.15/5.52 @ N2 ) ) ).
% 5.15/5.52
% 5.15/5.52 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.15/5.52 thf(fact_9981_and__not__num_Osimps_I3_J,axiom,
% 5.15/5.52 ! [N2: num] :
% 5.15/5.52 ( ( bit_and_not_num @ one @ ( bit1 @ N2 ) )
% 5.15/5.52 = none_num ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(3)
% 5.15/5.52 thf(fact_9982_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.15/5.52 ! [N2: nat,M: num] :
% 5.15/5.52 ( ( bit_take_bit_num @ N2 @ ( bit1 @ M ) )
% 5.15/5.52 = ( case_nat_option_num @ none_num
% 5.15/5.52 @ ^ [N3: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N3 @ M ) ) )
% 5.15/5.52 @ N2 ) ) ).
% 5.15/5.52
% 5.15/5.52 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.15/5.52 thf(fact_9983_and__not__num_Osimps_I7_J,axiom,
% 5.15/5.52 ! [M: num] :
% 5.15/5.52 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.15/5.52 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(7)
% 5.15/5.52 thf(fact_9984_and__not__num__eq__Some__iff,axiom,
% 5.15/5.52 ! [M: num,N2: num,Q3: num] :
% 5.15/5.52 ( ( ( bit_and_not_num @ M @ N2 )
% 5.15/5.52 = ( some_num @ Q3 ) )
% 5.15/5.52 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 = ( numeral_numeral_int @ Q3 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num_eq_Some_iff
% 5.15/5.52 thf(fact_9985_and__not__num_Osimps_I8_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.15/5.52 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.15/5.52 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(8)
% 5.15/5.52 thf(fact_9986_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.15/5.52 ! [I: nat,J: nat] :
% 5.15/5.52 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.15/5.52 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.15/5.52 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sorted_list_of_set_greaterThanLessThan
% 5.15/5.52 thf(fact_9987_and__not__num__eq__None__iff,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( ( bit_and_not_num @ M @ N2 )
% 5.15/5.52 = none_num )
% 5.15/5.52 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 = zero_zero_int ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num_eq_None_iff
% 5.15/5.52 thf(fact_9988_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.15/5.52 ! [N2: nat,J: nat,I: nat] :
% 5.15/5.52 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.15/5.52 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N2 )
% 5.15/5.52 = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % nth_sorted_list_of_set_greaterThanLessThan
% 5.15/5.52 thf(fact_9989_int__numeral__not__and__num,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.15/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % int_numeral_not_and_num
% 5.15/5.52 thf(fact_9990_int__numeral__and__not__num,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.15/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % int_numeral_and_not_num
% 5.15/5.52 thf(fact_9991_take__bit__num__def,axiom,
% 5.15/5.52 ( bit_take_bit_num
% 5.15/5.52 = ( ^ [N3: nat,M5: num] :
% 5.15/5.52 ( if_option_num
% 5.15/5.52 @ ( ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M5 ) )
% 5.15/5.52 = zero_zero_nat )
% 5.15/5.52 @ none_num
% 5.15/5.52 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M5 ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % take_bit_num_def
% 5.15/5.52 thf(fact_9992_greaterThanLessThan__upto,axiom,
% 5.15/5.52 ( set_or5832277885323065728an_int
% 5.15/5.52 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % greaterThanLessThan_upto
% 5.15/5.52 thf(fact_9993_Bit__Operations_Otake__bit__num__code,axiom,
% 5.15/5.52 ( bit_take_bit_num
% 5.15/5.52 = ( ^ [N3: nat,M5: num] :
% 5.15/5.52 ( produc478579273971653890on_num
% 5.15/5.52 @ ^ [A3: nat,X2: num] :
% 5.15/5.52 ( case_nat_option_num @ none_num
% 5.15/5.52 @ ^ [O: nat] :
% 5.15/5.52 ( case_num_option_num @ ( some_num @ one )
% 5.15/5.52 @ ^ [P5: num] :
% 5.15/5.52 ( case_o6005452278849405969um_num @ none_num
% 5.15/5.52 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.15/5.52 @ ( bit_take_bit_num @ O @ P5 ) )
% 5.15/5.52 @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 5.15/5.52 @ X2 )
% 5.15/5.52 @ A3 )
% 5.15/5.52 @ ( product_Pair_nat_num @ N3 @ M5 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Bit_Operations.take_bit_num_code
% 5.15/5.52 thf(fact_9994_isCont__Lb__Ub,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 & ( ord_less_eq_real @ X3 @ B ) )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.15/5.52 => ? [L6: real,M9: real] :
% 5.15/5.52 ( ! [X5: real] :
% 5.15/5.52 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.15/5.52 & ( ord_less_eq_real @ X5 @ B ) )
% 5.15/5.52 => ( ( ord_less_eq_real @ L6 @ ( F @ X5 ) )
% 5.15/5.52 & ( ord_less_eq_real @ ( F @ X5 ) @ M9 ) ) )
% 5.15/5.52 & ! [Y4: real] :
% 5.15/5.52 ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 5.15/5.52 & ( ord_less_eq_real @ Y4 @ M9 ) )
% 5.15/5.52 => ? [X3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 & ( ord_less_eq_real @ X3 @ B )
% 5.15/5.52 & ( ( F @ X3 )
% 5.15/5.52 = Y4 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_Lb_Ub
% 5.15/5.52 thf(fact_9995_isCont__real__sqrt,axiom,
% 5.15/5.52 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_real_sqrt
% 5.15/5.52 thf(fact_9996_isCont__real__root,axiom,
% 5.15/5.52 ! [X: real,N2: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N2 ) ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_real_root
% 5.15/5.52 thf(fact_9997_continuous__frac,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ~ ( member_real @ X @ ring_1_Ints_real )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ archim2898591450579166408c_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % continuous_frac
% 5.15/5.52 thf(fact_9998_isCont__inverse__function2,axiom,
% 5.15/5.52 ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X )
% 5.15/5.52 => ( ( ord_less_real @ X @ B )
% 5.15/5.52 => ( ! [Z2: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ Z2 )
% 5.15/5.52 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.15/5.52 => ( ( G @ ( F @ Z2 ) )
% 5.15/5.52 = Z2 ) ) )
% 5.15/5.52 => ( ! [Z2: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ Z2 )
% 5.15/5.52 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_inverse_function2
% 5.15/5.52 thf(fact_9999_isCont__arcosh,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_arcosh
% 5.15/5.52 thf(fact_10000_continuous__floor,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ~ ( member_real @ X @ ring_1_Ints_real )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( comp_int_real_real @ ring_1_of_int_real @ archim6058952711729229775r_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % continuous_floor
% 5.15/5.52 thf(fact_10001_DERIV__inverse__function,axiom,
% 5.15/5.52 ! [F: real > real,D4: real,G: real > real,X: real,A: real,B: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 5.15/5.52 => ( ( D4 != zero_zero_real )
% 5.15/5.52 => ( ( ord_less_real @ A @ X )
% 5.15/5.52 => ( ( ord_less_real @ X @ B )
% 5.15/5.52 => ( ! [Y3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ Y3 )
% 5.15/5.52 => ( ( ord_less_real @ Y3 @ B )
% 5.15/5.52 => ( ( F @ ( G @ Y3 ) )
% 5.15/5.52 = Y3 ) ) )
% 5.15/5.52 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_inverse_function
% 5.15/5.52 thf(fact_10002_isCont__arccos,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_arccos
% 5.15/5.52 thf(fact_10003_isCont__arcsin,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_arcsin
% 5.15/5.52 thf(fact_10004_LIM__less__bound,axiom,
% 5.15/5.52 ! [B: real,X: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ B @ X )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 5.15/5.52 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.15/5.52 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 5.15/5.52 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIM_less_bound
% 5.15/5.52 thf(fact_10005_isCont__artanh,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.15/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_artanh
% 5.15/5.52 thf(fact_10006_isCont__inverse__function,axiom,
% 5.15/5.52 ! [D: real,X: real,G: real > real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ D )
% 5.15/5.52 => ( ! [Z2: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X ) ) @ D )
% 5.15/5.52 => ( ( G @ ( F @ Z2 ) )
% 5.15/5.52 = Z2 ) )
% 5.15/5.52 => ( ! [Z2: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X ) ) @ D )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % isCont_inverse_function
% 5.15/5.52 thf(fact_10007_GMVT_H,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ! [Z2: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ Z2 )
% 5.15/5.52 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.15/5.52 => ( ! [Z2: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ Z2 )
% 5.15/5.52 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 5.15/5.52 => ( ! [Z2: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.15/5.52 => ( ( ord_less_real @ Z2 @ B )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ( ! [Z2: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.15/5.52 => ( ( ord_less_real @ Z2 @ B )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ? [C2: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ C2 )
% 5.15/5.52 & ( ord_less_real @ C2 @ B )
% 5.15/5.52 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 5.15/5.52 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C2 ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % GMVT'
% 5.15/5.52 thf(fact_10008_LIM__fun__gt__zero,axiom,
% 5.15/5.52 ! [F: real > real,L: real,C: real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.15/5.52 => ? [R3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.15/5.52 & ! [X5: real] :
% 5.15/5.52 ( ( ( X5 != C )
% 5.15/5.52 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.15/5.52 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIM_fun_gt_zero
% 5.15/5.52 thf(fact_10009_LIM__fun__not__zero,axiom,
% 5.15/5.52 ! [F: real > real,L: real,C: real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.15/5.52 => ( ( L != zero_zero_real )
% 5.15/5.52 => ? [R3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.15/5.52 & ! [X5: real] :
% 5.15/5.52 ( ( ( X5 != C )
% 5.15/5.52 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.15/5.52 => ( ( F @ X5 )
% 5.15/5.52 != zero_zero_real ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIM_fun_not_zero
% 5.15/5.52 thf(fact_10010_LIM__fun__less__zero,axiom,
% 5.15/5.52 ! [F: real > real,L: real,C: real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.15/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.15/5.52 => ? [R3: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.15/5.52 & ! [X5: real] :
% 5.15/5.52 ( ( ( X5 != C )
% 5.15/5.52 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.15/5.52 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIM_fun_less_zero
% 5.15/5.52 thf(fact_10011_LIM__cos__div__sin,axiom,
% 5.15/5.52 ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIM_cos_div_sin
% 5.15/5.52 thf(fact_10012_summable__Leibniz_I2_J,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.15/5.52 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.15/5.52 => ! [N9: nat] :
% 5.15/5.52 ( member_real
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.15/5.52 @ ( set_or1222579329274155063t_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz(2)
% 5.15/5.52 thf(fact_10013_summable__Leibniz_I3_J,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.15/5.52 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.15/5.52 => ! [N9: nat] :
% 5.15/5.52 ( member_real
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.15/5.52 @ ( set_or1222579329274155063t_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz(3)
% 5.15/5.52 thf(fact_10014_filterlim__Suc,axiom,
% 5.15/5.52 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.15/5.52
% 5.15/5.52 % filterlim_Suc
% 5.15/5.52 thf(fact_10015_mult__nat__right__at__top,axiom,
% 5.15/5.52 ! [C: nat] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.15/5.52 => ( filterlim_nat_nat
% 5.15/5.52 @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 5.15/5.52 @ at_top_nat
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % mult_nat_right_at_top
% 5.15/5.52 thf(fact_10016_mult__nat__left__at__top,axiom,
% 5.15/5.52 ! [C: nat] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.15/5.52 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % mult_nat_left_at_top
% 5.15/5.52 thf(fact_10017_monoseq__convergent,axiom,
% 5.15/5.52 ! [X8: nat > real,B3: real] :
% 5.15/5.52 ( ( topolo6980174941875973593q_real @ X8 )
% 5.15/5.52 => ( ! [I2: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I2 ) ) @ B3 )
% 5.15/5.52 => ~ ! [L6: real] :
% 5.15/5.52 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % monoseq_convergent
% 5.15/5.52 thf(fact_10018_LIMSEQ__root,axiom,
% 5.15/5.52 ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( root @ N3 @ ( semiri5074537144036343181t_real @ N3 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.15/5.52 @ at_top_nat ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_root
% 5.15/5.52 thf(fact_10019_nested__sequence__unique,axiom,
% 5.15/5.52 ! [F: nat > real,G: nat > real] :
% 5.15/5.52 ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N ) ) @ ( G @ N ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( G @ N ) )
% 5.15/5.52 => ( ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_nat )
% 5.15/5.52 => ? [L4: real] :
% 5.15/5.52 ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L4 )
% 5.15/5.52 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.15/5.52 & ! [N9: nat] : ( ord_less_eq_real @ L4 @ ( G @ N9 ) )
% 5.15/5.52 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % nested_sequence_unique
% 5.15/5.52 thf(fact_10020_LIMSEQ__inverse__zero,axiom,
% 5.15/5.52 ! [X8: nat > real] :
% 5.15/5.52 ( ! [R3: real] :
% 5.15/5.52 ? [N7: nat] :
% 5.15/5.52 ! [N: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ N7 @ N )
% 5.15/5.52 => ( ord_less_real @ R3 @ ( X8 @ N ) ) )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( inverse_inverse_real @ ( X8 @ N3 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_inverse_zero
% 5.15/5.52 thf(fact_10021_lim__inverse__n_H,axiom,
% 5.15/5.52 ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N3 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_nat ) ).
% 5.15/5.52
% 5.15/5.52 % lim_inverse_n'
% 5.15/5.52 thf(fact_10022_LIMSEQ__root__const,axiom,
% 5.15/5.52 ! [C: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ C )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( root @ N3 @ C )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_root_const
% 5.15/5.52 thf(fact_10023_LIMSEQ__inverse__real__of__nat,axiom,
% 5.15/5.52 ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_nat ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_inverse_real_of_nat
% 5.15/5.52 thf(fact_10024_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.15/5.52 ! [R2: real] :
% 5.15/5.52 ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ R2 )
% 5.15/5.52 @ at_top_nat ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_inverse_real_of_nat_add
% 5.15/5.52 thf(fact_10025_increasing__LIMSEQ,axiom,
% 5.15/5.52 ! [F: nat > real,L: real] :
% 5.15/5.52 ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ L )
% 5.15/5.52 => ( ! [E2: real] :
% 5.15/5.52 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.15/5.52 => ? [N9: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N9 ) @ E2 ) ) )
% 5.15/5.52 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % increasing_LIMSEQ
% 5.15/5.52 thf(fact_10026_LIMSEQ__realpow__zero,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.15/5.52 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_realpow_zero
% 5.15/5.52 thf(fact_10027_LIMSEQ__divide__realpow__zero,axiom,
% 5.15/5.52 ! [X: real,A: real] :
% 5.15/5.52 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N3 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_divide_realpow_zero
% 5.15/5.52 thf(fact_10028_LIMSEQ__abs__realpow__zero,axiom,
% 5.15/5.52 ! [C: real] :
% 5.15/5.52 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.15/5.52 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_abs_realpow_zero
% 5.15/5.52 thf(fact_10029_LIMSEQ__abs__realpow__zero2,axiom,
% 5.15/5.52 ! [C: real] :
% 5.15/5.52 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.15/5.52 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_abs_realpow_zero2
% 5.15/5.52 thf(fact_10030_LIMSEQ__inverse__realpow__zero,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_real @ one_one_real @ X )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N3 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_inverse_realpow_zero
% 5.15/5.52 thf(fact_10031_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.15/5.52 ! [R2: real] :
% 5.15/5.52 ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ R2 )
% 5.15/5.52 @ at_top_nat ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.15/5.52 thf(fact_10032_tendsto__exp__limit__sequentially,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ) @ N3 )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.15/5.52 @ at_top_nat ) ).
% 5.15/5.52
% 5.15/5.52 % tendsto_exp_limit_sequentially
% 5.15/5.52 thf(fact_10033_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.15/5.52 ! [R2: real] :
% 5.15/5.52 ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ R2 )
% 5.15/5.52 @ at_top_nat ) ).
% 5.15/5.52
% 5.15/5.52 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.15/5.52 thf(fact_10034_summable__Leibniz_I1_J,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.15/5.52 => ( summable_real
% 5.15/5.52 @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz(1)
% 5.15/5.52 thf(fact_10035_summable,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.15/5.52 => ( summable_real
% 5.15/5.52 @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable
% 5.15/5.52 thf(fact_10036_cos__diff__limit__1,axiom,
% 5.15/5.52 ! [Theta: nat > real,Theta2: real] :
% 5.15/5.52 ( ( filterlim_nat_real
% 5.15/5.52 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.15/5.52 @ at_top_nat )
% 5.15/5.52 => ~ ! [K3: nat > int] :
% 5.15/5.52 ~ ( filterlim_nat_real
% 5.15/5.52 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % cos_diff_limit_1
% 5.15/5.52 thf(fact_10037_cos__limit__1,axiom,
% 5.15/5.52 ! [Theta: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real
% 5.15/5.52 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.15/5.52 @ at_top_nat )
% 5.15/5.52 => ? [K3: nat > int] :
% 5.15/5.52 ( filterlim_nat_real
% 5.15/5.52 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % cos_limit_1
% 5.15/5.52 thf(fact_10038_summable__Leibniz_I4_J,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] :
% 5.15/5.52 ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.15/5.52 @ at_top_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz(4)
% 5.15/5.52 thf(fact_10039_zeroseq__arctan__series,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [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 @ X @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % zeroseq_arctan_series
% 5.15/5.52 thf(fact_10040_summable__Leibniz_H_I3_J,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] :
% 5.15/5.52 ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.15/5.52 @ at_top_nat ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz'(3)
% 5.15/5.52 thf(fact_10041_summable__Leibniz_H_I2_J,axiom,
% 5.15/5.52 ! [A: nat > real,N2: nat] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.15/5.52 => ( ord_less_eq_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz'(2)
% 5.15/5.52 thf(fact_10042_sums__alternating__upper__lower,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.15/5.52 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ? [L4: real] :
% 5.15/5.52 ( ! [N9: nat] :
% 5.15/5.52 ( ord_less_eq_real
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.15/5.52 @ L4 )
% 5.15/5.52 & ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] :
% 5.15/5.52 ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ L4 )
% 5.15/5.52 @ at_top_nat )
% 5.15/5.52 & ! [N9: nat] :
% 5.15/5.52 ( ord_less_eq_real @ L4
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 5.15/5.52 & ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] :
% 5.15/5.52 ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ L4 )
% 5.15/5.52 @ at_top_nat ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sums_alternating_upper_lower
% 5.15/5.52 thf(fact_10043_summable__Leibniz_I5_J,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] :
% 5.15/5.52 ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.15/5.52 @ at_top_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz(5)
% 5.15/5.52 thf(fact_10044_summable__Leibniz_H_I5_J,axiom,
% 5.15/5.52 ! [A: nat > real] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.15/5.52 => ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] :
% 5.15/5.52 ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.15/5.52 @ at_top_nat ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz'(5)
% 5.15/5.52 thf(fact_10045_summable__Leibniz_H_I4_J,axiom,
% 5.15/5.52 ! [A: nat > real,N2: nat] :
% 5.15/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.15/5.52 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.15/5.52 => ( ord_less_eq_real
% 5.15/5.52 @ ( suminf_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.15/5.52 @ ( groups6591440286371151544t_real
% 5.15/5.52 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.15/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_Leibniz'(4)
% 5.15/5.52 thf(fact_10046_real__bounded__linear,axiom,
% 5.15/5.52 ( real_V5970128139526366754l_real
% 5.15/5.52 = ( ^ [F3: real > real] :
% 5.15/5.52 ? [C3: real] :
% 5.15/5.52 ( F3
% 5.15/5.52 = ( ^ [X2: real] : ( times_times_real @ X2 @ C3 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % real_bounded_linear
% 5.15/5.52 thf(fact_10047_tendsto__exp__limit__at__right,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( filterlim_real_real
% 5.15/5.52 @ ^ [Y2: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y2 ) ) @ ( divide_divide_real @ one_one_real @ Y2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % tendsto_exp_limit_at_right
% 5.15/5.52 thf(fact_10048_dist__real__def,axiom,
% 5.15/5.52 ( real_V975177566351809787t_real
% 5.15/5.52 = ( ^ [X2: real,Y2: real] : ( abs_abs_real @ ( minus_minus_real @ X2 @ Y2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % dist_real_def
% 5.15/5.52 thf(fact_10049_tendsto__arcosh__at__left__1,axiom,
% 5.15/5.52 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % tendsto_arcosh_at_left_1
% 5.15/5.52 thf(fact_10050_greaterThan__0,axiom,
% 5.15/5.52 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.15/5.52 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % greaterThan_0
% 5.15/5.52 thf(fact_10051_greaterThan__Suc,axiom,
% 5.15/5.52 ! [K: nat] :
% 5.15/5.52 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.15/5.52 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % greaterThan_Suc
% 5.15/5.52 thf(fact_10052_INT__greaterThan__UNIV,axiom,
% 5.15/5.52 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.15/5.52 = bot_bot_set_nat ) ).
% 5.15/5.52
% 5.15/5.52 % INT_greaterThan_UNIV
% 5.15/5.52 thf(fact_10053_filterlim__tan__at__right,axiom,
% 5.15/5.52 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 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % filterlim_tan_at_right
% 5.15/5.52 thf(fact_10054_tendsto__arctan__at__bot,axiom,
% 5.15/5.52 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.15/5.52
% 5.15/5.52 % tendsto_arctan_at_bot
% 5.15/5.52 thf(fact_10055_tanh__real__at__bot,axiom,
% 5.15/5.52 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.15/5.52
% 5.15/5.52 % tanh_real_at_bot
% 5.15/5.52 thf(fact_10056_ln__at__0,axiom,
% 5.15/5.52 filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % ln_at_0
% 5.15/5.52 thf(fact_10057_filterlim__inverse__at__bot__neg,axiom,
% 5.15/5.52 filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % filterlim_inverse_at_bot_neg
% 5.15/5.52 thf(fact_10058_artanh__real__at__right__1,axiom,
% 5.15/5.52 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 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % artanh_real_at_right_1
% 5.15/5.52 thf(fact_10059_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.15/5.52 ! [B: real,F: real > real,Flim: real] :
% 5.15/5.52 ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ X3 @ B )
% 5.15/5.52 => ? [Y4: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.15/5.52 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_pos_imp_increasing_at_bot
% 5.15/5.52 thf(fact_10060_filterlim__pow__at__bot__odd,axiom,
% 5.15/5.52 ! [N2: nat,F: real > real,F5: filter_real] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.15/5.52 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 5.15/5.52 @ at_bot_real
% 5.15/5.52 @ F5 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % filterlim_pow_at_bot_odd
% 5.15/5.52 thf(fact_10061_filterlim__pow__at__bot__even,axiom,
% 5.15/5.52 ! [N2: nat,F: real > real,F5: filter_real] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.15/5.52 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 5.15/5.52 @ at_top_real
% 5.15/5.52 @ F5 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % filterlim_pow_at_bot_even
% 5.15/5.52 thf(fact_10062_sqrt__at__top,axiom,
% 5.15/5.52 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.15/5.52
% 5.15/5.52 % sqrt_at_top
% 5.15/5.52 thf(fact_10063_ln__at__top,axiom,
% 5.15/5.52 filterlim_real_real @ ln_ln_real @ at_top_real @ at_top_real ).
% 5.15/5.52
% 5.15/5.52 % ln_at_top
% 5.15/5.52 thf(fact_10064_exp__at__top,axiom,
% 5.15/5.52 filterlim_real_real @ exp_real @ at_top_real @ at_top_real ).
% 5.15/5.52
% 5.15/5.52 % exp_at_top
% 5.15/5.52 thf(fact_10065_filterlim__real__sequentially,axiom,
% 5.15/5.52 filterlim_nat_real @ semiri5074537144036343181t_real @ at_top_real @ at_top_nat ).
% 5.15/5.52
% 5.15/5.52 % filterlim_real_sequentially
% 5.15/5.52 thf(fact_10066_filterlim__uminus__at__bot__at__top,axiom,
% 5.15/5.52 filterlim_real_real @ uminus_uminus_real @ at_bot_real @ at_top_real ).
% 5.15/5.52
% 5.15/5.52 % filterlim_uminus_at_bot_at_top
% 5.15/5.52 thf(fact_10067_filterlim__uminus__at__top__at__bot,axiom,
% 5.15/5.52 filterlim_real_real @ uminus_uminus_real @ at_top_real @ at_bot_real ).
% 5.15/5.52
% 5.15/5.52 % filterlim_uminus_at_top_at_bot
% 5.15/5.52 thf(fact_10068_tanh__real__at__top,axiom,
% 5.15/5.52 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.15/5.52
% 5.15/5.52 % tanh_real_at_top
% 5.15/5.52 thf(fact_10069_ln__x__over__x__tendsto__0,axiom,
% 5.15/5.52 ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_real ) ).
% 5.15/5.52
% 5.15/5.52 % ln_x_over_x_tendsto_0
% 5.15/5.52 thf(fact_10070_artanh__real__at__left__1,axiom,
% 5.15/5.52 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % artanh_real_at_left_1
% 5.15/5.52 thf(fact_10071_filterlim__inverse__at__right__top,axiom,
% 5.15/5.52 filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 5.15/5.52
% 5.15/5.52 % filterlim_inverse_at_right_top
% 5.15/5.52 thf(fact_10072_filterlim__inverse__at__top__right,axiom,
% 5.15/5.52 filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % filterlim_inverse_at_top_right
% 5.15/5.52 thf(fact_10073_tendsto__power__div__exp__0,axiom,
% 5.15/5.52 ! [K: nat] :
% 5.15/5.52 ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.15/5.52 @ at_top_real ) ).
% 5.15/5.52
% 5.15/5.52 % tendsto_power_div_exp_0
% 5.15/5.52 thf(fact_10074_tendsto__exp__limit__at__top,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( filterlim_real_real
% 5.15/5.52 @ ^ [Y2: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y2 ) ) @ Y2 )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.15/5.52 @ at_top_real ) ).
% 5.15/5.52
% 5.15/5.52 % tendsto_exp_limit_at_top
% 5.15/5.52 thf(fact_10075_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.15/5.52 ! [B: real,F: real > real,Flim: real] :
% 5.15/5.52 ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ B @ X3 )
% 5.15/5.52 => ? [Y4: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.15/5.52 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_neg_imp_decreasing_at_top
% 5.15/5.52 thf(fact_10076_tendsto__arctan__at__top,axiom,
% 5.15/5.52 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.15/5.52
% 5.15/5.52 % tendsto_arctan_at_top
% 5.15/5.52 thf(fact_10077_filterlim__tan__at__left,axiom,
% 5.15/5.52 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 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % filterlim_tan_at_left
% 5.15/5.52 thf(fact_10078_lhopital__left__at__top,axiom,
% 5.15/5.52 ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.15/5.52 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ Y )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ Y )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_left_at_top
% 5.15/5.52 thf(fact_10079_eventually__sequentially__Suc,axiom,
% 5.15/5.52 ! [P: nat > $o] :
% 5.15/5.52 ( ( eventually_nat
% 5.15/5.52 @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 5.15/5.52 @ at_top_nat )
% 5.15/5.52 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_sequentially_Suc
% 5.15/5.52 thf(fact_10080_eventually__sequentially__seg,axiom,
% 5.15/5.52 ! [P: nat > $o,K: nat] :
% 5.15/5.52 ( ( eventually_nat
% 5.15/5.52 @ ^ [N3: nat] : ( P @ ( plus_plus_nat @ N3 @ K ) )
% 5.15/5.52 @ at_top_nat )
% 5.15/5.52 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_sequentially_seg
% 5.15/5.52 thf(fact_10081_sequentially__offset,axiom,
% 5.15/5.52 ! [P: nat > $o,K: nat] :
% 5.15/5.52 ( ( eventually_nat @ P @ at_top_nat )
% 5.15/5.52 => ( eventually_nat
% 5.15/5.52 @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 5.15/5.52 @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % sequentially_offset
% 5.15/5.52 thf(fact_10082_eventually__False__sequentially,axiom,
% 5.15/5.52 ~ ( eventually_nat
% 5.15/5.52 @ ^ [N3: nat] : $false
% 5.15/5.52 @ at_top_nat ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_False_sequentially
% 5.15/5.52 thf(fact_10083_eventually__sequentiallyI,axiom,
% 5.15/5.52 ! [C: nat,P: nat > $o] :
% 5.15/5.52 ( ! [X3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ C @ X3 )
% 5.15/5.52 => ( P @ X3 ) )
% 5.15/5.52 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_sequentiallyI
% 5.15/5.52 thf(fact_10084_eventually__sequentially,axiom,
% 5.15/5.52 ! [P: nat > $o] :
% 5.15/5.52 ( ( eventually_nat @ P @ at_top_nat )
% 5.15/5.52 = ( ? [N6: nat] :
% 5.15/5.52 ! [N3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.15/5.52 => ( P @ N3 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_sequentially
% 5.15/5.52 thf(fact_10085_le__sequentially,axiom,
% 5.15/5.52 ! [F5: filter_nat] :
% 5.15/5.52 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.15/5.52 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % le_sequentially
% 5.15/5.52 thf(fact_10086_eventually__at__right__to__0,axiom,
% 5.15/5.52 ! [P: real > $o,A: real] :
% 5.15/5.52 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 = ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_at_right_to_0
% 5.15/5.52 thf(fact_10087_eventually__at__left__to__right,axiom,
% 5.15/5.52 ! [P: real > $o,A: real] :
% 5.15/5.52 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 = ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( P @ ( uminus_uminus_real @ X2 ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_at_left_to_right
% 5.15/5.52 thf(fact_10088_eventually__at__right__real,axiom,
% 5.15/5.52 ! [A: real,B: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_at_right_real
% 5.15/5.52 thf(fact_10089_eventually__at__left__real,axiom,
% 5.15/5.52 ! [B: real,A: real] :
% 5.15/5.52 ( ( ord_less_real @ B @ A )
% 5.15/5.52 => ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_at_left_real
% 5.15/5.52 thf(fact_10090_eventually__at__right__to__top,axiom,
% 5.15/5.52 ! [P: real > $o] :
% 5.15/5.52 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 = ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( P @ ( inverse_inverse_real @ X2 ) )
% 5.15/5.52 @ at_top_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_at_right_to_top
% 5.15/5.52 thf(fact_10091_eventually__at__top__to__right,axiom,
% 5.15/5.52 ! [P: real > $o] :
% 5.15/5.52 ( ( eventually_real @ P @ at_top_real )
% 5.15/5.52 = ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( P @ ( inverse_inverse_real @ X2 ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_at_top_to_right
% 5.15/5.52 thf(fact_10092_lhopital__at__top__at__top,axiom,
% 5.15/5.52 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ at_top_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ at_top_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_at_top_at_top
% 5.15/5.52 thf(fact_10093_lhopital,axiom,
% 5.15/5.52 ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ F5
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ F5
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital
% 5.15/5.52 thf(fact_10094_lhopital__right__at__top__at__top,axiom,
% 5.15/5.52 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ at_top_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ at_top_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_right_at_top_at_top
% 5.15/5.52 thf(fact_10095_lhopital__at__top__at__bot,axiom,
% 5.15/5.52 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ at_bot_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ at_bot_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_at_top_at_bot
% 5.15/5.52 thf(fact_10096_lhopital__left__at__top__at__top,axiom,
% 5.15/5.52 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ at_top_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ at_top_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_left_at_top_at_top
% 5.15/5.52 thf(fact_10097_lhopital__at__top,axiom,
% 5.15/5.52 ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.15/5.52 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ Y )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ Y )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_at_top
% 5.15/5.52 thf(fact_10098_lhospital__at__top__at__top,axiom,
% 5.15/5.52 ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X: real] :
% 5.15/5.52 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ at_top_real )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ at_top_real )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ at_top_real )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ X )
% 5.15/5.52 @ at_top_real )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ X )
% 5.15/5.52 @ at_top_real ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhospital_at_top_at_top
% 5.15/5.52 thf(fact_10099_lhopital__right,axiom,
% 5.15/5.52 ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ F5
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ F5
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_right
% 5.15/5.52 thf(fact_10100_lhopital__right__0,axiom,
% 5.15/5.52 ! [F0: real > real,G0: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.15/5.52 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G0 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ F5
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F0 @ X2 ) @ ( G0 @ X2 ) )
% 5.15/5.52 @ F5
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_right_0
% 5.15/5.52 thf(fact_10101_lhopital__left,axiom,
% 5.15/5.52 ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ F5
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ F5
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_left
% 5.15/5.52 thf(fact_10102_lhopital__right__at__top__at__bot,axiom,
% 5.15/5.52 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ at_bot_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ at_bot_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_right_at_top_at_bot
% 5.15/5.52 thf(fact_10103_lhopital__left__at__top__at__bot,axiom,
% 5.15/5.52 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.15/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ at_bot_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ at_bot_real
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_left_at_top_at_bot
% 5.15/5.52 thf(fact_10104_lhopital__right__at__top,axiom,
% 5.15/5.52 ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.15/5.52 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ Y )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ Y )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_right_at_top
% 5.15/5.52 thf(fact_10105_lhopital__right__0__at__top,axiom,
% 5.15/5.52 ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X: real] :
% 5.15/5.52 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] :
% 5.15/5.52 ( ( G2 @ X2 )
% 5.15/5.52 != zero_zero_real )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( eventually_real
% 5.15/5.52 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ X )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.15/5.52 => ( filterlim_real_real
% 5.15/5.52 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ X )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % lhopital_right_0_at_top
% 5.15/5.52 thf(fact_10106_Bseq__realpow,axiom,
% 5.15/5.52 ! [X: real] :
% 5.15/5.52 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.15/5.52 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.15/5.52 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Bseq_realpow
% 5.15/5.52 thf(fact_10107_card__greaterThanAtMost,axiom,
% 5.15/5.52 ! [L: nat,U: nat] :
% 5.15/5.52 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 5.15/5.52 = ( minus_minus_nat @ U @ L ) ) ).
% 5.15/5.52
% 5.15/5.52 % card_greaterThanAtMost
% 5.15/5.52 thf(fact_10108_GreatestI__ex__nat,axiom,
% 5.15/5.52 ! [P: nat > $o,B: nat] :
% 5.15/5.52 ( ? [X_12: nat] : ( P @ X_12 )
% 5.15/5.52 => ( ! [Y3: nat] :
% 5.15/5.52 ( ( P @ Y3 )
% 5.15/5.52 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.15/5.52 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % GreatestI_ex_nat
% 5.15/5.52 thf(fact_10109_Greatest__le__nat,axiom,
% 5.15/5.52 ! [P: nat > $o,K: nat,B: nat] :
% 5.15/5.52 ( ( P @ K )
% 5.15/5.52 => ( ! [Y3: nat] :
% 5.15/5.52 ( ( P @ Y3 )
% 5.15/5.52 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.15/5.52 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Greatest_le_nat
% 5.15/5.52 thf(fact_10110_GreatestI__nat,axiom,
% 5.15/5.52 ! [P: nat > $o,K: nat,B: nat] :
% 5.15/5.52 ( ( P @ K )
% 5.15/5.52 => ( ! [Y3: nat] :
% 5.15/5.52 ( ( P @ Y3 )
% 5.15/5.52 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.15/5.52 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % GreatestI_nat
% 5.15/5.52 thf(fact_10111_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.15/5.52 ! [L: nat,U: nat] :
% 5.15/5.52 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.15/5.52 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.15/5.52
% 5.15/5.52 % atLeastSucAtMost_greaterThanAtMost
% 5.15/5.52 thf(fact_10112_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.15/5.52 ! [I: nat,J: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.15/5.52 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.15/5.52 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % sorted_list_of_set_greaterThanAtMost
% 5.15/5.52 thf(fact_10113_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.15/5.52 ! [N2: nat,J: nat,I: nat] :
% 5.15/5.52 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I ) )
% 5.15/5.52 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N2 )
% 5.15/5.52 = ( suc @ ( plus_plus_nat @ I @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % nth_sorted_list_of_set_greaterThanAtMost
% 5.15/5.52 thf(fact_10114_atLeast__Suc__greaterThan,axiom,
% 5.15/5.52 ! [K: nat] :
% 5.15/5.52 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.15/5.52 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.15/5.52
% 5.15/5.52 % atLeast_Suc_greaterThan
% 5.15/5.52 thf(fact_10115_decseq__bounded,axiom,
% 5.15/5.52 ! [X8: nat > real,B3: real] :
% 5.15/5.52 ( ( order_9091379641038594480t_real @ X8 )
% 5.15/5.52 => ( ! [I2: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I2 ) )
% 5.15/5.52 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % decseq_bounded
% 5.15/5.52 thf(fact_10116_greaterThanAtMost__upto,axiom,
% 5.15/5.52 ( set_or6656581121297822940st_int
% 5.15/5.52 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % greaterThanAtMost_upto
% 5.15/5.52 thf(fact_10117_decseq__convergent,axiom,
% 5.15/5.52 ! [X8: nat > real,B3: real] :
% 5.15/5.52 ( ( order_9091379641038594480t_real @ X8 )
% 5.15/5.52 => ( ! [I2: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I2 ) )
% 5.15/5.52 => ~ ! [L6: real] :
% 5.15/5.52 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.15/5.52 => ~ ! [I4: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I4 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % decseq_convergent
% 5.15/5.52 thf(fact_10118_UN__atLeast__UNIV,axiom,
% 5.15/5.52 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.15/5.52 = top_top_set_nat ) ).
% 5.15/5.52
% 5.15/5.52 % UN_atLeast_UNIV
% 5.15/5.52 thf(fact_10119_atLeast__Suc,axiom,
% 5.15/5.52 ! [K: nat] :
% 5.15/5.52 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.15/5.52 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % atLeast_Suc
% 5.15/5.52 thf(fact_10120_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.15/5.52 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.15/5.52 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.15/5.52 = Y )
% 5.15/5.52 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.15/5.52 ( X
% 5.15/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 = ( Xa2 != one_one_nat ) ) )
% 5.15/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 = ( ~ ( ( Deg2 = Xa2 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 & ( case_o184042715313410164at_nat
% 5.15/5.52 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 @ ( produc6081775807080527818_nat_o
% 5.15/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 & ! [I3: nat] :
% 5.15/5.52 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.15/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.15/5.52 & ( ( Mi3 = Ma3 )
% 5.15/5.52 => ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 & ( ( Mi3 != Ma3 )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.15/5.52 & ! [X2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.15/5.52 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.52 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.15/5.52 @ Mima ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % VEBT_internal.valid'.elims(1)
% 5.15/5.52 thf(fact_10121_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.15/5.52 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.52 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.15/5.52 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.15/5.52 ( X
% 5.15/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.52 => ( Xa2 != one_one_nat ) )
% 5.15/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.52 => ~ ( ( Deg2 = Xa2 )
% 5.15/5.52 & ! [X5: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 & ( case_o184042715313410164at_nat
% 5.15/5.52 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 @ ( produc6081775807080527818_nat_o
% 5.15/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 & ! [I3: nat] :
% 5.15/5.52 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.15/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.15/5.52 & ( ( Mi3 = Ma3 )
% 5.15/5.52 => ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 & ( ( Mi3 != Ma3 )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.15/5.52 & ! [X2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.15/5.52 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.52 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.15/5.52 @ Mima ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % VEBT_internal.valid'.elims(2)
% 5.15/5.52 thf(fact_10122_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.15/5.52 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.15/5.52 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.15/5.52 = ( ( Deg = Deg4 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.52 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.15/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 & ( case_o184042715313410164at_nat
% 5.15/5.52 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X4 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 @ ( produc6081775807080527818_nat_o
% 5.15/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.15/5.52 & ! [I3: nat] :
% 5.15/5.52 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X4 ) )
% 5.15/5.52 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.15/5.52 & ( ( Mi3 = Ma3 )
% 5.15/5.52 => ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 & ( ( Mi3 != Ma3 )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.15/5.52 & ! [X2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X2 )
% 5.15/5.52 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.52 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.15/5.52 @ Mima2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % VEBT_internal.valid'.simps(2)
% 5.15/5.52 thf(fact_10123_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.15/5.52 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.52 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.15/5.52 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.15/5.52 ( X
% 5.15/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.52 => ( Xa2 = one_one_nat ) )
% 5.15/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.52 => ( ( Deg2 = Xa2 )
% 5.15/5.52 & ! [X3: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 & ( case_o184042715313410164at_nat
% 5.15/5.52 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 @ ( produc6081775807080527818_nat_o
% 5.15/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 & ! [I3: nat] :
% 5.15/5.52 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.15/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.15/5.52 & ( ( Mi3 = Ma3 )
% 5.15/5.52 => ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 & ( ( Mi3 != Ma3 )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.15/5.52 & ! [X2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.15/5.52 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.52 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.15/5.52 @ Mima ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % VEBT_internal.valid'.elims(3)
% 5.15/5.52 thf(fact_10124_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.15/5.52 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.15/5.52 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.15/5.52 = Y )
% 5.15/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.52 => ( ! [Uu2: $o,Uv2: $o] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.52 => ( ( Y
% 5.15/5.52 = ( Xa2 = one_one_nat ) )
% 5.15/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.15/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.52 => ( ( Y
% 5.15/5.52 = ( ( Deg2 = Xa2 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 & ( case_o184042715313410164at_nat
% 5.15/5.52 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 @ ( produc6081775807080527818_nat_o
% 5.15/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 & ! [I3: nat] :
% 5.15/5.52 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.15/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.15/5.52 & ( ( Mi3 = Ma3 )
% 5.15/5.52 => ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 & ( ( Mi3 != Ma3 )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.15/5.52 & ! [X2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.15/5.52 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.52 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.15/5.52 @ Mima ) ) )
% 5.15/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % VEBT_internal.valid'.pelims(1)
% 5.15/5.52 thf(fact_10125_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.15/5.52 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.52 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.15/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.52 => ( ! [Uu2: $o,Uv2: $o] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.15/5.52 => ( Xa2 != one_one_nat ) ) )
% 5.15/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.15/5.52 => ~ ( ( Deg2 = Xa2 )
% 5.15/5.52 & ! [X5: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 & ( case_o184042715313410164at_nat
% 5.15/5.52 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 @ ( produc6081775807080527818_nat_o
% 5.15/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 & ! [I3: nat] :
% 5.15/5.52 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.15/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.15/5.52 & ( ( Mi3 = Ma3 )
% 5.15/5.52 => ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 & ( ( Mi3 != Ma3 )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.15/5.52 & ! [X2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.15/5.52 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.52 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.15/5.52 @ Mima ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % VEBT_internal.valid'.pelims(2)
% 5.15/5.52 thf(fact_10126_Sup__int__def,axiom,
% 5.15/5.52 ( complete_Sup_Sup_int
% 5.15/5.52 = ( ^ [X4: set_int] :
% 5.15/5.52 ( the_int
% 5.15/5.52 @ ^ [X2: int] :
% 5.15/5.52 ( ( member_int @ X2 @ X4 )
% 5.15/5.52 & ! [Y2: int] :
% 5.15/5.52 ( ( member_int @ Y2 @ X4 )
% 5.15/5.52 => ( ord_less_eq_int @ Y2 @ X2 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Sup_int_def
% 5.15/5.52 thf(fact_10127_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.15/5.52 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.15/5.52 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.15/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.15/5.52 => ( ! [Uu2: $o,Uv2: $o] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.15/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.15/5.52 => ( Xa2 = one_one_nat ) ) )
% 5.15/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.15/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.15/5.52 => ( ( Deg2 = Xa2 )
% 5.15/5.52 & ! [X3: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.15/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 & ( case_o184042715313410164at_nat
% 5.15/5.52 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.15/5.52 & ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 @ ( produc6081775807080527818_nat_o
% 5.15/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.15/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 & ! [I3: nat] :
% 5.15/5.52 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.15/5.52 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X4 ) )
% 5.15/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.15/5.52 & ( ( Mi3 = Ma3 )
% 5.15/5.52 => ! [X2: vEBT_VEBT] :
% 5.15/5.52 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.15/5.52 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.15/5.52 & ( ( Mi3 != Ma3 )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.15/5.52 & ! [X2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.15/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.15/5.52 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.15/5.52 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.15/5.52 @ Mima ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % VEBT_internal.valid'.pelims(3)
% 5.15/5.52 thf(fact_10128_GMVT,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 & ( ord_less_eq_real @ X3 @ B ) )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 & ( ord_less_real @ X3 @ B ) )
% 5.15/5.52 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.15/5.52 & ( ord_less_eq_real @ X3 @ B ) )
% 5.15/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 & ( ord_less_real @ X3 @ B ) )
% 5.15/5.52 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.15/5.52 => ? [G_c: real,F_c: real,C2: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.15/5.52 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_real @ A @ C2 )
% 5.15/5.52 & ( ord_less_real @ C2 @ B )
% 5.15/5.52 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.15/5.52 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % GMVT
% 5.15/5.52 thf(fact_10129_real__differentiable__def,axiom,
% 5.15/5.52 ! [F: real > real,X: real,S: set_real] :
% 5.15/5.52 ( ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.15/5.52 = ( ? [D6: real] : ( has_fi5821293074295781190e_real @ F @ D6 @ ( topolo2177554685111907308n_real @ X @ S ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % real_differentiable_def
% 5.15/5.52 thf(fact_10130_real__differentiableE,axiom,
% 5.15/5.52 ! [F: real > real,X: real,S: set_real] :
% 5.15/5.52 ( ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.15/5.52 => ~ ! [Df: real] :
% 5.15/5.52 ~ ( has_fi5821293074295781190e_real @ F @ Df @ ( topolo2177554685111907308n_real @ X @ S ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % real_differentiableE
% 5.15/5.52 thf(fact_10131_MVT,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_real @ X3 @ B )
% 5.15/5.52 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ? [L4: real,Z2: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.15/5.52 & ( ord_less_real @ Z2 @ B )
% 5.15/5.52 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 5.15/5.52 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.15/5.52 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % MVT
% 5.15/5.52 thf(fact_10132_continuous__on__arcosh,axiom,
% 5.15/5.52 ! [A2: set_real] :
% 5.15/5.52 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.15/5.52 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % continuous_on_arcosh
% 5.15/5.52 thf(fact_10133_continuous__on__arsinh_H,axiom,
% 5.15/5.52 ! [A2: set_real,F: real > real] :
% 5.15/5.52 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.15/5.52 => ( topolo5044208981011980120l_real @ A2
% 5.15/5.52 @ ^ [X2: real] : ( arsinh_real @ ( F @ X2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % continuous_on_arsinh'
% 5.15/5.52 thf(fact_10134_continuous__on__arcosh_H,axiom,
% 5.15/5.52 ! [A2: set_real,F: real > real] :
% 5.15/5.52 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ A2 )
% 5.15/5.52 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.15/5.52 => ( topolo5044208981011980120l_real @ A2
% 5.15/5.52 @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % continuous_on_arcosh'
% 5.15/5.52 thf(fact_10135_continuous__image__closed__interval,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ? [C2: real,D3: real] :
% 5.15/5.52 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.15/5.52 = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 5.15/5.52 & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % continuous_image_closed_interval
% 5.15/5.52 thf(fact_10136_continuous__on__arccos_H,axiom,
% 5.15/5.52 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.15/5.52
% 5.15/5.52 % continuous_on_arccos'
% 5.15/5.52 thf(fact_10137_continuous__on__arcsin_H,axiom,
% 5.15/5.52 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.15/5.52
% 5.15/5.52 % continuous_on_arcsin'
% 5.15/5.52 thf(fact_10138_continuous__on__artanh,axiom,
% 5.15/5.52 ! [A2: set_real] :
% 5.15/5.52 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.15/5.52 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % continuous_on_artanh
% 5.15/5.52 thf(fact_10139_continuous__on__artanh_H,axiom,
% 5.15/5.52 ! [A2: set_real,F: real > real] :
% 5.15/5.52 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( member_real @ X3 @ A2 )
% 5.15/5.52 => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.15/5.52 => ( topolo5044208981011980120l_real @ A2
% 5.15/5.52 @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % continuous_on_artanh'
% 5.15/5.52 thf(fact_10140_Rolle__deriv,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ( ( F @ A )
% 5.15/5.52 = ( F @ B ) )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_real @ X3 @ B )
% 5.15/5.52 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ? [Z2: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.15/5.52 & ( ord_less_real @ Z2 @ B )
% 5.15/5.52 & ( ( F4 @ Z2 )
% 5.15/5.52 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Rolle_deriv
% 5.15/5.52 thf(fact_10141_mvt,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_real @ X3 @ B )
% 5.15/5.52 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ~ ! [Xi: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ Xi )
% 5.15/5.52 => ( ( ord_less_real @ Xi @ B )
% 5.15/5.52 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.15/5.52 != ( F4 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % mvt
% 5.15/5.52 thf(fact_10142_DERIV__pos__imp__increasing__open,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_real @ X3 @ B )
% 5.15/5.52 => ? [Y4: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_pos_imp_increasing_open
% 5.15/5.52 thf(fact_10143_DERIV__neg__imp__decreasing__open,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_real @ X3 @ B )
% 5.15/5.52 => ? [Y4: real] :
% 5.15/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_neg_imp_decreasing_open
% 5.15/5.52 thf(fact_10144_DERIV__isconst__end,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_real @ X3 @ B )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ( ( F @ B )
% 5.15/5.52 = ( F @ A ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_isconst_end
% 5.15/5.52 thf(fact_10145_DERIV__isconst2,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real,X: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_real @ X3 @ B )
% 5.15/5.52 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ( ( ord_less_eq_real @ A @ X )
% 5.15/5.52 => ( ( ord_less_eq_real @ X @ B )
% 5.15/5.52 => ( ( F @ X )
% 5.15/5.52 = ( F @ A ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % DERIV_isconst2
% 5.15/5.52 thf(fact_10146_Rolle,axiom,
% 5.15/5.52 ! [A: real,B: real,F: real > real] :
% 5.15/5.52 ( ( ord_less_real @ A @ B )
% 5.15/5.52 => ( ( ( F @ A )
% 5.15/5.52 = ( F @ B ) )
% 5.15/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.15/5.52 => ( ! [X3: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ X3 )
% 5.15/5.52 => ( ( ord_less_real @ X3 @ B )
% 5.15/5.52 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.15/5.52 => ? [Z2: real] :
% 5.15/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.15/5.52 & ( ord_less_real @ Z2 @ B )
% 5.15/5.52 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % Rolle
% 5.15/5.52 thf(fact_10147_uniformity__complex__def,axiom,
% 5.15/5.52 ( topolo896644834953643431omplex
% 5.15/5.52 = ( comple8358262395181532106omplex
% 5.15/5.52 @ ( image_5971271580939081552omplex
% 5.15/5.52 @ ^ [E3: real] :
% 5.15/5.52 ( princi3496590319149328850omplex
% 5.15/5.52 @ ( collec8663557070575231912omplex
% 5.15/5.52 @ ( produc6771430404735790350plex_o
% 5.15/5.52 @ ^ [X2: complex,Y2: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X2 @ Y2 ) @ E3 ) ) ) )
% 5.15/5.52 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % uniformity_complex_def
% 5.15/5.52 thf(fact_10148_uniformity__real__def,axiom,
% 5.15/5.52 ( topolo1511823702728130853y_real
% 5.15/5.52 = ( comple2936214249959783750l_real
% 5.15/5.52 @ ( image_2178119161166701260l_real
% 5.15/5.52 @ ^ [E3: real] :
% 5.15/5.52 ( princi6114159922880469582l_real
% 5.15/5.52 @ ( collec3799799289383736868l_real
% 5.15/5.52 @ ( produc5414030515140494994real_o
% 5.15/5.52 @ ^ [X2: real,Y2: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X2 @ Y2 ) @ E3 ) ) ) )
% 5.15/5.52 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % uniformity_real_def
% 5.15/5.52 thf(fact_10149_open__real__def,axiom,
% 5.15/5.52 ( topolo4860482606490270245n_real
% 5.15/5.52 = ( ^ [U4: set_real] :
% 5.15/5.52 ! [X2: real] :
% 5.15/5.52 ( ( member_real @ X2 @ U4 )
% 5.15/5.52 => ( eventu3244425730907250241l_real
% 5.15/5.52 @ ( produc5414030515140494994real_o
% 5.15/5.52 @ ^ [X9: real,Y2: real] :
% 5.15/5.52 ( ( X9 = X2 )
% 5.15/5.52 => ( member_real @ Y2 @ U4 ) ) )
% 5.15/5.52 @ topolo1511823702728130853y_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % open_real_def
% 5.15/5.52 thf(fact_10150_open__complex__def,axiom,
% 5.15/5.52 ( topolo4110288021797289639omplex
% 5.15/5.52 = ( ^ [U4: set_complex] :
% 5.15/5.52 ! [X2: complex] :
% 5.15/5.52 ( ( member_complex @ X2 @ U4 )
% 5.15/5.52 => ( eventu5826381225784669381omplex
% 5.15/5.52 @ ( produc6771430404735790350plex_o
% 5.15/5.52 @ ^ [X9: complex,Y2: complex] :
% 5.15/5.52 ( ( X9 = X2 )
% 5.15/5.52 => ( member_complex @ Y2 @ U4 ) ) )
% 5.15/5.52 @ topolo896644834953643431omplex ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % open_complex_def
% 5.15/5.52 thf(fact_10151_eventually__prod__sequentially,axiom,
% 5.15/5.52 ! [P: product_prod_nat_nat > $o] :
% 5.15/5.52 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.15/5.52 = ( ? [N6: nat] :
% 5.15/5.52 ! [M5: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ N6 @ M5 )
% 5.15/5.52 => ! [N3: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ N6 @ N3 )
% 5.15/5.52 => ( P @ ( product_Pair_nat_nat @ N3 @ M5 ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_prod_sequentially
% 5.15/5.52 thf(fact_10152_incseq__bounded,axiom,
% 5.15/5.52 ! [X8: nat > real,B3: real] :
% 5.15/5.52 ( ( order_mono_nat_real @ X8 )
% 5.15/5.52 => ( ! [I2: nat] : ( ord_less_eq_real @ ( X8 @ I2 ) @ B3 )
% 5.15/5.52 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % incseq_bounded
% 5.15/5.52 thf(fact_10153_mono__Suc,axiom,
% 5.15/5.52 order_mono_nat_nat @ suc ).
% 5.15/5.52
% 5.15/5.52 % mono_Suc
% 5.15/5.52 thf(fact_10154_mono__times__nat,axiom,
% 5.15/5.52 ! [N2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % mono_times_nat
% 5.15/5.52 thf(fact_10155_filtermap__at__right__shift,axiom,
% 5.15/5.52 ! [D: real,A: real] :
% 5.15/5.52 ( ( filtermap_real_real
% 5.15/5.52 @ ^ [X2: real] : ( minus_minus_real @ X2 @ D )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.15/5.52 = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % filtermap_at_right_shift
% 5.15/5.52 thf(fact_10156_incseq__convergent,axiom,
% 5.15/5.52 ! [X8: nat > real,B3: real] :
% 5.15/5.52 ( ( order_mono_nat_real @ X8 )
% 5.15/5.52 => ( ! [I2: nat] : ( ord_less_eq_real @ ( X8 @ I2 ) @ B3 )
% 5.15/5.52 => ~ ! [L6: real] :
% 5.15/5.52 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.15/5.52 => ~ ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ L6 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % incseq_convergent
% 5.15/5.52 thf(fact_10157_at__right__to__0,axiom,
% 5.15/5.52 ! [A: real] :
% 5.15/5.52 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.15/5.52 = ( filtermap_real_real
% 5.15/5.52 @ ^ [X2: real] : ( plus_plus_real @ X2 @ A )
% 5.15/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % at_right_to_0
% 5.15/5.52 thf(fact_10158_at__right__minus,axiom,
% 5.15/5.52 ! [A: real] :
% 5.15/5.52 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.15/5.52 = ( filtermap_real_real @ uminus_uminus_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5984915006950818249n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % at_right_minus
% 5.15/5.52 thf(fact_10159_at__left__minus,axiom,
% 5.15/5.52 ! [A: real] :
% 5.15/5.52 ( ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) )
% 5.15/5.52 = ( filtermap_real_real @ uminus_uminus_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % at_left_minus
% 5.15/5.52 thf(fact_10160_mono__ge2__power__minus__self,axiom,
% 5.15/5.52 ! [K: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.15/5.52 => ( order_mono_nat_nat
% 5.15/5.52 @ ^ [M5: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M5 ) @ M5 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % mono_ge2_power_minus_self
% 5.15/5.52 thf(fact_10161_tendsto__at__topI__sequentially__real,axiom,
% 5.15/5.52 ! [F: real > real,Y: real] :
% 5.15/5.52 ( ( order_mono_real_real @ F )
% 5.15/5.52 => ( ( filterlim_nat_real
% 5.15/5.52 @ ^ [N3: nat] : ( F @ ( semiri5074537144036343181t_real @ N3 ) )
% 5.15/5.52 @ ( topolo2815343760600316023s_real @ Y )
% 5.15/5.52 @ at_top_nat )
% 5.15/5.52 => ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Y ) @ at_top_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % tendsto_at_topI_sequentially_real
% 5.15/5.52 thf(fact_10162_and__not__num_Oelims,axiom,
% 5.15/5.52 ! [X: num,Xa2: num,Y: option_num] :
% 5.15/5.52 ( ( ( bit_and_not_num @ X @ Xa2 )
% 5.15/5.52 = Y )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y != none_num ) ) )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ( ? [N: num] :
% 5.15/5.52 ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ one ) ) ) )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ( ? [N: num] :
% 5.15/5.52 ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y != none_num ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.15/5.52 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.15/5.52 @ ( bit_and_not_num @ M3 @ N ) ) ) ) )
% 5.15/5.52 => ~ ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.elims
% 5.15/5.52 thf(fact_10163_and__not__num_Osimps_I5_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(5)
% 5.15/5.52 thf(fact_10164_and__not__num_Osimps_I6_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(6)
% 5.15/5.52 thf(fact_10165_and__not__num_Osimps_I9_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_not_num.simps(9)
% 5.15/5.52 thf(fact_10166_and__num_Oelims,axiom,
% 5.15/5.52 ! [X: num,Xa2: num,Y: option_num] :
% 5.15/5.52 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 5.15/5.52 = Y )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ one ) ) ) )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ( ? [N: num] :
% 5.15/5.52 ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y != none_num ) ) )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ( ? [N: num] :
% 5.15/5.52 ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ one ) ) ) )
% 5.15/5.52 => ( ( ? [M3: num] :
% 5.15/5.52 ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y != none_num ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N ) ) ) ) )
% 5.15/5.52 => ( ( ? [M3: num] :
% 5.15/5.52 ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ one ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N ) ) ) ) )
% 5.15/5.52 => ~ ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.15/5.52 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.15/5.52 @ ( bit_un7362597486090784418nd_num @ M3 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.elims
% 5.15/5.52 thf(fact_10167_and__num_Osimps_I5_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(5)
% 5.15/5.52 thf(fact_10168_and__num_Osimps_I1_J,axiom,
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.15/5.52 = ( some_num @ one ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(1)
% 5.15/5.52 thf(fact_10169_and__num_Osimps_I7_J,axiom,
% 5.15/5.52 ! [M: num] :
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.15/5.52 = ( some_num @ one ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(7)
% 5.15/5.52 thf(fact_10170_and__num_Osimps_I3_J,axiom,
% 5.15/5.52 ! [N2: num] :
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( some_num @ one ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(3)
% 5.15/5.52 thf(fact_10171_and__num_Osimps_I4_J,axiom,
% 5.15/5.52 ! [M: num] :
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.15/5.52 = none_num ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(4)
% 5.15/5.52 thf(fact_10172_and__num_Osimps_I2_J,axiom,
% 5.15/5.52 ! [N2: num] :
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N2 ) )
% 5.15/5.52 = none_num ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(2)
% 5.15/5.52 thf(fact_10173_and__num_Osimps_I6_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(6)
% 5.15/5.52 thf(fact_10174_and__num_Osimps_I8_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(8)
% 5.15/5.52 thf(fact_10175_and__num_Osimps_I9_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.15/5.52 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.15/5.52 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % and_num.simps(9)
% 5.15/5.52 thf(fact_10176_xor__num_Oelims,axiom,
% 5.15/5.52 ! [X: num,Xa2: num,Y: option_num] :
% 5.15/5.52 ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 5.15/5.52 = Y )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y != none_num ) ) )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ ( bit1 @ N ) ) ) ) )
% 5.15/5.52 => ( ( ( X = one )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ ( bit0 @ N ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ ( bit1 @ M3 ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit0 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N ) ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ( ( Xa2 = one )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.15/5.52 => ( ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit0 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N ) ) ) ) ) )
% 5.15/5.52 => ~ ! [M3: num] :
% 5.15/5.52 ( ( X
% 5.15/5.52 = ( bit1 @ M3 ) )
% 5.15/5.52 => ! [N: num] :
% 5.15/5.52 ( ( Xa2
% 5.15/5.52 = ( bit1 @ N ) )
% 5.15/5.52 => ( Y
% 5.15/5.52 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.elims
% 5.15/5.52 thf(fact_10177_and__num__dict,axiom,
% 5.15/5.52 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.15/5.52
% 5.15/5.52 % and_num_dict
% 5.15/5.52 thf(fact_10178_xor__num_Osimps_I5_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(5)
% 5.15/5.52 thf(fact_10179_xor__num_Osimps_I1_J,axiom,
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.15/5.52 = none_num ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(1)
% 5.15/5.52 thf(fact_10180_xor__num_Osimps_I9_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(9)
% 5.15/5.52 thf(fact_10181_xor__num_Osimps_I2_J,axiom,
% 5.15/5.52 ! [N2: num] :
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( some_num @ ( bit1 @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(2)
% 5.15/5.52 thf(fact_10182_xor__num_Osimps_I3_J,axiom,
% 5.15/5.52 ! [N2: num] :
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( some_num @ ( bit0 @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(3)
% 5.15/5.52 thf(fact_10183_xor__num_Osimps_I4_J,axiom,
% 5.15/5.52 ! [M: num] :
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.15/5.52 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(4)
% 5.15/5.52 thf(fact_10184_xor__num_Osimps_I7_J,axiom,
% 5.15/5.52 ! [M: num] :
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.15/5.52 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(7)
% 5.15/5.52 thf(fact_10185_xor__num_Osimps_I8_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.15/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(8)
% 5.15/5.52 thf(fact_10186_xor__num_Osimps_I6_J,axiom,
% 5.15/5.52 ! [M: num,N2: num] :
% 5.15/5.52 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.15/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % xor_num.simps(6)
% 5.15/5.52 thf(fact_10187_xor__num__dict,axiom,
% 5.15/5.52 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.15/5.52
% 5.15/5.52 % xor_num_dict
% 5.15/5.52 thf(fact_10188_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.15/5.52 ! [F: nat > real,G: nat > nat] :
% 5.15/5.52 ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.15/5.52 => ( ( order_mono_nat_real @ F )
% 5.15/5.52 => ( ( order_5726023648592871131at_nat @ G )
% 5.15/5.52 => ( ( bfun_nat_real
% 5.15/5.52 @ ^ [X2: nat] : ( F @ ( G @ X2 ) )
% 5.15/5.52 @ at_top_nat )
% 5.15/5.52 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % nonneg_incseq_Bseq_subseq_iff
% 5.15/5.52 thf(fact_10189_strict__mono__imp__increasing,axiom,
% 5.15/5.52 ! [F: nat > nat,N2: nat] :
% 5.15/5.52 ( ( order_5726023648592871131at_nat @ F )
% 5.15/5.52 => ( ord_less_eq_nat @ N2 @ ( F @ N2 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % strict_mono_imp_increasing
% 5.15/5.52 thf(fact_10190_eventually__subseq,axiom,
% 5.15/5.52 ! [R2: nat > nat,P: nat > $o] :
% 5.15/5.52 ( ( order_5726023648592871131at_nat @ R2 )
% 5.15/5.52 => ( ( eventually_nat @ P @ at_top_nat )
% 5.15/5.52 => ( eventually_nat
% 5.15/5.52 @ ^ [N3: nat] : ( P @ ( R2 @ N3 ) )
% 5.15/5.52 @ at_top_nat ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % eventually_subseq
% 5.15/5.52 thf(fact_10191_pos__deriv__imp__strict__mono,axiom,
% 5.15/5.52 ! [F: real > real,F4: real > real] :
% 5.15/5.52 ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.15/5.52 => ( ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( F4 @ X3 ) )
% 5.15/5.52 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % pos_deriv_imp_strict_mono
% 5.15/5.52 thf(fact_10192_inj__sgn__power,axiom,
% 5.15/5.52 ! [N2: nat] :
% 5.15/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.15/5.52 => ( inj_on_real_real
% 5.15/5.52 @ ^ [Y2: real] : ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N2 ) )
% 5.15/5.52 @ top_top_set_real ) ) ).
% 5.15/5.52
% 5.15/5.52 % inj_sgn_power
% 5.15/5.52 thf(fact_10193_log__inj,axiom,
% 5.15/5.52 ! [B: real] :
% 5.15/5.52 ( ( ord_less_real @ one_one_real @ B )
% 5.15/5.52 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % log_inj
% 5.15/5.52 thf(fact_10194_inj__on__diff__nat,axiom,
% 5.15/5.52 ! [N5: set_nat,K: nat] :
% 5.15/5.52 ( ! [N: nat] :
% 5.15/5.52 ( ( member_nat @ N @ N5 )
% 5.15/5.52 => ( ord_less_eq_nat @ K @ N ) )
% 5.15/5.52 => ( inj_on_nat_nat
% 5.15/5.52 @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ K )
% 5.15/5.52 @ N5 ) ) ).
% 5.15/5.52
% 5.15/5.52 % inj_on_diff_nat
% 5.15/5.52 thf(fact_10195_inj__Suc,axiom,
% 5.15/5.52 ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 5.15/5.52
% 5.15/5.52 % inj_Suc
% 5.15/5.52 thf(fact_10196_summable__reindex,axiom,
% 5.15/5.52 ! [F: nat > real,G: nat > nat] :
% 5.15/5.52 ( ( summable_real @ F )
% 5.15/5.52 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.15/5.52 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.15/5.52 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % summable_reindex
% 5.15/5.52 thf(fact_10197_suminf__reindex__mono,axiom,
% 5.15/5.52 ! [F: nat > real,G: nat > nat] :
% 5.15/5.52 ( ( summable_real @ F )
% 5.15/5.52 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.15/5.52 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.15/5.52 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % suminf_reindex_mono
% 5.15/5.52 thf(fact_10198_inj__on__char__of__nat,axiom,
% 5.15/5.52 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % inj_on_char_of_nat
% 5.15/5.52 thf(fact_10199_suminf__reindex,axiom,
% 5.15/5.52 ! [F: nat > real,G: nat > nat] :
% 5.15/5.52 ( ( summable_real @ F )
% 5.15/5.52 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.15/5.52 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.15/5.52 => ( ! [X3: nat] :
% 5.15/5.52 ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 5.15/5.52 => ( ( F @ X3 )
% 5.15/5.52 = zero_zero_real ) )
% 5.15/5.52 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 5.15/5.52 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % suminf_reindex
% 5.15/5.52 thf(fact_10200_open__bool__def,axiom,
% 5.15/5.52 ( topolo9180104560040979295open_o
% 5.15/5.52 = ( topolo4667128019001906403logy_o @ ( sup_sup_set_set_o @ ( image_o_set_o @ set_ord_lessThan_o @ top_top_set_o ) @ ( image_o_set_o @ set_or6416164934427428222Than_o @ top_top_set_o ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % open_bool_def
% 5.15/5.52 thf(fact_10201_sup__nat__def,axiom,
% 5.15/5.52 sup_sup_nat = ord_max_nat ).
% 5.15/5.52
% 5.15/5.52 % sup_nat_def
% 5.15/5.52 thf(fact_10202_sup__enat__def,axiom,
% 5.15/5.52 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.15/5.52
% 5.15/5.52 % sup_enat_def
% 5.15/5.52 thf(fact_10203_atLeastLessThan__add__Un,axiom,
% 5.15/5.52 ! [I: nat,J: nat,K: nat] :
% 5.15/5.52 ( ( ord_less_eq_nat @ I @ J )
% 5.15/5.52 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.15/5.52 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % atLeastLessThan_add_Un
% 5.15/5.52 thf(fact_10204_open__nat__def,axiom,
% 5.15/5.52 ( topolo4328251076210115529en_nat
% 5.15/5.52 = ( topolo1613498594424996677gy_nat @ ( sup_sup_set_set_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) ) ) ) ).
% 5.15/5.52
% 5.15/5.52 % open_nat_def
% 5.15/5.52
% 5.15/5.52 % Helper facts (38)
% 5.15/5.52 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.15/5.52 ! [X: int,Y: int] :
% 5.15/5.52 ( ( if_int @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.15/5.52 ! [X: int,Y: int] :
% 5.15/5.52 ( ( if_int @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.15/5.52 ! [X: nat,Y: nat] :
% 5.15/5.52 ( ( if_nat @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.15/5.52 ! [X: nat,Y: nat] :
% 5.15/5.52 ( ( if_nat @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.15/5.52 ! [X: num,Y: num] :
% 5.15/5.52 ( ( if_num @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.15/5.52 ! [X: num,Y: num] :
% 5.15/5.52 ( ( if_num @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.15/5.52 ! [X: rat,Y: rat] :
% 5.15/5.52 ( ( if_rat @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.15/5.52 ! [X: rat,Y: rat] :
% 5.15/5.52 ( ( if_rat @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.15/5.52 ! [X: real,Y: real] :
% 5.15/5.52 ( ( if_real @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.15/5.52 ! [X: real,Y: real] :
% 5.15/5.52 ( ( if_real @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.15/5.52 ! [P: real > $o] :
% 5.15/5.52 ( ( P @ ( fChoice_real @ P ) )
% 5.15/5.52 = ( ? [X4: real] : ( P @ X4 ) ) ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.15/5.52 ! [X: complex,Y: complex] :
% 5.15/5.52 ( ( if_complex @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.15/5.52 ! [X: complex,Y: complex] :
% 5.15/5.52 ( ( if_complex @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.15/5.52 ! [X: extended_enat,Y: extended_enat] :
% 5.15/5.52 ( ( if_Extended_enat @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.15/5.52 ! [X: extended_enat,Y: extended_enat] :
% 5.15/5.52 ( ( if_Extended_enat @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.15/5.52 ! [X: code_integer,Y: code_integer] :
% 5.15/5.52 ( ( if_Code_integer @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.15/5.52 ! [X: code_integer,Y: code_integer] :
% 5.15/5.52 ( ( if_Code_integer @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.15/5.52 ! [X: set_nat,Y: set_nat] :
% 5.15/5.52 ( ( if_set_nat @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.15/5.52 ! [X: set_nat,Y: set_nat] :
% 5.15/5.52 ( ( if_set_nat @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.15/5.52 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.15/5.52 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.15/5.52 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.15/5.52 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.15/5.52 ! [X: list_int,Y: list_int] :
% 5.15/5.52 ( ( if_list_int @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.15/5.52 ! [X: list_int,Y: list_int] :
% 5.15/5.52 ( ( if_list_int @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.15/5.52 ! [X: int > int,Y: int > int] :
% 5.15/5.52 ( ( if_int_int @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.15/5.52 ! [X: int > int,Y: int > int] :
% 5.15/5.52 ( ( if_int_int @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.15/5.52 ! [X: option_nat,Y: option_nat] :
% 5.15/5.52 ( ( if_option_nat @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.15/5.52 ! [X: option_nat,Y: option_nat] :
% 5.15/5.52 ( ( if_option_nat @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.15/5.52 ! [X: option_num,Y: option_num] :
% 5.15/5.52 ( ( if_option_num @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.15/5.52 ! [X: option_num,Y: option_num] :
% 5.15/5.52 ( ( if_option_num @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.15/5.52 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.15/5.52 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.15/5.52 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.15/5.52 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.15/5.52 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.15/5.52 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.15/5.52 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.15/5.52 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.15/5.52 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.15/5.52 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.15/5.52 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.15/5.52 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.15/5.52 ! [P: $o] :
% 5.15/5.52 ( ( P = $true )
% 5.15/5.52 | ( P = $false ) ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.15/5.52 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.15/5.52 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 5.15/5.52 = Y ) ).
% 5.15/5.52
% 5.15/5.52 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.15/5.52 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.15/5.52 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 5.15/5.52 = X ) ).
% 5.15/5.52
% 5.15/5.52 % Conjectures (1)
% 5.15/5.52 thf(conj_0,conjecture,
% 5.15/5.52 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.15/5.52 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.15/5.52 @ ( if_nat
% 5.15/5.52 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 5.15/5.52 & ~ ( ( xa = mi )
% 5.15/5.52 | ( xa = ma ) ) )
% 5.15/5.52 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ xa @ mi ) @ mi @ xa ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 6.31/6.63 @ one_one_nat ) ) ) ).
% 6.31/6.63
% 6.31/6.63 %------------------------------------------------------------------------------
% 6.31/6.63 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.84N0gWK5Rs/cvc5---1.0.5_15619.p...
% 6.31/6.63 (declare-sort $$unsorted 0)
% 6.31/6.63 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.31/6.63 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.31/6.63 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.31/6.63 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.31/6.63 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.31/6.63 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.31/6.63 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.31/6.63 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.31/6.63 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.31/6.63 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.31/6.63 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.31/6.63 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.31/6.63 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.31/6.63 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.31/6.63 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.31/6.63 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.31/6.63 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.31/6.63 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.31/6.63 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.31/6.63 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.31/6.63 (declare-sort tptp.list_P7524865323317820941T_VEBT 0)
% 6.31/6.63 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.31/6.63 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.31/6.63 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.31/6.63 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.31/6.63 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.31/6.63 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.31/6.63 (declare-sort tptp.list_P8526636022914148096eger_o 0)
% 6.31/6.63 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.31/6.63 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.31/6.63 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.31/6.63 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.31/6.63 (declare-sort tptp.list_P1726324292696863441at_num 0)
% 6.31/6.63 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.31/6.63 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 6.31/6.63 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 6.31/6.63 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.31/6.63 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 6.31/6.63 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.31/6.63 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.31/6.63 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.31/6.63 (declare-sort tptp.list_P5087981734274514673_int_o 0)
% 6.31/6.63 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.31/6.63 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.31/6.63 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.31/6.63 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.31/6.63 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.31/6.63 (declare-sort tptp.product_prod_num_num 0)
% 6.31/6.63 (declare-sort tptp.product_prod_nat_num 0)
% 6.31/6.63 (declare-sort tptp.product_prod_nat_nat 0)
% 6.31/6.63 (declare-sort tptp.product_prod_nat_int 0)
% 6.31/6.63 (declare-sort tptp.product_prod_int_int 0)
% 6.31/6.63 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.31/6.63 (declare-sort tptp.set_list_complex 0)
% 6.31/6.63 (declare-sort tptp.set_set_complex 0)
% 6.31/6.63 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.31/6.63 (declare-sort tptp.set_list_nat 0)
% 6.31/6.63 (declare-sort tptp.set_list_int 0)
% 6.31/6.63 (declare-sort tptp.product_prod_nat_o 0)
% 6.31/6.63 (declare-sort tptp.list_set_nat 0)
% 6.31/6.63 (declare-sort tptp.list_Code_integer 0)
% 6.31/6.63 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.31/6.63 (declare-sort tptp.set_set_nat 0)
% 6.31/6.63 (declare-sort tptp.set_set_int 0)
% 6.31/6.63 (declare-sort tptp.set_Code_integer 0)
% 6.31/6.63 (declare-sort tptp.set_Product_unit 0)
% 6.31/6.63 (declare-sort tptp.list_complex 0)
% 6.31/6.63 (declare-sort tptp.set_list_o 0)
% 6.31/6.63 (declare-sort tptp.set_complex 0)
% 6.31/6.63 (declare-sort tptp.filter_real 0)
% 6.31/6.63 (declare-sort tptp.set_set_o 0)
% 6.31/6.63 (declare-sort tptp.option_num 0)
% 6.31/6.63 (declare-sort tptp.option_nat 0)
% 6.31/6.63 (declare-sort tptp.filter_nat 0)
% 6.31/6.63 (declare-sort tptp.set_char 0)
% 6.31/6.63 (declare-sort tptp.list_real 0)
% 6.31/6.63 (declare-sort tptp.set_real 0)
% 6.31/6.63 (declare-sort tptp.list_num 0)
% 6.31/6.63 (declare-sort tptp.list_nat 0)
% 6.31/6.63 (declare-sort tptp.list_int 0)
% 6.31/6.63 (declare-sort tptp.vEBT_VEBT 0)
% 6.31/6.63 (declare-sort tptp.set_rat 0)
% 6.31/6.63 (declare-sort tptp.set_num 0)
% 6.31/6.63 (declare-sort tptp.set_nat 0)
% 6.31/6.63 (declare-sort tptp.set_int 0)
% 6.31/6.63 (declare-sort tptp.code_integer 0)
% 6.31/6.63 (declare-sort tptp.extended_enat 0)
% 6.31/6.63 (declare-sort tptp.list_o 0)
% 6.31/6.63 (declare-sort tptp.complex 0)
% 6.31/6.63 (declare-sort tptp.set_o 0)
% 6.31/6.63 (declare-sort tptp.char 0)
% 6.31/6.63 (declare-sort tptp.real 0)
% 6.31/6.63 (declare-sort tptp.rat 0)
% 6.31/6.63 (declare-sort tptp.num 0)
% 6.31/6.63 (declare-sort tptp.nat 0)
% 6.31/6.63 (declare-sort tptp.int 0)
% 6.31/6.63 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.31/6.63 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.31/6.63 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.31/6.63 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.31/6.63 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.31/6.63 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.31/6.63 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.31/6.63 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.31/6.63 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.31/6.63 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.31/6.63 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.31/6.63 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.31/6.63 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.31/6.63 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.31/6.63 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.31/6.63 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.31/6.63 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.31/6.63 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.31/6.63 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.31/6.63 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.31/6.63 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.31/6.63 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.31/6.63 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.31/6.63 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.31/6.63 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.31/6.63 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.31/6.63 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.31/6.63 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.31/6.63 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.31/6.63 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.31/6.63 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.31/6.63 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.31/6.63 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.31/6.63 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.31/6.63 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.31/6.63 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.31/6.63 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.31/6.63 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.31/6.63 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.31/6.63 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.31/6.63 (declare-fun tptp.eventu5826381225784669381omplex ((-> tptp.produc4411394909380815293omplex Bool) tptp.filter6041513312241820739omplex) Bool)
% 6.31/6.63 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.31/6.63 (declare-fun tptp.eventu3244425730907250241l_real ((-> tptp.produc2422161461964618553l_real Bool) tptp.filter2146258269922977983l_real) Bool)
% 6.31/6.63 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.31/6.63 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.31/6.63 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.31/6.63 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.31/6.63 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.31/6.63 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.31/6.63 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.31/6.63 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.31/6.63 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.31/6.63 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.31/6.63 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.31/6.63 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.31/6.63 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.31/6.63 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.31/6.63 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.31/6.63 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.31/6.63 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.31/6.63 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.31/6.63 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.31/6.63 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.31/6.63 (declare-fun tptp.finite2998713641127702882nt_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 6.31/6.63 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.31/6.63 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.31/6.63 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 6.31/6.63 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 6.31/6.63 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.31/6.63 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.31/6.63 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.31/6.63 (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)
% 6.31/6.63 (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)
% 6.31/6.63 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.31/6.63 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 6.31/6.63 (declare-fun tptp.comp_int_real_real ((-> tptp.int tptp.real) (-> tptp.real tptp.int) tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.31/6.63 (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)
% 6.31/6.63 (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)
% 6.31/6.63 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.31/6.63 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.31/6.63 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.31/6.63 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.31/6.63 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.one_one_int () tptp.int)
% 6.31/6.63 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.31/6.63 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.31/6.63 (declare-fun tptp.one_one_real () tptp.real)
% 6.31/6.63 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.uminus1680532995456772888plex_o ((-> tptp.complex Bool) tptp.complex) Bool)
% 6.31/6.63 (declare-fun tptp.uminus_uminus_int_o ((-> tptp.int Bool) tptp.int) Bool)
% 6.31/6.63 (declare-fun tptp.uminus_uminus_nat_o ((-> tptp.nat Bool) tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.uminus7117520113953359693_int_o ((-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.31/6.63 (declare-fun tptp.uminus_uminus_real_o ((-> tptp.real Bool) tptp.real) Bool)
% 6.31/6.63 (declare-fun tptp.uminus6401447641752708672_nat_o ((-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.uminus6221592323253981072nt_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.31/6.63 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.31/6.63 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.31/6.63 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.31/6.63 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.31/6.63 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.31/6.63 (declare-fun tptp.groups8507830703676809646_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups8255218700646806128omplex ((-> tptp.set_nat tptp.complex) tptp.set_set_nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups5107569545109728110t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups1794756597179926696omplex ((-> tptp.vEBT_VEBT tptp.complex) tptp.set_VEBT_VEBT) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups769130701875090982BT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.set_VEBT_VEBT) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups771621172384141258BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups136491112297645522BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups2240296850493347238T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.31/6.63 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.31/6.63 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.31/6.63 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups5726676334696518183BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 6.31/6.63 (declare-fun tptp.groups2703838992350267259T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 6.31/6.63 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.31/6.63 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.31/6.63 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.31/6.63 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.31/6.63 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.31/6.63 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.31/6.63 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.31/6.63 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.31/6.63 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.31/6.63 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.31/6.63 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.31/6.63 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.31/6.63 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.31/6.63 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.31/6.63 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.31/6.63 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.sup_sup_set_set_o (tptp.set_set_o tptp.set_set_o) tptp.set_set_o)
% 6.31/6.63 (declare-fun tptp.sup_sup_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.31/6.63 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.31/6.63 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.31/6.63 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 6.31/6.63 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.31/6.63 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.31/6.63 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.31/6.63 (declare-fun tptp.nil_int () tptp.list_int)
% 6.31/6.63 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.31/6.63 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.31/6.63 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.31/6.63 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.31/6.63 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.31/6.63 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.31/6.63 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.31/6.63 (declare-fun tptp.list_update_set_nat (tptp.list_set_nat tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.31/6.63 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.31/6.63 (declare-fun tptp.nth_Pr8522763379788166057eger_o (tptp.list_P8526636022914148096eger_o tptp.nat) tptp.produc6271795597528267376eger_o)
% 6.31/6.63 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 6.31/6.63 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 6.31/6.63 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.nth_Pr8326237132889035090at_num (tptp.list_P1726324292696863441at_num tptp.nat) tptp.product_prod_nat_num)
% 6.31/6.63 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 6.31/6.63 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.31/6.63 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.31/6.63 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.31/6.63 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.31/6.63 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.31/6.63 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.31/6.63 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.31/6.63 (declare-fun tptp.produc3607205314601156340eger_o (tptp.list_Code_integer tptp.list_o) tptp.list_P8526636022914148096eger_o)
% 6.31/6.63 (declare-fun tptp.product_int_o (tptp.list_int tptp.list_o) tptp.list_P5087981734274514673_int_o)
% 6.31/6.63 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 6.31/6.63 (declare-fun tptp.produc662631939642741121T_VEBT (tptp.list_int tptp.list_VEBT_VEBT) tptp.list_P7524865323317820941T_VEBT)
% 6.31/6.63 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.31/6.63 (declare-fun tptp.product_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 6.31/6.63 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 6.31/6.63 (declare-fun tptp.product_nat_num (tptp.list_nat tptp.list_num) tptp.list_P1726324292696863441at_num)
% 6.31/6.63 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.31/6.63 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.31/6.63 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.31/6.63 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.31/6.63 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.31/6.63 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.31/6.63 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.31/6.63 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.31/6.63 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.31/6.63 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.31/6.63 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.31/6.63 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.31/6.63 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.31/6.63 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.31/6.63 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.31/6.63 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s4246224855604898693_int_o (tptp.list_P5087981734274514673_int_o) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s5157815400016825771nt_int (tptp.list_P5707943133018811711nt_int) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s6639371672096860321T_VEBT (tptp.list_P7524865323317820941T_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.31/6.63 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.31/6.63 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.one () tptp.num)
% 6.31/6.63 (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)
% 6.31/6.63 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.31/6.63 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.31/6.63 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.31/6.63 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.31/6.63 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.31/6.63 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.31/6.63 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.31/6.63 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.31/6.63 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.none_num () tptp.option_num)
% 6.31/6.63 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.31/6.63 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.31/6.63 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.31/6.63 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.31/6.63 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.31/6.63 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.31/6.63 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.31/6.63 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.31/6.63 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.31/6.63 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.31/6.63 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 6.31/6.63 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.31/6.63 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.31/6.63 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.63 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.31/6.63 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.31/6.63 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.31/6.63 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.order_mono_real_real ((-> tptp.real tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.31/6.63 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.31/6.63 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.31/6.63 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.31/6.63 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.31/6.63 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.31/6.63 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.31/6.63 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.31/6.63 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.31/6.63 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.31/6.63 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.31/6.63 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.31/6.63 (declare-fun tptp.produc2899441246263362727at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc6121120109295599847at_nat) tptp.produc5542196010084753463at_nat)
% 6.31/6.63 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.31/6.63 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.31/6.63 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.31/6.63 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 6.31/6.63 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 6.31/6.63 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.31/6.63 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.31/6.63 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.31/6.63 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 6.31/6.63 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.31/6.63 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.31/6.63 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.31/6.63 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.31/6.63 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.31/6.63 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.31/6.63 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.31/6.63 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.31/6.63 (declare-fun tptp.produc7828578312038201481er_o_o ((-> tptp.code_integer Bool Bool) tptp.produc6271795597528267376eger_o) Bool)
% 6.31/6.63 (declare-fun tptp.produc1043322548047392435omplex ((-> tptp.code_integer Bool tptp.set_complex) tptp.produc6271795597528267376eger_o) tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.produc1253318751659547953et_int ((-> tptp.code_integer Bool tptp.set_int) tptp.produc6271795597528267376eger_o) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.produc5431169771168744661et_nat ((-> tptp.code_integer Bool tptp.set_nat) tptp.produc6271795597528267376eger_o) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.produc242741666403216561t_real ((-> tptp.code_integer Bool tptp.set_real) tptp.produc6271795597528267376eger_o) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.produc4188289175737317920o_char ((-> tptp.code_integer Bool tptp.char) tptp.produc6271795597528267376eger_o) tptp.char)
% 6.31/6.63 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.31/6.63 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.31/6.63 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.31/6.63 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.31/6.63 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.31/6.63 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.31/6.63 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.31/6.63 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.31/6.63 (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)
% 6.31/6.63 (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)
% 6.31/6.63 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.31/6.63 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.31/6.63 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.produc4927758841916487424_num_o ((-> tptp.nat tptp.num Bool) tptp.product_prod_nat_num) Bool)
% 6.31/6.63 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.produc6231982587499038204omplex ((-> tptp.nat tptp.num tptp.set_complex) tptp.product_prod_nat_num) tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.produc1435849484188172666t_real ((-> tptp.nat tptp.num tptp.set_real) tptp.product_prod_nat_num) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.produc5703948589228662326_num_o ((-> tptp.num tptp.num Bool) tptp.product_prod_num_num) Bool)
% 6.31/6.63 (declare-fun tptp.produc2866383454006189126omplex ((-> tptp.num tptp.num tptp.set_complex) tptp.product_prod_num_num) tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.produc6406642877701697732et_int ((-> tptp.num tptp.num tptp.set_int) tptp.product_prod_num_num) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.produc1361121860356118632et_nat ((-> tptp.num tptp.num tptp.set_nat) tptp.product_prod_num_num) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.produc8296048397933160132t_real ((-> tptp.num tptp.num tptp.set_real) tptp.product_prod_num_num) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.31/6.63 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.31/6.63 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.31/6.63 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.31/6.63 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.31/6.63 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 6.31/6.63 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.31/6.63 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.31/6.63 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.31/6.63 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.31/6.63 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.31/6.63 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.31/6.63 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.31/6.63 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.31/6.63 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.31/6.63 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.31/6.63 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.31/6.63 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.31/6.63 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.31/6.63 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.31/6.63 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.31/6.63 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.31/6.63 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.31/6.63 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.31/6.63 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.31/6.63 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.31/6.63 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.31/6.63 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.31/6.63 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.31/6.63 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.31/6.63 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 6.31/6.63 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.31/6.63 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.31/6.63 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.31/6.63 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.31/6.63 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.31/6.63 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.31/6.63 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.31/6.63 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.31/6.63 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.31/6.63 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.31/6.63 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 6.31/6.63 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 6.31/6.63 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.collect_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool)) tptp.set_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.image_o_set_o ((-> Bool tptp.set_o) tptp.set_o) tptp.set_set_o)
% 6.31/6.63 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.31/6.63 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.31/6.63 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.31/6.63 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.image_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.31/6.63 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 6.31/6.63 (declare-fun tptp.insert5033312907999012233nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.31/6.63 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 6.31/6.63 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.31/6.63 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.31/6.63 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.31/6.63 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.set_or6416164934427428222Than_o (Bool) tptp.set_o)
% 6.31/6.63 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.set_ord_lessThan_o (Bool) tptp.set_o)
% 6.31/6.63 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.31/6.63 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.31/6.63 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.31/6.63 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.31/6.63 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.31/6.63 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.31/6.63 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.31/6.63 (declare-fun tptp.char_of_integer (tptp.code_integer) tptp.char)
% 6.31/6.63 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.31/6.63 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.31/6.63 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo4667128019001906403logy_o (tptp.set_set_o tptp.set_o) Bool)
% 6.31/6.63 (declare-fun tptp.topolo1613498594424996677gy_nat (tptp.set_set_nat tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.topolo2919662092509805066nteger ((-> tptp.nat tptp.code_integer)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo7278393974255667507et_nat ((-> tptp.nat tptp.set_nat)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo9180104560040979295open_o (tptp.set_o) Bool)
% 6.31/6.63 (declare-fun tptp.topolo4110288021797289639omplex (tptp.set_complex) Bool)
% 6.31/6.63 (declare-fun tptp.topolo4328251076210115529en_nat (tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.topolo4860482606490270245n_real (tptp.set_real) Bool)
% 6.31/6.63 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.31/6.63 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.31/6.63 (declare-fun tptp.topolo6517432010174082258omplex ((-> tptp.nat tptp.complex)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.31/6.63 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.31/6.63 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.31/6.63 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.diffs_Code_integer ((-> tptp.nat tptp.code_integer) tptp.nat) tptp.code_integer)
% 6.31/6.63 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.31/6.63 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.31/6.63 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.31/6.63 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.pi () tptp.real)
% 6.31/6.63 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.31/6.63 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.31/6.63 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.31/6.63 (declare-fun tptp.vEBT_T_i_n_s_e_r_t (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_T_i_n_s_e_r_t2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_T5076183648494686801_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_T9217963907923527482_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_T_m_a_x_t (tptp.vEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_T_m_a_x_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_T_m_e_m_b_e_r (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_T_m_e_m_b_e_r2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_T8099345112685741742_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_T5837161174952499735_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_T_m_i_n_N_u_l_l (tptp.vEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_T5462971552011256508_l_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_T_m_i_n_t (tptp.vEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_T_m_i_n_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_height (tptp.vEBT_VEBT) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_height_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.31/6.63 (declare-fun tptp.vEBT_V1502963449132264192at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.option4927543243414619207at_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.31/6.63 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.31/6.63 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.31/6.63 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.31/6.63 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.63 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.31/6.63 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.31/6.63 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.31/6.63 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.31/6.63 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.31/6.63 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.31/6.63 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.31/6.63 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.31/6.63 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.31/6.63 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.31/6.63 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.31/6.63 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.31/6.63 (declare-fun tptp.deg () tptp.nat)
% 6.31/6.63 (declare-fun tptp.m () tptp.nat)
% 6.31/6.63 (declare-fun tptp.ma () tptp.nat)
% 6.31/6.63 (declare-fun tptp.mi () tptp.nat)
% 6.31/6.63 (declare-fun tptp.na () tptp.nat)
% 6.31/6.63 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.31/6.63 (declare-fun tptp.xa () tptp.nat)
% 6.31/6.63 (assert (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi))
% 6.31/6.63 (assert (forall ((X tptp.nat)) (=> (forall ((N tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N) N)))) (not (forall ((N tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N) (@ tptp.suc N)))))))))
% 6.31/6.63 (assert (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.31/6.63 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)) tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.31/6.63 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.31/6.63 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.31/6.63 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.31/6.63 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.63 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc (@ (@ tptp.minus_minus_nat tptp.deg) _let_2))))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi)) tptp.mi) tptp.xa))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_4))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_6))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) _let_3) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)) (not (or (= tptp.xa tptp.mi) (= tptp.xa tptp.ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_4))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_7))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t tptp.summary) _let_6)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N2) tptp.one_one_complex) (= N2 tptp.one))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real N2) tptp.one_one_real) (= N2 tptp.one))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_rat N2) tptp.one_one_rat) (= N2 tptp.one))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat N2) tptp.one_one_nat) (= N2 tptp.one))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int N2) tptp.one_one_int) (= N2 tptp.one))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N2)) (= tptp.one N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N2)) (= tptp.one N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N2)) (= tptp.one N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N2)) (= tptp.one N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N2)) (= tptp.one N2))))
% 6.31/6.63 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.63 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.31/6.63 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) Xs) (@ (@ tptp.ord_less_eq_nat Y2) X2)))))))
% 6.31/6.63 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) Xs) (@ (@ tptp.ord_less_eq_nat X2) Y2)))))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22))))
% 6.31/6.63 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N2)) (= M N2))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.31/6.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit0 N2)))))
% 6.31/6.63 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N2)))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit1 N2)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.31/6.63 (assert (forall ((A tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.member5262025264175285858nt_int A) (@ tptp.collec213857154873943460nt_int P)) (@ P A))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.31/6.63 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.31/6.63 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.31/6.63 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)))
% 6.31/6.63 (assert (forall ((A2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X2) A2))) A2)))
% 6.31/6.63 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)))
% 6.31/6.63 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A2))) A2)))
% 6.31/6.63 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)))
% 6.31/6.63 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)))
% 6.31/6.63 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.product_prod_int_int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec213857154873943460nt_int P) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.31/6.63 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X3 tptp.complex)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 6.31/6.63 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 6.31/6.63 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.31/6.63 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (= (@ _let_1 (@ _let_1 I)) I)))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) (@ tptp.suc J))))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.bit1 N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.31/6.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))))
% 6.31/6.63 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_set_nat (@ F N4)) (@ F N2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_rat (@ F N4)) (@ F N2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_num (@ F N4)) (@ F N2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F N2))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M2) (exists ((M3 tptp.nat)) (= M2 (@ tptp.suc M3))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M4)) N) (@ P M4))) (@ P N))) (@ P N2))))
% 6.31/6.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 6.31/6.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X3)))))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (forall ((X3 tptp.nat)) (@ (@ R X3) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((N tptp.nat)) (@ (@ R N) (@ tptp.suc N))) (@ (@ R M) N2)))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (=> (@ (@ tptp.ord_less_nat N) J) (=> (@ P (@ tptp.suc N)) (@ P N))))) (@ P I))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N) (=> (@ (@ tptp.ord_less_nat N) J) (=> (@ P N) (@ P (@ tptp.suc N)))))) (@ P J))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.minus_minus_nat J) I) K) (= J (@ (@ tptp.plus_plus_nat K) I))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 6.31/6.63 (assert (forall ((J tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I) K)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N2) (@ (@ tptp.plus_plus_num N2) tptp.one))))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (assert (= tptp.ord_less_eq_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M5) N3) (= M5 N3)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (assert (= tptp.ord_less_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M5) N3) (not (= M5 N3))))))
% 6.31/6.63 (assert (= tptp.ord_less_eq_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (exists ((K2 tptp.nat)) (= N3 (@ (@ tptp.plus_plus_nat M5) K2))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K))))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) D)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex C) D)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (=> (= J (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K3) (=> (@ _let_1 J2) (=> (@ (@ P J2) K3) (@ _let_1 K3))))))) (@ (@ P I) J))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M) (exists ((M6 tptp.nat)) (and (= M (@ tptp.suc M6)) (@ (@ tptp.ord_less_nat N2) M6))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (and (@ P N2) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ P I3)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (or (@ P N2) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N2) (@ P I3)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)))
% 6.31/6.63 (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))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.31/6.63 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_i_n_N_u_l_l T)) tptp.one_one_nat)))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.31/6.63 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.31/6.63 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (not (@ P N)) (exists ((M4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N) (not (@ P M4)))))) (@ P N2))))
% 6.31/6.63 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N) (@ P M4))) (@ P N))) (@ P N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.31/6.63 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.31/6.63 (assert (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))))
% 6.31/6.63 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 6.31/6.63 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (not (= (@ tptp.size_size_VEBT_VEBT X) (@ tptp.size_size_VEBT_VEBT Y))) (not (= X Y)))))
% 6.31/6.63 (assert (forall ((X tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y))) (not (= X Y)))))
% 6.31/6.63 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_num (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_num (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N4))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N4) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N4))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K3)))))))
% 6.31/6.63 (assert (= tptp.ord_less_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (exists ((K2 tptp.nat)) (= N3 (@ tptp.suc (@ (@ tptp.plus_plus_nat M5) K2)))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (forall ((Q2 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q2)))))))))
% 6.31/6.63 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.31/6.63 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.31/6.63 (assert (= tptp.suc (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))))))
% 6.31/6.63 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.31/6.63 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.31/6.63 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.31/6.63 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.31/6.63 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.31/6.63 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)) Mi) X))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X Mi) (= X Ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_6))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary) _let_5)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))))
% 6.31/6.63 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.31/6.63 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.31/6.63 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.31/6.63 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.31/6.63 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.31/6.63 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.31/6.63 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.31/6.63 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.31/6.63 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.31/6.63 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X32 tptp.num)) (not (= Y (@ tptp.bit1 X32)))))))))
% 6.31/6.63 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))))
% 6.31/6.63 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))))
% 6.31/6.63 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))))
% 6.31/6.63 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.31/6.63 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.31/6.63 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.31/6.63 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.31/6.63 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.31/6.63 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.31/6.63 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X))))))))
% 6.31/6.63 (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)))))))))))
% 6.31/6.63 (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))))))))))
% 6.31/6.63 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high X) _let_4))) (let ((_let_6 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_3) TreeList) Summary)) X) (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= X Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (= X Ma)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ _let_6 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5)) (@ (@ tptp.vEBT_VEBT_low X) _let_4)))) tptp.one_one_nat)))))))))))))))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)) Mi) X))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_4))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X Mi) (= X Ma))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))))))))
% 6.31/6.63 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.31/6.63 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.31/6.63 (assert (= tptp.m tptp.na))
% 6.31/6.63 (assert (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I4)))))
% 6.31/6.63 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.31/6.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.31/6.63 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N2) tptp.one_one_rat)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N2) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N2) tptp.one_one_complex)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)))
% 6.31/6.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.31/6.63 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.64 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I4)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) tptp.na) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X5) (@ (@ tptp.ord_less_eq_nat X5) tptp.ma)))))))))
% 6.31/6.64 (assert (=> (= tptp.mi tptp.ma) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))))
% 6.31/6.64 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((I tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N2) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N2) K)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (K tptp.rat) (N2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N2) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N2) K)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N2) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N2) K)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N2) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N2) K)))))
% 6.31/6.64 (assert (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))))
% 6.31/6.64 (assert (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N2) K)) J)))))))))
% 6.31/6.64 (assert (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))))
% 6.31/6.64 (assert (forall ((I 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 I) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N5)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N5)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N5)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N5)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N5)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N5)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N5)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N5)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.31/6.64 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.31/6.64 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.31/6.64 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.31/6.64 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X)) _let_1)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X)) _let_1)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X)) _let_1)))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X)) _let_1)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X2) N3))) (@ (@ tptp.vEBT_VEBT_low X2) N3)))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))))
% 6.31/6.64 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.31/6.64 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) X)))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) Y)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((Summary tptp.vEBT_VEBT) (Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height Summary))) (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N2))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N2))) TreeList3) S2))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) N2))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N2))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) (@ tptp.set_set_nat2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ P (@ (@ tptp.nth_set_nat Xs2) N2))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N2))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N2))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N2 tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N2))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N2))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT T) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 6.31/6.64 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat _let_1) (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.times_times_nat _let_1) N2))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X5) tptp.na) (forall ((Xa tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t X5) Xa)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height X5))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.31/6.64 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t tptp.summary) X)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height tptp.summary))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z3 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z3) (@ (@ tptp.ord_less_nat X) Z3)) (@ (@ tptp.ord_less_eq_nat Y) Z3)))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z3 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z3) (@ (@ tptp.ord_less_nat Z3) X)) (@ (@ tptp.ord_less_eq_nat Z3) Y)))))))
% 6.31/6.64 (assert (forall ((S3 tptp.set_real)) (=> (exists ((X5 tptp.real)) (@ (@ tptp.member_real X5) S3)) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Z4)))) (exists ((Y3 tptp.real)) (and (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Y3))) (forall ((Z4 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Z4))) (@ (@ tptp.ord_less_eq_real Y3) Z4)))))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X) N))))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y2) (= X2 Y2)))))
% 6.31/6.64 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (E tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) E)) C))))
% 6.31/6.64 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 6.31/6.64 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N2))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N2))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N2))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N2))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N2))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L))))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I) J)) U)) K))))
% 6.31/6.64 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N2) Q3)) (@ (@ tptp.divide_divide_nat (@ _let_1 N2)) Q3)))))
% 6.31/6.64 (assert (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.31/6.64 (assert (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)))
% 6.31/6.64 (assert (= (lambda ((X2 tptp.rat)) X2) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.31/6.64 (assert (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.31/6.64 (assert (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y) B))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) A)) B))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) A)) B))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) (@ (@ tptp.times_times_complex Y) Y)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex X) Y)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) E)) C) D))))
% 6.31/6.64 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D))))
% 6.31/6.64 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D))))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) tptp.one_one_complex))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.power_power_rat Y) N2)) tptp.one_one_rat))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (I tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) I))))
% 6.31/6.64 (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)))
% 6.31/6.64 (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)))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height _let_1))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.31/6.64 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.31/6.64 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.31/6.64 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.31/6.64 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))
% 6.31/6.64 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 6.31/6.64 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M) N2)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))))
% 6.31/6.64 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N2)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))))
% 6.31/6.64 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N2)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.31/6.64 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X) X)) X)) X))))
% 6.31/6.64 (assert (forall ((X tptp.real)) (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X) X)) X)) X))))
% 6.31/6.64 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X) X)) X)) X))))
% 6.31/6.64 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.power_power_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X) X)) X)) X))))
% 6.31/6.64 (assert (forall ((X tptp.int)) (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X) X)) X)) X))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) Y)) tptp.one_one_nat)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Q3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q3))) (= (@ (@ tptp.divide_divide_nat M) N2) Q3))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) L)) tptp.one_one_nat)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N2))))))
% 6.31/6.64 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N2)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) Y)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.31/6.64 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)))))
% 6.31/6.64 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((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 ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((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 ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X3) N2))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.31/6.64 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((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 ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((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 ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X3) N2))) (and (@ (@ tptp.ord_less_nat Mi) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex A) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) A) B)))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.31/6.64 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.31/6.64 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex C))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_complex A) B)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N2) N2)))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N2) (@ tptp.bit0 N2))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.extended_enat Bool)) (N2 tptp.extended_enat)) (=> (forall ((N tptp.extended_enat)) (=> (forall ((M4 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M4) N) (@ P M4))) (@ P N))) (@ P N2))))
% 6.31/6.64 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real B2) A3))))
% 6.31/6.64 (assert (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat B2) A3))))
% 6.31/6.64 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A3))))
% 6.31/6.64 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A3))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.31/6.64 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 6.31/6.64 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.31/6.64 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_rat I) K) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_complex A2) B) (@ _let_1 (@ (@ tptp.plus_plus_complex A) B)))))))
% 6.31/6.64 (assert (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.64 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.64 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.64 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.64 (assert (forall ((B3 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (let ((_let_2 (@ tptp.plus_plus_complex K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ (@ tptp.plus_plus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.31/6.64 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real B2) A3))))
% 6.31/6.64 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A3))))
% 6.31/6.64 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A3))))
% 6.31/6.64 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A3))))
% 6.31/6.64 (assert (= tptp.plus_plus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex B2) A3))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex B))) (let ((_let_2 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex B) A) (@ (@ tptp.plus_plus_complex C) A)) (= B C))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) _let_2))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))))
% 6.31/6.64 (assert (forall ((C tptp.rat)) (= (lambda ((X2 tptp.rat)) (@ (@ tptp.times_times_rat X2) C)) (@ tptp.times_times_rat C))))
% 6.31/6.64 (assert (forall ((C tptp.nat)) (= (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C)) (@ tptp.times_times_nat C))))
% 6.31/6.64 (assert (forall ((C tptp.int)) (= (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int X2) C)) (@ tptp.times_times_int C))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C2))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (exists ((C3 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A3) C3))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.31/6.64 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_complex A2) B) (@ _let_1 (@ (@ tptp.minus_minus_complex A) B)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A2) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.minus_minus_complex A) B) C) (= A (@ (@ tptp.plus_plus_complex C) B)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.minus_minus_complex C) B)) (= (@ (@ tptp.plus_plus_complex A) B) C))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 C)) B)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex C) B) A) (= C (@ (@ tptp.minus_minus_complex A) B)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))))
% 6.31/6.64 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))))
% 6.31/6.64 (assert (forall ((L tptp.num) (R2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q3) 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))))))))))
% 6.31/6.64 (assert (forall ((L tptp.num) (R2 tptp.int) (Q3 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q3) 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))))))))))
% 6.31/6.64 (assert (forall ((L tptp.num) (R2 tptp.code_integer) (Q3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q3) 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))))))))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N2)) (@ tptp.set_complex2 Xs2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N2)) (@ tptp.set_real2 Xs2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs2) N2)) (@ tptp.set_set_nat2 Xs2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N2)) (@ tptp.set_nat2 Xs2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N2)) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N2)) (@ tptp.set_o2 Xs2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N2)) (@ tptp.set_int2 Xs2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_nat Xs2) N2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_o Xs2) N2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_int Xs2) N2))))))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I3) X))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I3) X))))))
% 6.31/6.64 (assert (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (@ (@ tptp.nth_set_nat Xs2) I3) X))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) X))))))
% 6.31/6.64 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) X))))))
% 6.31/6.64 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) X))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) X))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I2)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P X)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I2)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P X)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (X tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ P (@ (@ tptp.nth_set_nat Xs2) I2)))) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (@ P X)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I2)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I2)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I2)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X)))))
% 6.31/6.64 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))
% 6.31/6.64 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 6.31/6.64 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N))))) (=> (forall ((N tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N))))) (=> (forall ((M3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) tptp.one)))) (=> (forall ((M3 tptp.num) (N tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) (@ tptp.bit0 N))))) (=> (forall ((M3 tptp.num) (N tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) (@ tptp.bit1 N))))) (=> (forall ((M3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) tptp.one)))) (=> (forall ((M3 tptp.num) (N tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) (@ tptp.bit0 N))))) (not (forall ((M3 tptp.num) (N tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) (@ tptp.bit1 N))))))))))))))))
% 6.31/6.64 (assert (forall ((X5 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X5) X_1))))
% 6.31/6.64 (assert (forall ((X5 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X5) X_1))))
% 6.31/6.64 (assert (forall ((X5 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X5))))
% 6.31/6.64 (assert (forall ((X5 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X5))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) B3) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 (@ tptp.set_complex2 Xs2)) (@ _let_1 B3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) B3) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 Xs2)) (@ _let_1 B3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_set_nat) (B3 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs2)) B3) (forall ((X2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs2)) (@ _let_1 B3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) B3) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs2)) (@ _let_1 B3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) B3) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs2)) (@ _let_1 B3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) B3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs2)) (@ _let_1 B3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs2 Ys)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (not (= Xs2 Ys)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (not (= Xs2 Ys)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N2))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W)) (@ (@ tptp.times_times_complex Y) Z)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W)) (@ (@ tptp.times_times_real Y) Z)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W)) (@ (@ tptp.times_times_rat Y) Z)))))
% 6.31/6.64 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex Y) W)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) W)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) W)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.31/6.64 (assert (forall ((P (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.31/6.64 (assert (forall ((P (-> tptp.list_int Bool)) (Xs2 tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 6.31/6.64 (assert (= (lambda ((Y5 tptp.list_nat) (Z5 tptp.list_nat)) (= Y5 Z5)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys3) I3))))))))
% 6.31/6.64 (assert (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z5 tptp.list_VEBT_VEBT)) (= Y5 Z5)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I3) (@ (@ tptp.nth_VEBT_VEBT Ys3) I3))))))))
% 6.31/6.64 (assert (= (lambda ((Y5 tptp.list_o) (Z5 tptp.list_o)) (= Y5 Z5)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I3) (@ (@ tptp.nth_o Ys3) I3))))))))
% 6.31/6.64 (assert (= (lambda ((Y5 tptp.list_int) (Z5 tptp.list_int)) (= Y5 Z5)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I3) (@ (@ tptp.nth_int Ys3) I3))))))))
% 6.31/6.64 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.nat)) (@ (@ P I3) X4)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_nat Xs) I3)))))))))
% 6.31/6.64 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.vEBT_VEBT)) (@ (@ P I3) X4)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_VEBT_VEBT Xs) I3)))))))))
% 6.31/6.64 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 Bool)) (@ (@ P I3) X4)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_o Xs) I3)))))))))
% 6.31/6.64 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X4 tptp.int)) (@ (@ P I3) X4)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_int Xs) I3)))))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) (@ (@ tptp.nth_nat Ys) I2)))) (= Xs2 Ys)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) (@ (@ tptp.nth_VEBT_VEBT Ys) I2)))) (= Xs2 Ys)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I2) (@ (@ tptp.nth_o Ys) I2)))) (= Xs2 Ys)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I2) (@ (@ tptp.nth_int Ys) I2)))) (= Xs2 Ys)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I3)))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ P X2))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I3)))))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N2) (=> (= N2 (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))))))))))
% 6.31/6.64 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.31/6.64 (assert (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.64 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) Xs) (@ (@ tptp.ord_less_nat X2) Y2) (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) Xs) (=> (@ (@ tptp.ord_less_nat X2) Z3) (@ (@ tptp.ord_less_eq_nat Y2) Z3))))))))
% 6.31/6.64 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) Xs) (@ (@ tptp.ord_less_nat Y2) X2) (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) Xs) (=> (@ (@ tptp.ord_less_nat Z3) X2) (@ (@ tptp.ord_less_eq_nat Z3) Y2))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A2) Z) (=> (@ tptp.finite_finite_nat B3) (=> (= A2 B3) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A2) X) X_1))))))))
% 6.31/6.64 (assert (forall ((Z tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X) X_1)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X))))
% 6.31/6.64 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat X5) A))))))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs2) A) X_1))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat A) X5))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))))
% 6.31/6.64 (assert (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.31/6.64 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.31/6.64 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.31/6.64 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.31/6.64 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.31/6.64 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A4) B4)) C))))))
% 6.31/6.64 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A4) B4)) C))))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A4) B4)) C))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A4) B4)) C))))))
% 6.31/6.64 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A4) B4)) C))))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) B4)) C))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.31/6.64 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A4) B4)) C))))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A4) B4)) C))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N2)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)))
% 6.31/6.64 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_o) (N2 tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (= (@ tptp.size_size_list_o Xs) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (= (@ tptp.size_size_list_int Xs) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (= (@ tptp.size_size_list_nat Xs) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_o) (N2 tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N2))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N2))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D3 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= tptp.modulo_modulo_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M5) N3)) M5) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M5) N3)) N3)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 6.31/6.64 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (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))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (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))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))))
% 6.31/6.64 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (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))))))
% 6.31/6.64 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (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))))))
% 6.31/6.64 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_1))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.31/6.64 (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)))
% 6.31/6.64 (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)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.31/6.64 (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)))
% 6.31/6.64 (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)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 6.31/6.64 (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)))
% 6.31/6.64 (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)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 6.31/6.64 (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)))
% 6.31/6.64 (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)))
% 6.31/6.64 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (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))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (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))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_1))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (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))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (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))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q2 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q2))))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (forall ((S2 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q3) S2))))))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (forall ((S2 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q3) S2))))))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q3)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N2)) Q3))) (@ _let_1 N2)))))))
% 6.31/6.64 (assert (= tptp.modulo_modulo_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.minus_minus_nat M5) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M5) N3)) N3)))))
% 6.31/6.64 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy)) tptp.one_one_nat)))
% 6.31/6.64 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary)) X) tptp.one_one_nat)))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 6.31/6.64 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V))) TreeList) Summary)) X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.31/6.64 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N2) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M3) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))))
% 6.31/6.64 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.31/6.64 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.31/6.64 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.31/6.64 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList) Summary)))))
% 6.31/6.64 (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 ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B5 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B5) A2)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B5) A2)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B5) A2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z3 tptp.real)) (= (@ (@ tptp.power_power_real Z3) N2) tptp.one_one_real)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) tptp.one_one_complex)))))))
% 6.31/6.64 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y2 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y2))))))
% 6.31/6.64 (assert (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y2 tptp.nat)) (= X (@ tptp.some_nat Y2))))))
% 6.31/6.64 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y2 tptp.num)) (= X (@ tptp.some_num Y2))))))
% 6.31/6.64 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y2 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y2)))) (= X tptp.none_P5556105721700978146at_nat))))
% 6.31/6.64 (assert (forall ((X tptp.option_nat)) (= (forall ((Y2 tptp.nat)) (not (= X (@ tptp.some_nat Y2)))) (= X tptp.none_nat))))
% 6.31/6.64 (assert (forall ((X tptp.option_num)) (= (forall ((Y2 tptp.num)) (not (= X (@ tptp.some_num Y2)))) (= X tptp.none_num))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.31/6.64 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X22 Y22))))
% 6.31/6.64 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y22)) (= X22 Y22))))
% 6.31/6.64 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y22)) (= X22 Y22))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat X) Maxi))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int Q))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (or (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int Q))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (and (@ P X2) (@ Q X2))))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (or (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (and (@ P X2) (@ Q X2))))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ P X2) (@ Q X2))))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (or (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ P X2) (@ Q X2))))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ P X2) (@ Q X2))))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.some_nat M) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)))))
% 6.31/6.64 (assert (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N tptp.nat)) (forall ((X5 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X5)) N)))))))
% 6.31/6.64 (assert (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N tptp.nat)) (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X5)) N)))))))
% 6.31/6.64 (assert (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N tptp.nat)) (forall ((X5 tptp.list_int)) (=> (@ (@ tptp.member_list_int X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X5)) N)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (R (-> tptp.real tptp.nat Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_complex) (R (-> tptp.real tptp.complex Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_int) (R (-> tptp.real tptp.int Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A3 tptp.real)) (and (@ (@ tptp.member_real A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_complex) (R (-> tptp.nat tptp.complex Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_int) (R (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A3 tptp.nat)) (and (@ (@ tptp.member_nat A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_nat) (R (-> tptp.complex tptp.nat Bool))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((A3 tptp.complex)) (and (@ (@ tptp.member_complex A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (R (-> tptp.complex tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) B3) (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((A3 tptp.complex)) (and (@ (@ tptp.member_complex A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_int) (R (-> tptp.complex tptp.int Bool))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((A3 tptp.complex)) (and (@ (@ tptp.member_complex A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_nat) (R (-> tptp.int tptp.nat Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A3 tptp.int)) (and (@ (@ tptp.member_int A3) A2) (@ (@ R A3) X3)))))))))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (=> (not (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P))) (exists ((X_1 tptp.product_prod_int_int)) (@ P X_1)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.set_nat Bool))) (=> (not (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P))) (exists ((X_1 tptp.set_nat)) (@ P X_1)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_1 tptp.nat)) (@ P X_1)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P))) (exists ((X_1 tptp.complex)) (@ P X_1)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_1 tptp.int)) (@ P X_1)))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real A) X3) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_set_nat A) X3) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (@ (@ tptp.ord_less_eq_rat A) X3) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (@ (@ tptp.ord_less_eq_num A) X3) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat A) X3) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int A) X3) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real X3) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_set_nat X3) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (@ (@ tptp.ord_less_eq_rat X3) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (@ (@ tptp.ord_less_eq_num X3) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat X3) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int X3) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B6 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B6 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_nat B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B6 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_num B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.nat) (B6 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A5 tptp.nat) (B6 tptp.nat)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_nat B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.nat) (B6 tptp.num)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_num B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.num) (B6 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A5 tptp.num) (B6 tptp.nat)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_nat B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.num) (B6 tptp.num)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_num B6)) (@ (@ P X) Y)))) _let_1))))))
% 6.31/6.64 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.31/6.64 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (forall ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (and (@ P4 tptp.none_nat) (forall ((X2 tptp.nat)) (@ P4 (@ tptp.some_nat X2)))))))
% 6.31/6.64 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X2 tptp.num)) (@ P4 (@ tptp.some_num X2)))))))
% 6.31/6.64 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X2 tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.31/6.64 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (exists ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (or (@ P4 tptp.none_nat) (exists ((X2 tptp.nat)) (@ P4 (@ tptp.some_nat X2)))))))
% 6.31/6.64 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X2 tptp.num)) (@ P4 (@ tptp.some_num X2)))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (@ tptp.some_nat X23))))))))
% 6.31/6.64 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))))
% 6.31/6.64 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.31/6.64 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 6.31/6.64 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 6.31/6.64 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 6.31/6.64 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 6.31/6.64 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 6.31/6.64 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 6.31/6.64 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 6.31/6.64 (assert (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)))
% 6.31/6.64 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.31/6.64 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.31/6.64 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.31/6.64 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) tptp.none_nat)))))))
% 6.31/6.64 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) tptp.none_nat)))))))
% 6.31/6.64 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ tptp.some_nat Mi))))))
% 6.31/6.64 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ tptp.some_nat Ma))))))
% 6.31/6.64 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)))))
% 6.31/6.64 (assert (= tptp.ord_less_nat (lambda ((Y2 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Sx)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Px)))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_eq_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X) tptp.none_nat))))))
% 6.31/6.64 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.31/6.64 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.none_nat)))
% 6.31/6.64 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.none_nat)))
% 6.31/6.64 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.31/6.64 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.31/6.64 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.31/6.64 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Ma))))
% 6.31/6.64 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Mi))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat Y2) X)))) tptp.bot_bot_set_nat)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat X) Y2)))) tptp.bot_bot_set_nat)))))
% 6.31/6.64 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N2)) tptp.bot_bot_set_nat)))
% 6.31/6.64 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.31/6.64 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.31/6.64 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.31/6.64 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.31/6.64 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.31/6.64 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.31/6.64 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.31/6.64 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N2)) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))))
% 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 (@ (@ tptp.plus_plus_nat M) N2)) (or (@ _let_1 M) (@ _let_1 N2))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M) _let_1) (or (= M tptp.zero_zero_nat) (= X _let_1))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.31/6.64 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.31/6.64 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.31/6.64 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X Y))))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))))
% 6.31/6.64 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A) B)))))
% 6.31/6.64 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F A) B)))))
% 6.31/6.64 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F A) B)))))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.64 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.31/6.64 (assert (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.31/6.64 (assert (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.31/6.64 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.31/6.64 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.31/6.64 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.31/6.64 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.31/6.64 (assert (= (lambda ((Y5 tptp.complex) (Z5 tptp.complex)) (= Y5 Z5)) (lambda ((A3 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B2) tptp.zero_zero_complex))))
% 6.31/6.64 (assert (= (lambda ((Y5 tptp.real) (Z5 tptp.real)) (= Y5 Z5)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))))
% 6.31/6.64 (assert (= (lambda ((Y5 tptp.rat) (Z5 tptp.rat)) (= Y5 Z5)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))))
% 6.31/6.64 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.31/6.64 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.31/6.64 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.31/6.64 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M) N2))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))))
% 6.31/6.64 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va3 tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va3))))))))))
% 6.31/6.64 (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 ((M4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N) (not (@ P M4))))))) (@ P N2)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.31/6.64 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.31/6.64 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.31/6.64 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.31/6.64 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X3) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X3) Xa) (= X3 Xa))))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 6.31/6.64 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C2 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.31/6.64 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.31/6.64 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X) Z) (@ (@ tptp.times_times_complex W) Y)))))))
% 6.31/6.64 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X) Z) (@ (@ tptp.times_times_real W) Y)))))))
% 6.31/6.64 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X) Z) (@ (@ tptp.times_times_rat W) Y)))))))
% 6.31/6.64 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))))
% 6.31/6.64 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.31/6.64 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ P (@ tptp.suc I3))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N2) (@ P (@ tptp.suc I3))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N2) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K3) (not (@ P I4)))) (@ P K3)))))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.plus_plus_nat I) K3) J))))))
% 6.31/6.64 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.64 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.64 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.64 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.31/6.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((I tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q2 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q2))))))
% 6.31/6.64 (assert (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw) (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)))
% 6.31/6.64 (assert (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)))
% 6.31/6.64 (assert (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw) (@ tptp.some_nat V)) tptp.none_nat) tptp.none_nat)))
% 6.31/6.64 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A5 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A5)) (forall ((B6 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B6)) (not (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A5) B6)))))))))))))))
% 6.31/6.64 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A5 tptp.num)) (=> (= Xa2 (@ tptp.some_num A5)) (forall ((B6 tptp.num)) (=> (= Xb (@ tptp.some_num B6)) (not (= Y (@ tptp.some_num (@ (@ X A5) B6)))))))))))))))
% 6.31/6.64 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A5 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A5)) (forall ((B6 tptp.nat)) (=> (= Xb (@ tptp.some_nat B6)) (not (= Y (@ tptp.some_nat (@ (@ X A5) B6)))))))))))))))
% 6.31/6.64 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y) E2)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.31/6.64 (assert (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.31/6.64 (assert (forall ((Y tptp.rat) (X tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 6.31/6.64 (assert (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 6.31/6.64 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.31/6.64 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.31/6.64 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.31/6.64 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 6.31/6.64 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))))))))
% 6.31/6.64 (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))))))))))))
% 6.31/6.64 (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))))))))))))
% 6.31/6.64 (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))))))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 6.31/6.64 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.31/6.64 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.31/6.64 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.31/6.64 (assert (forall ((Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.31/6.64 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.31/6.64 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.31/6.64 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.31/6.64 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.31/6.64 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.31/6.64 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.31/6.64 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.31/6.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.65 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat))))
% 6.31/6.65 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int))))
% 6.31/6.65 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.65 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.31/6.65 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.31/6.65 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.65 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.65 (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)))))
% 6.31/6.65 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K3) (not (@ P I4)))) (@ P (@ tptp.suc K3))))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))) N2))))
% 6.31/6.65 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 6.31/6.65 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 6.31/6.65 (assert (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs2)))))
% 6.31/6.65 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 6.31/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.31/6.65 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 6.31/6.65 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (assert (forall ((I tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N2))))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (assert (forall ((Q3 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q3)) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N2) Q3))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))
% 6.31/6.65 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.31/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))))
% 6.31/6.65 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S)) X) tptp.one_one_nat)))
% 6.31/6.65 (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))))
% 6.31/6.65 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S)) X) tptp.one_one_nat)))
% 6.31/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.31/6.65 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.31/6.65 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 6.31/6.65 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))))))
% 6.31/6.65 (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))))))))))))
% 6.31/6.65 (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)))))))))))
% 6.31/6.65 (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)))))))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.31/6.65 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.31/6.65 (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)))))))))))))
% 6.31/6.65 (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)))))))))))))
% 6.31/6.65 (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)))))))))))))
% 6.31/6.65 (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)))))))))))))
% 6.31/6.65 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.31/6.65 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.31/6.65 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N5)) (@ _let_1 N2))))))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N5)) (@ _let_1 N2))))))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N5)) (@ _let_1 N2))))))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N5)) (@ _let_1 N2))))))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N5)) (@ _let_1 N2))))))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N5)) (@ _let_1 N2))))))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) (@ _let_1 N2))))))))
% 6.31/6.65 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N5)) (@ _let_1 N2))))))))
% 6.31/6.65 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.31/6.65 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.31/6.65 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.31/6.65 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.31/6.65 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat))))
% 6.31/6.65 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int))))
% 6.31/6.65 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.65 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (assert (= tptp.divide_divide_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M5) N3) (= N3 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M5) N3)) N3))))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (assert (= tptp.plus_plus_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N3) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)) N3))))))
% 6.31/6.65 (assert (forall ((Q3 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N2) Q3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q3)) N2)))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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 ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J3)) (@ P I3))))))))))
% 6.31/6.65 (assert (= tptp.times_times_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N3) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)) N3))))))
% 6.31/6.65 (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 ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J3)) (@ P J3))))))))))
% 6.31/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 6.31/6.65 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X) tptp.one_one_nat)))
% 6.31/6.65 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X) tptp.one_one_nat)))
% 6.31/6.65 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X) (or (= X Mi) (= X Ma)))))
% 6.31/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve) tptp.none_nat)))
% 6.31/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve)) Vf) tptp.none_nat)))
% 6.31/6.65 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.31/6.65 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.31/6.65 (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)))))))))))))
% 6.31/6.65 (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)))))))))))))
% 6.31/6.65 (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))))))))))))
% 6.31/6.65 (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))))))))))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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)))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S 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) S) (@ (@ 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))) S))) V))))))
% 6.31/6.65 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S 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) S) (@ (@ 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))) S))) V))))))
% 6.31/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.31/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.31/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.31/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.31/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.31/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))
% 6.31/6.65 (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))))
% 6.31/6.65 (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))))
% 6.31/6.65 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ 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 Q3)) tptp.zero_zero_nat)))))
% 6.31/6.65 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ 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 Q3)) tptp.zero_zero_int)))))
% 6.31/6.65 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))))
% 6.31/6.65 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ 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 Q3)) tptp.zero_zero_nat)))))
% 6.31/6.65 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ 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 Q3)) tptp.zero_zero_int)))))
% 6.31/6.65 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))))
% 6.31/6.65 (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))))))))))))
% 6.31/6.65 (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))))))))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M5 tptp.nat)) (@ (@ (@ tptp.if_complex (= M5 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.31/6.65 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M5 tptp.nat)) (@ (@ (@ tptp.if_real (= M5 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.31/6.65 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M5 tptp.nat)) (@ (@ (@ tptp.if_rat (= M5 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.31/6.65 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M5 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.31/6.65 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M5 tptp.nat)) (@ (@ (@ tptp.if_int (= M5 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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))))))
% 6.31/6.65 (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)))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))
% 6.31/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi) tptp.none_nat)))
% 6.31/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj) tptp.none_nat)))
% 6.31/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X) Y))))))
% 6.31/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.31/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))))
% 6.31/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.31/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.31/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.31/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.31/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 6.31/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 6.31/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 6.31/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 6.31/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (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))))))))
% 6.31/6.65 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((X tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A5 tptp.product_prod_nat_nat) (B6 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A5)) (@ tptp.some_P7363390416028606310at_nat B6)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B6 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A5)) (@ tptp.some_nat B6)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A5 tptp.num) (B6 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A5)) (@ tptp.some_num B6)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X3)) (@ tptp.some_P7363390416028606310at_nat Y3)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y3 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc7036089656553540234on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num Bool)) (X3 tptp.num) (Y3 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X3)) (@ tptp.some_num Y3)))))))))))
% 6.37/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N2)) (@ _let_1 M)))))))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N2)) (@ _let_1 N2)))))))))
% 6.37/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.37/6.65 (assert (forall ((M tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.37/6.65 (assert (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.37/6.65 (assert (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (assert (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.37/6.65 (assert (forall ((U tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 6.37/6.65 (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))))))))))
% 6.37/6.65 (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))))))))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat X) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.37/6.65 (assert (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.37/6.65 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.37/6.65 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.37/6.65 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ tptp.ord_less_nat X))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= X Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X Ma)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_4 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi) X) (@ _let_4 Ma))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) tptp.zero_zero_nat)) tptp.zero_zero_nat)))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (forall ((Uu2 Bool) (B6 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uu2) B6)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B6 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B6) (= Y tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N tptp.nat)) (= Xa2 (@ tptp.suc N))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A5 Bool)) (=> (exists ((Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))))) (=> (forall ((A5 Bool) (B6 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (=> (exists ((Va3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va3)))) (not (and (=> B6 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B6) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N2))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.37/6.65 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X) Xa2) Y) (=> (=> (exists ((A5 Bool) (B6 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B6))) (not (= Y (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))))) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) _let_1) (=> (=> (exists ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2))) (not (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_5))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (= Y (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_1))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_6))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary2) _let_5)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) C)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.37/6.65 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2))))))
% 6.37/6.65 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B6 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B6))))))
% 6.37/6.65 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= N2 tptp.one_one_nat) (exists ((A5 Bool) (B6 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B6)))))))
% 6.37/6.65 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y22)) (= X22 Y22))))
% 6.37/6.65 (assert (forall ((X33 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X33) (@ tptp.bit1 Y32)) (= X33 Y32))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y222 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 6.37/6.65 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.37/6.65 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat)))
% 6.37/6.65 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N2) tptp.zero_z5237406670263579293d_enat) N2)))
% 6.37/6.65 (assert (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.vEBT_Leaf A) B)) X) tptp.one_one_nat)))
% 6.37/6.65 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) Deg3))))))))
% 6.37/6.65 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.37/6.65 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.37/6.65 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.37/6.65 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))))
% 6.37/6.65 (assert (forall ((N2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N2)))
% 6.37/6.65 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (=> (= (@ (@ tptp.modulo_modulo_int A2) N2) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N2)) (@ (@ tptp.divide_divide_int B3) N2))))))))
% 6.37/6.65 (assert (forall ((K tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N2) K))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N2) (@ P M5))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M5) N2) (@ P M5))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.37/6.65 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 (@ (@ tptp.vEBT_Leaf A) B)) X) tptp.one_one_nat)))
% 6.37/6.65 (assert (forall ((Uu Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf Uu) true)) tptp.one_one_nat)))
% 6.37/6.65 (assert (forall ((Uv Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf true) Uv)) tptp.one_one_nat)))
% 6.37/6.65 (assert (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf false) false)) tptp.one_one_nat))
% 6.37/6.65 (assert (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A4) B))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B4))))))))
% 6.37/6.65 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A4) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B4)) (@ _let_1 B))))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((K tptp.int) (I tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I) K)) (@ (@ tptp.ord_less_eq_int K) I))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((X tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K)) X)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I) K) I) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q2 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q2))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B6 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B6)) X3)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2)) X3)))))))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2)))))))))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.37/6.65 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.37/6.65 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.37/6.65 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.37/6.65 (assert (forall ((X tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.37/6.65 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))))))))))
% 6.37/6.65 (assert (forall ((Uv Bool) (Uw Bool) (N2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N2)) tptp.none_nat)))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N)) Y))))))
% 6.37/6.65 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q3 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 Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q3) Q5)))))))))
% 6.37/6.65 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q3 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 Q3)) 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) Q3))))))))
% 6.37/6.65 (assert (forall ((B tptp.int) (Q3 tptp.int) (R2 tptp.int) (B4 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) 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) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q5) Q3))))))))))
% 6.37/6.65 (assert (forall ((B tptp.int) (Q3 tptp.int) (R2 tptp.int) (B4 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 B4) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q3) Q5)))))))))))
% 6.37/6.65 (assert (forall ((B4 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 B4) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q5)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B6 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A5) B6)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t (@ (@ tptp.vEBT_Leaf A) B)) X) (@ _let_1 (@ (@ (@ tptp.if_nat (= X tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.37/6.65 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N2)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N2))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) Y))))))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real X3) N2) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N2) A)) (= Y4 X3)))))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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 ((I3 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) I3)) J3))) (@ P I3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I3 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) I3)) J3))) (@ P I3))))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q3))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q3))))))
% 6.37/6.65 (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 ((I3 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) I3)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I3 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) I3)) J3))) (@ P J3))))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.37/6.65 (assert (forall ((A Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))
% 6.37/6.65 (assert (forall ((B Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))
% 6.37/6.65 (assert (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_i_n_N_u_l_l X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) _let_1) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) _let_1) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) _let_1))))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X) tptp.one_one_nat)))
% 6.37/6.65 (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 ((I3 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) I3)) J3))) (@ (@ P I3) J3)))))))
% 6.37/6.65 (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 ((I3 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) I3)) J3))) (@ (@ P I3) J3)))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A5 Bool) (Uw2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A5 Bool) (B6 Bool) (Va3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B6)) (@ tptp.suc (@ tptp.suc Va3)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2)) Vf2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2)) X3)))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B6 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B6)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2)) Ve2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2)) X3))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2)) X3)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2)) X3)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B6 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B6)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2)) X3)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2)) X3)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B6 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B6)) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2)) X3)))))))))))
% 6.37/6.65 (assert (forall ((B Bool) (A Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.37/6.65 (assert (forall ((B4 tptp.real) (A4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A4)) (@ (@ tptp.ord_less_real A4) B4))))
% 6.37/6.65 (assert (forall ((B4 tptp.rat) (A4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A4)) (@ (@ tptp.ord_less_rat A4) B4))))
% 6.37/6.65 (assert (forall ((B4 tptp.num) (A4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A4)) (@ (@ tptp.ord_less_num A4) B4))))
% 6.37/6.65 (assert (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))))
% 6.37/6.65 (assert (forall ((B4 tptp.int) (A4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A4)) (@ (@ tptp.ord_less_int A4) B4))))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.37/6.65 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.37/6.65 (assert (forall ((X22 tptp.num) (X33 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X33)))))
% 6.37/6.65 (assert (forall ((X33 tptp.num)) (not (= tptp.one (@ tptp.bit1 X33)))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.vEBT_Leaf A) B)) X) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= X tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))))
% 6.37/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X) tptp.one_one_nat)))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X) Z)))))
% 6.37/6.65 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X) tptp.one_one_nat)))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A5 Bool) (B6 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (not (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B6 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B6) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Mi2)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A5 Bool) (B6 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (not (and (=> B6 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B6) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))))
% 6.37/6.65 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 T) X)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X) Xa2) Y) (=> (=> (exists ((A5 Bool) (B6 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B6))) _let_1) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ tptp.ord_less_nat Xa2))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2))) (not (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_3 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa2) (@ _let_3 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.37/6.65 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ tptp.divide_divide_nat B3) N2))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A2) N2)))))
% 6.37/6.65 (assert (forall ((A2 tptp.int) (N2 tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N2)) N2)) (@ (@ tptp.modulo_modulo_int A2) N2)))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2))) (= Y (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (not (= Y _let_1)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X) Xa2) Y) (=> (=> (exists ((A5 Bool) (B6 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B6))) (not (= Y (@ (@ tptp.plus_plus_nat _let_1) (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va3))) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va3))) TreeList3) Summary2))) (not (= Y (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ _let_5 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3)))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X) Xa2) Y) (=> (=> (exists ((A5 Bool) (B6 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B6))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) _let_1) (=> (=> (exists ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) _let_1) (=> (=> (exists ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2)) (not (= Y (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_5) (@ (@ tptp.vEBT_VEBT_low _let_3) _let_2))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_5)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary2) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))))))))))
% 6.37/6.65 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A5 Bool) (B6 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A5) B6))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ 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_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ 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_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (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))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M3)) (=> (= M3 N) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N) M3)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 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))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M3)) (=> (= M3 (@ tptp.suc N)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N) M3)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))))))))))
% 6.37/6.65 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A3 Bool) (B2 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B2))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) N3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (= A23 (@ (@ tptp.plus_plus_nat N3) N3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N3))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N3) _let_1)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) N3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 N3)) (= A23 (@ (@ tptp.plus_plus_nat N3) N3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N3))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N3) _let_3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ 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 TreeList2) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N3))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_i_n_t X) Y) (=> (forall ((A5 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((B6 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B6))) (not (= Y (@ _let_1 (@ (@ (@ tptp.if_nat A5) tptp.zero_zero_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B6))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B6 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B6) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B6 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (=> (= Xa2 _let_1) (=> (and (=> B6 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B6) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B6)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((I tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))))
% 6.37/6.65 (assert (forall ((I tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I) (@ (@ tptp.ord_less_eq_rat I) U)))))
% 6.37/6.65 (assert (forall ((I tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I) (@ (@ tptp.ord_less_eq_num I) U)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_eq_nat I) U)))))
% 6.37/6.65 (assert (forall ((I tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I) (@ (@ tptp.ord_less_eq_int I) U)))))
% 6.37/6.65 (assert (forall ((I tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I) (@ (@ tptp.ord_less_eq_real I) U)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.37/6.65 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M7 tptp.nat)) (=> (@ P X) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M7))) (not (forall ((M3 tptp.nat)) (=> (@ P M3) (not (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M3)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A5 tptp.nat) (B6 tptp.nat) (Acc tptp.num)) (not (= X (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A5) (@ (@ tptp.product_Pair_nat_num B6) Acc)))))))))
% 6.37/6.65 (assert (forall ((X tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B6 tptp.nat) (Acc tptp.nat)) (not (= X (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B6) Acc)))))))))
% 6.37/6.65 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.one_one_nat)))
% 6.37/6.65 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M5 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_nat X2) M5)))))))
% 6.37/6.65 (assert (forall ((N5 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N5) (@ (@ tptp.ord_less_nat X3) N2))) (@ tptp.finite_finite_nat N5))))
% 6.37/6.65 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M5 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_eq_nat X2) M5)))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ P K2) (@ (@ tptp.ord_less_nat K2) I)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_i_n_t T)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ tptp.vEBT_Leaf A) B)) (@ _let_1 (@ (@ (@ tptp.if_nat A) tptp.zero_zero_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.37/6.65 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X _let_1) (=> (= Y (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2))) (=> (= X _let_1) (=> (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat _let_3)))) (let ((_let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_4))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_3))))) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_4))) (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_7))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t Summary2) _let_6)) tptp.one_one_nat))) tptp.one_one_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) Mi2) Xa2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_5))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 _let_6) (@ (@ tptp.vEBT_VEBT_low _let_4) _let_3))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_6)) (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 Summary2) _let_5)) tptp.one_one_nat))) tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ tptp.numeral_numeral_nat _let_3))) (let ((_let_5 (@ (@ tptp.divide_divide_nat _let_1) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_5))) (let ((_let_7 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X _let_2) (=> (= Y (@ (@ tptp.plus_plus_nat _let_4) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_3)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ _let_7 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_5)))) tptp.one_one_nat))))))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ tptp.ord_less_nat Xa2))) (=> (= X _let_2) (=> (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_5 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa2) (@ _let_5 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B6) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B6) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B6) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X _let_1) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va2) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.37/6.65 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ P (@ (@ tptp.plus_plus_int Y2) X2))))))))))))))
% 6.37/6.65 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) A2) (@ P (@ (@ tptp.minus_minus_int Y2) X2))))))))))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_int A) I3) (@ (@ tptp.ord_less_eq_int I3) B)))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I3) (@ (@ tptp.ord_less_int I3) B)))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D))))) (= (exists ((X4 tptp.int)) (@ P X4)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X2))))))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I3) (@ (@ tptp.ord_less_eq_int I3) B)))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.ord_less_int A) I3) (@ (@ tptp.ord_less_int I3) B)))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (@ (@ tptp.ord_less_real X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (@ (@ tptp.ord_less_rat X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (@ (@ tptp.ord_less_num X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (@ (@ tptp.ord_less_nat X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (@ (@ tptp.ord_less_int X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (@ (@ tptp.ord_less_real T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (@ (@ tptp.ord_less_rat T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (@ (@ tptp.ord_less_num T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (@ (@ tptp.ord_less_nat T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (@ (@ tptp.ord_less_int T) X5))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (= X5 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (@ (@ tptp.ord_less_real T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (@ (@ tptp.ord_less_rat T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (@ (@ tptp.ord_less_num T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (@ (@ tptp.ord_less_nat T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (@ (@ tptp.ord_less_int T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (@ (@ tptp.ord_less_eq_real T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (@ (@ tptp.ord_less_eq_num T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (@ (@ tptp.ord_less_eq_int T) X5))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (@ (@ tptp.ord_less_eq_real X5) T))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (@ (@ tptp.ord_less_eq_rat X5) T))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (@ (@ tptp.ord_less_eq_num X5) T))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (@ (@ tptp.ord_less_eq_nat X5) T))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (@ (@ tptp.ord_less_eq_int X5) T))))))
% 6.37/6.65 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (@ (@ tptp.ord_less_eq_real T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (@ (@ tptp.ord_less_eq_num T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))))
% 6.37/6.65 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (@ (@ tptp.ord_less_eq_int T) X5)))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K3 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X3 tptp.real) (K3 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K3 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X3 tptp.real) (K3 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X3 tptp.rat) (K3 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.37/6.65 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.37/6.65 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K3 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K3) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((X_12 tptp.int)) (@ P6 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) (@ (@ tptp.times_times_int K) D))))))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K) D))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ tptp.vEBT_T_m_a_x_t X) Y) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B6)) (not (= Y (@ _let_1 (@ (@ (@ tptp.if_nat B6) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A5 tptp.real) (B6 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B6) (=> (@ (@ P B6) C2) (=> (@ (@ tptp.ord_less_eq_real A5) B6) (=> (@ (@ tptp.ord_less_eq_real B6) C2) (@ _let_1 C2))))))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A5 tptp.real) (B6 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X3) (@ (@ tptp.ord_less_eq_real X3) B6) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B6) A5)) D5)) (@ (@ P A5) B6)))))))) (@ (@ P A) B))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) K)))
% 6.37/6.65 (assert (= tptp.unique5052692396658037445od_int (lambda ((M5 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N3))) (let ((_let_2 (@ tptp.numeral_numeral_int M5))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.37/6.65 (assert (= tptp.unique5052692396658037445od_int (lambda ((M5 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N3))) (let ((_let_2 (@ tptp.numeral_numeral_int M5))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.37/6.65 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M5 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N3))) (let ((_let_2 (@ tptp.numeral_numeral_nat M5))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.37/6.65 (assert (= tptp.unique3479559517661332726nteger (lambda ((M5 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M5))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.37/6.65 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M5 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N3))) (let ((_let_2 (@ tptp.numeral_numeral_nat M5))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ tptp.vEBT_Leaf A) B)) (@ _let_1 (@ (@ (@ tptp.if_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 6.37/6.65 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.one_one_nat)))
% 6.37/6.65 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_T_m_a_x_t T)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 6.37/6.65 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M5 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M5) N3)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M5))) (@ (@ tptp.unique5026877609467782581ep_nat N3) (@ (@ tptp.unique5055182867167087721od_nat M5) (@ tptp.bit0 N3)))))))
% 6.37/6.65 (assert (= tptp.unique5052692396658037445od_int (lambda ((M5 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M5) N3)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M5))) (@ (@ tptp.unique5024387138958732305ep_int N3) (@ (@ tptp.unique5052692396658037445od_int M5) (@ tptp.bit0 N3)))))))
% 6.37/6.65 (assert (= tptp.unique3479559517661332726nteger (lambda ((M5 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M5) N3)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M5))) (@ (@ tptp.unique4921790084139445826nteger N3) (@ (@ tptp.unique3479559517661332726nteger M5) (@ tptp.bit0 N3)))))))
% 6.37/6.65 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_a_x_t (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 6.37/6.65 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 6.37/6.65 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 6.37/6.65 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 6.37/6.65 (assert (forall ((Q3 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q3) R2)) (= R2 tptp.zero_zero_nat))))
% 6.37/6.65 (assert (forall ((Q3 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q3) R2)) (= R2 tptp.zero_zero_int))))
% 6.37/6.65 (assert (forall ((B tptp.int) (A tptp.int) (Q3 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 Q3))) (=> (@ (@ 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)))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs2) Ys)) N2) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8326237132889035090at_num (@ (@ tptp.product_nat_num Xs2) Ys)) N2) (@ (@ tptp.product_Pair_nat_num (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.product_nat_nat Xs2) Ys)) N2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) N2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) N2) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs2) Ys)) N2) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.product_nat_int Xs2) Ys)) N2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y I3) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.times_times_complex (@ X I3)) (@ Y I3)) tptp.one_one_complex))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y I3) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.times_times_complex (@ X I3)) (@ Y I3)) tptp.one_one_complex))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ X I3) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ Y I3) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ (@ tptp.times_times_complex (@ X I3)) (@ Y I3)) tptp.one_one_complex))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ X I3) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ Y I3) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ (@ tptp.times_times_complex (@ X I3)) (@ Y I3)) tptp.one_one_complex))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y I3) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.times_times_real (@ X I3)) (@ Y I3)) tptp.one_one_real))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y I3) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.times_times_real (@ X I3)) (@ Y I3)) tptp.one_one_real))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ X I3) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ Y I3) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ (@ tptp.times_times_real (@ X I3)) (@ Y I3)) tptp.one_one_real))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ X I3) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ Y I3) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ (@ tptp.times_times_real (@ X I3)) (@ Y I3)) tptp.one_one_real))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y I3) tptp.one_one_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.times_times_rat (@ X I3)) (@ Y I3)) tptp.one_one_rat))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y I3) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.times_times_rat (@ X I3)) (@ Y I3)) tptp.one_one_rat))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y I3) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I3)) (@ Y I3)) tptp.zero_zero_complex))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y I3) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I3)) (@ Y I3)) tptp.zero_zero_complex))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ X I3) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ Y I3) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I3)) (@ Y I3)) tptp.zero_zero_complex))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ X I3) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ Y I3) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X I3)) (@ Y I3)) tptp.zero_zero_complex))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I3 tptp.complex)) (and (@ (@ tptp.member_complex I3) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ X I3) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ Y I3) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I3 tptp.int)) (and (@ (@ tptp.member_int I3) I5) (not (= (@ (@ tptp.plus_plus_real (@ X I3)) (@ Y I3)) tptp.zero_zero_real))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ X I3) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ Y I3) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I3 tptp.real)) (and (@ (@ tptp.member_real I3) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I3)) (@ Y I3)) tptp.zero_zero_rat))))))))))
% 6.37/6.65 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ X I3) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ Y I3) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (and (@ (@ tptp.member_nat I3) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I3)) (@ Y I3)) tptp.zero_zero_rat))))))))))
% 6.37/6.65 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.37/6.65 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.37/6.65 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.37/6.65 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.37/6.65 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.37/6.65 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.37/6.65 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.37/6.65 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6639371672096860321T_VEBT (@ (@ tptp.produc662631939642741121T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_o)) (= (@ tptp.size_s4246224855604898693_int_o (@ (@ tptp.product_int_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.size_s5157815400016825771nt_int (@ (@ tptp.product_int_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (Q3 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 Q3) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= Q3 Q5))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (Q3 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 Q3) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R2 R4))))))
% 6.37/6.65 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.37/6.65 (assert (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R2)) (= (@ (@ tptp.divide_divide_int K) L) Q3))))
% 6.37/6.65 (assert (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R2)) (= (@ (@ tptp.modulo_modulo_int K) L) R2))))
% 6.37/6.65 (assert (forall ((L tptp.int) (K tptp.int) (Q3 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q3) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.37/6.65 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.37/6.65 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.37/6.65 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.37/6.65 (assert (forall ((K tptp.int) (L tptp.int) (Q3 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 Q3) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q3)) 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) (= Q3 tptp.zero_zero_int)))))))))))
% 6.37/6.65 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X) Y)))))
% 6.37/6.65 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))))
% 6.37/6.65 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 6.37/6.65 (assert (forall ((B tptp.int) (A tptp.int) (Q3 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 Q3))) (=> (@ (@ 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)))))))))))
% 6.37/6.65 (assert (forall ((X1 tptp.code_integer) (X22 Bool) (Y1 tptp.code_integer) (Y22 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o X1) X22) (@ (@ tptp.produc6677183202524767010eger_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.37/6.65 (assert (forall ((X1 tptp.num) (X22 tptp.num) (Y1 tptp.num) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X22) (@ (@ tptp.product_Pair_num_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.37/6.65 (assert (forall ((X1 tptp.nat) (X22 tptp.num) (Y1 tptp.nat) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num X1) X22) (@ (@ tptp.product_Pair_nat_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.37/6.65 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.37/6.65 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B Bool) (A4 tptp.code_integer) (B4 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A4) B4)) (and (= A A4) (= B B4)))))
% 6.37/6.65 (assert (forall ((A tptp.num) (B tptp.num) (A4 tptp.num) (B4 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A4) B4)) (and (= A A4) (= B B4)))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.num) (A4 tptp.nat) (B4 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A4) B4)) (and (= A A4) (= B B4)))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat) (A4 tptp.nat) (B4 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A4) B4)) (and (= A A4) (= B B4)))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int) (B4 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A4) B4)) (and (= A A4) (= B B4)))))
% 6.37/6.65 (assert (forall ((Y tptp.produc6271795597528267376eger_o)) (not (forall ((A5 tptp.code_integer) (B6 Bool)) (not (= Y (@ (@ tptp.produc6677183202524767010eger_o A5) B6)))))))
% 6.37/6.65 (assert (forall ((Y tptp.product_prod_num_num)) (not (forall ((A5 tptp.num) (B6 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_num_num A5) B6)))))))
% 6.37/6.65 (assert (forall ((Y tptp.product_prod_nat_num)) (not (forall ((A5 tptp.nat) (B6 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_nat_num A5) B6)))))))
% 6.37/6.65 (assert (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A5 tptp.nat) (B6 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A5) B6)))))))
% 6.37/6.65 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A5 tptp.int) (B6 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A5) B6)))))))
% 6.37/6.65 (assert (forall ((P2 tptp.produc6271795597528267376eger_o)) (exists ((X3 tptp.code_integer) (Y3 Bool)) (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_num_num)) (exists ((X3 tptp.num) (Y3 tptp.num)) (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_nat_num)) (exists ((X3 tptp.nat) (Y3 tptp.num)) (= P2 (@ (@ tptp.product_Pair_nat_num X3) Y3)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= P2 (@ (@ tptp.product_Pair_nat_nat X3) Y3)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y3 tptp.int)) (= P2 (@ (@ tptp.product_Pair_int_int X3) Y3)))))
% 6.37/6.65 (assert (forall ((P (-> tptp.produc6271795597528267376eger_o Bool)) (P2 tptp.produc6271795597528267376eger_o)) (=> (forall ((A5 tptp.code_integer) (B6 Bool)) (@ P (@ (@ tptp.produc6677183202524767010eger_o A5) B6))) (@ P P2))))
% 6.37/6.65 (assert (forall ((P (-> tptp.product_prod_num_num Bool)) (P2 tptp.product_prod_num_num)) (=> (forall ((A5 tptp.num) (B6 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A5) B6))) (@ P P2))))
% 6.37/6.65 (assert (forall ((P (-> tptp.product_prod_nat_num Bool)) (P2 tptp.product_prod_nat_num)) (=> (forall ((A5 tptp.nat) (B6 tptp.num)) (@ P (@ (@ tptp.product_Pair_nat_num A5) B6))) (@ P P2))))
% 6.37/6.65 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (forall ((A5 tptp.nat) (B6 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A5) B6))) (@ P P2))))
% 6.37/6.65 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P2 tptp.product_prod_int_int)) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A5) B6))) (@ P P2))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B Bool) (A4 tptp.code_integer) (B4 Bool)) (=> (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A4) B4)) (not (=> (= A A4) (= B (not B4)))))))
% 6.37/6.65 (assert (forall ((A tptp.num) (B tptp.num) (A4 tptp.num) (B4 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.num) (A4 tptp.nat) (B4 tptp.num)) (=> (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat) (A4 tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.37/6.65 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_height (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat)))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.37/6.65 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.37/6.65 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.37/6.65 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X)) I) Y) (@ _let_1 Y)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_o) (I tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I) X)) (@ tptp.size_size_list_o Xs2))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I) X)) (@ tptp.size_size_list_int Xs2))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)))
% 6.37/6.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (not (= I J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I) X)) J) (@ (@ tptp.nth_int Xs2) J)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X)) J) (@ (@ tptp.nth_nat Xs2) J)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X)) J) (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs2) I) (@ (@ tptp.nth_int Xs2) I)) Xs2)))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I) (@ (@ tptp.nth_nat Xs2) I)) Xs2)))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ (@ tptp.nth_VEBT_VEBT Xs2) I)) Xs2)))
% 6.37/6.65 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 6.37/6.65 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.37/6.65 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.37/6.65 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.37/6.65 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.37/6.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.37/6.65 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.37/6.65 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X) Xs2))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_o) (I tptp.nat) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I) (= (@ (@ (@ tptp.list_update_o Xs2) I) X) Xs2))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I) (= (@ (@ (@ tptp.list_update_int Xs2) I) X) Xs2))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X)) I) X))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X)) I) X))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I) X)) I) X))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I) X)) I) X))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs2))))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBT2 Xs2))))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_o2 Xs2))))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_int2 Xs2))))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (I6 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X7 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs2))) (=> (not (= I I6)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I) X)) I6) X7) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I6) X7)) I) X))))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.37/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z)) (@ (@ tptp.plus_plus_real Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z)) (@ (@ tptp.minus_minus_real Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 6.37/6.65 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))))
% 6.37/6.65 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q3)) (@ (@ tptp.plus_plus_nat N2) Q3)))))
% 6.37/6.65 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))))
% 6.37/6.65 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))))
% 6.37/6.65 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.37/6.65 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B2)) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B2)) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B2)) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B2 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B2)) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_complex) (A2 tptp.set_complex) (X tptp.complex) (I tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (=> (@ (@ tptp.member_complex X) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) I) X))) A2)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_real) (A2 tptp.set_real) (X tptp.real) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A2) (=> (@ (@ tptp.member_real X) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I) X))) A2)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_set_nat) (A2 tptp.set_set_nat) (X tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs2)) A2) (=> (@ (@ tptp.member_set_nat X) A2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs2) I) X))) A2)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I) X))) A2)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X))) A2)))))
% 6.37/6.65 (assert (forall ((Xs2 tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I) X))) A2)))))
% 6.37/6.65 (assert (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))
% 6.37/6.65 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))
% 6.37/6.65 (assert (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))
% 6.37/6.65 (assert (= tptp.neg_nu7009210354673126013omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex X2) X2))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N2)) (@ tptp.bit1 (@ tptp.bitM N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N2) X))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N2) X))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs2) N2) X))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N2) X))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N2) X))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N2) X))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N2) X))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I) X) Xs2) (= (@ (@ tptp.nth_nat Xs2) I) X)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I) X)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I) X) Xs2) (= (@ (@ tptp.nth_o Xs2) I) X)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I) X) Xs2) (= (@ (@ tptp.nth_int Xs2) I) X)))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J)))))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X Bool) (J tptp.nat)) (let ((_let_1 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I) X)) J) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J))))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J)))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N2))))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N2)) tptp.one) (@ tptp.bit0 N2))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2))) tptp.one_one_complex))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B6 tptp.nat)) (= (@ (@ P A5) B6) (@ (@ P B6) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B6 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B6) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B6))))) (@ (@ P A) B))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B6 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A5) B6)))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList3) Summary2))))))))
% 6.37/6.65 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B6))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B6))) (=> (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) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B6))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B6))) (=> (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) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.37/6.65 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.37/6.65 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.37/6.65 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y)) Z) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y)) Z) (and (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (and (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z) (and (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 6.37/6.65 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (and (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.37/6.65 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.37/6.65 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.37/6.65 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q3) Q3)))
% 6.37/6.65 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q3) tptp.zero_z5237406670263579293d_enat) Q3)))
% 6.37/6.65 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K3 tptp.nat) (M3 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K3) M3)))))))
% 6.37/6.65 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N tptp.nat)) (not (= X (@ tptp.suc N))))))))
% 6.37/6.65 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C) D)) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.37/6.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.37/6.65 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.37/6.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.37/6.65 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.37/6.65 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.37/6.65 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (not (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= A3 (@ (@ tptp.ord_max_rat A3) B2)))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= A3 (@ (@ tptp.ord_max_num A3) B2)))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.ord_max_nat A3) B2)))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.ord_max_int A3) B2)))))
% 6.37/6.65 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.37/6.65 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.37/6.65 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.37/6.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.37/6.65 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.37/6.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.37/6.65 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.37/6.65 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) A3))))
% 6.37/6.65 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) B2))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) B2))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) B2))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) B2))))
% 6.37/6.65 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) B2))))
% 6.37/6.65 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)) (not (= A3 B2))))))
% 6.37/6.65 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B2)) (not (= A3 B2))))))
% 6.37/6.65 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (= A3 (@ (@ tptp.ord_max_rat A3) B2)) (not (= A3 B2))))))
% 6.37/6.65 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (= A3 (@ (@ tptp.ord_max_num A3) B2)) (not (= A3 B2))))))
% 6.37/6.65 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B2)) (not (= A3 B2))))))
% 6.37/6.65 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B2)) (not (= A3 B2))))))
% 6.37/6.65 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))))))
% 6.37/6.65 (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))))))))))
% 6.37/6.65 (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))))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.37/6.65 (assert (forall ((X (-> tptp.nat tptp.nat)) (X22 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.37/6.65 (assert (forall ((X (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.37/6.65 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.37/6.65 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.37/6.65 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.37/6.65 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.37/6.65 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) A)) (@ _let_1 B)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex A) B)) (@ _let_1 B)))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B)) (@ _let_1 B)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.37/6.65 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.37/6.65 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B2 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.37/6.65 (assert (forall ((P2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P2) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.times_times_nat X3) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.37/6.65 (assert (forall ((P2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P2) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.times_times_int X3) Y3)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B7 tptp.nat) (C4 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B7) C4)) (@ (@ tptp.dvd_dvd_nat B7) B) (@ (@ tptp.dvd_dvd_nat C4) C))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B7 tptp.int) (C4 tptp.int)) (and (= A (@ (@ tptp.times_times_int B7) C4)) (@ (@ tptp.dvd_dvd_int B7) B) (@ (@ tptp.dvd_dvd_int C4) C))))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K2 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B2) K2))))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K2 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K2))))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (exists ((K2 tptp.rat)) (= A3 (@ (@ tptp.times_times_rat B2) K2))))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K2 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K2))))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K2 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K2))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.37/6.65 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K3))))))))
% 6.37/6.65 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K3 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K3))))))))
% 6.37/6.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K3 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K3))))))))
% 6.37/6.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K3))))))))
% 6.37/6.65 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K3 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K3))))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.37/6.65 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.37/6.65 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ _let_1 C))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ _let_1 B))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))))
% 6.37/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)))))
% 6.37/6.65 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) A)))) (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) B)))) (@ (@ tptp.dvd_dvd_complex A) B))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.37/6.65 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.37/6.65 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.37/6.65 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.37/6.65 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.37/6.65 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.37/6.65 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y2)) __flatten_var_0))) F)))
% 6.37/6.65 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y2)) __flatten_var_0))) F)))
% 6.37/6.65 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y2)))) F)))
% 6.37/6.65 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y2)))) F)))
% 6.37/6.65 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y2)))) F)))
% 6.37/6.65 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.37/6.65 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.37/6.65 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.37/6.65 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 6.37/6.65 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) A)))) (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.37/6.65 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.37/6.65 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.37/6.65 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S)))) (=> (@ (@ tptp.ord_less_real Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S)))) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S)))) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S)))) (=> (@ (@ tptp.ord_less_int Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S))))) (=> (@ (@ tptp.ord_less_real Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S))))) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S))))) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S))))) (=> (@ (@ tptp.ord_less_int Z2) X5) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S)))) (=> (@ (@ tptp.ord_less_real X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S)))) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S)))) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S)))) (=> (@ (@ tptp.ord_less_int X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S))))) (=> (@ (@ tptp.ord_less_real X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S))))) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S))))) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S))))) (=> (@ (@ tptp.ord_less_int X5) Z2) (= _let_1 _let_1)))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B2) A3) tptp.zero_zero_nat))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B2) A3) tptp.zero_zero_int))))
% 6.37/6.65 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B2) A3) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.37/6.65 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) M))))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) M))))))
% 6.37/6.65 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) M))))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) M))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.37/6.65 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.37/6.65 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X3 tptp.nat) (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 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((K tptp.int) (M tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T)))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y3)) D3)))))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (@ (@ tptp.dvd_dvd_int D2) I)))))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C2 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C2)))))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C2)))))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C2)))))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X2 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X2))) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X2) tptp.zero_z3403309356797280102nteger)) (@ P X2))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X2 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X2))) (exists ((X2 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X2) tptp.zero_zero_complex)) (@ P X2))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X2 tptp.real)) (@ P (@ (@ tptp.times_times_real L) X2))) (exists ((X2 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X2) tptp.zero_zero_real)) (@ P X2))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X2 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X2))) (exists ((X2 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X2) tptp.zero_zero_rat)) (@ P X2))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X2 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X2) tptp.zero_zero_nat)) (@ P X2))))))
% 6.37/6.65 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X2 tptp.int)) (@ P (@ (@ tptp.times_times_int L) X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X2) tptp.zero_zero_int)) (@ P X2))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))))
% 6.37/6.65 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X5) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T)))))))))
% 6.37/6.65 (assert (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X5 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K4) D4))) T)))))))))
% 6.37/6.65 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D4))) T)))))))))
% 6.37/6.65 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D4))) T)))))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D4))) T)))))))))
% 6.37/6.65 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X5) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T))))))))
% 6.37/6.65 (assert (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X5 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K4) D4))) T))))))))
% 6.37/6.65 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D4))) T))))))))
% 6.37/6.65 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D4))) T))))))))
% 6.37/6.65 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D4))) T))))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X3 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) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (= tptp.nat_set_decode (lambda ((X2 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 X2) (@ (@ tptp.power_power_nat _let_1) N3))))))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (M tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (@ (@ tptp.dvd_dvd_nat Q3) (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.37/6.65 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.37/6.65 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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 ((B6 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B6 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B6) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B6) (=> (= (@ _let_1 B6) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B6) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B6)))))))))))))))
% 6.37/6.65 (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 ((B6 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B6 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B6) tptp.one_one_nat) (=> (= (@ _let_1 A) B6) (=> (= (@ _let_1 B6) A) (=> (= (@ (@ tptp.times_times_nat A) B6) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B6)))))))))))))))
% 6.37/6.65 (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 ((B6 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B6 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B6) tptp.one_one_int) (=> (= (@ _let_1 A) B6) (=> (= (@ _let_1 B6) A) (=> (= (@ (@ tptp.times_times_int A) B6) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B6)))))))))))))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B6 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B6))))))))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B6 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B6))))))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B6 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B6))))))))
% 6.37/6.65 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.37/6.65 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.37/6.65 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (= (lambda ((Y5 tptp.code_integer) (Z5 tptp.code_integer)) (= Y5 Z5)) (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide6298287555418463151nteger A3) _let_1) (@ (@ tptp.divide6298287555418463151nteger B2) _let_1))))))))
% 6.37/6.65 (assert (= (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B2) _let_1))))))))
% 6.37/6.65 (assert (= (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) (lambda ((A3 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B2) _let_1))))))))
% 6.37/6.65 (assert (forall ((X tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.37/6.65 (assert (forall ((X tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X) (@ (@ tptp.power_power_rat X) N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N2)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N2)))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y)) (= X Y)))))))
% 6.37/6.65 (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)))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((Q3 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 Q3))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q3)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q3)))))))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B6 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B6)) tptp.one_one_Code_integer))))))))
% 6.37/6.65 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B6 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B6)) tptp.one_one_nat))))))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B6 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B6)) tptp.one_one_int))))))))
% 6.37/6.65 (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))))))))))
% 6.37/6.65 (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))))))))))
% 6.37/6.65 (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))))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.37/6.65 (assert (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.37/6.65 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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)))))))))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X3) Xa))))) (not (@ tptp.finite_finite_real X8))))))
% 6.37/6.65 (assert (forall ((X8 tptp.set_rat)) (=> (not (= X8 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X8) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X8) (@ (@ tptp.ord_less_rat X3) Xa))))) (not (@ tptp.finite_finite_rat X8))))))
% 6.37/6.65 (assert (forall ((X8 tptp.set_num)) (=> (not (= X8 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) X8) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X8) (@ (@ tptp.ord_less_num X3) Xa))))) (not (@ tptp.finite_finite_num X8))))))
% 6.37/6.65 (assert (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X3) Xa))))) (not (@ tptp.finite_finite_nat X8))))))
% 6.37/6.65 (assert (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X3) Xa))))) (not (@ tptp.finite_finite_int X8))))))
% 6.37/6.65 (assert (forall ((S3 tptp.set_real)) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) S3) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S3) (@ (@ tptp.ord_less_real Xa) X3))))))))))
% 6.37/6.65 (assert (forall ((S3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat S3) (=> (not (= S3 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) S3) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S3) (@ (@ tptp.ord_less_rat Xa) X3))))))))))
% 6.37/6.65 (assert (forall ((S3 tptp.set_num)) (=> (@ tptp.finite_finite_num S3) (=> (not (= S3 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) S3) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S3) (@ (@ tptp.ord_less_num Xa) X3))))))))))
% 6.37/6.65 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) S3) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S3) (@ (@ tptp.ord_less_nat Xa) X3))))))))))
% 6.37/6.65 (assert (forall ((S3 tptp.set_int)) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) S3) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S3) (@ (@ tptp.ord_less_int Xa) X3))))))))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.37/6.65 (assert (= tptp.divmod_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M5) N3))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M5)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M5) N3)) N3))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N3 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A3) _let_1))) (@ (@ (@ tptp.if_Code_integer (= 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 A3) _let_1))))))))))
% 6.37/6.65 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A3) _let_1))) (@ (@ (@ tptp.if_int (= 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 A3) _let_1))))))))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.37/6.65 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 6.37/6.65 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I))))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I))))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.37/6.65 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (C (-> tptp.code_integer Bool Bool))) (=> (forall ((A5 tptp.code_integer) (B6 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B6)) (@ (@ C A5) B6))) (@ (@ tptp.produc7828578312038201481er_o_o C) P2))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_num_num) (C (-> tptp.num tptp.num Bool))) (=> (forall ((A5 tptp.num) (B6 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B6)) (@ (@ C A5) B6))) (@ (@ tptp.produc5703948589228662326_num_o C) P2))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_nat_num) (C (-> tptp.nat tptp.num Bool))) (=> (forall ((A5 tptp.nat) (B6 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B6)) (@ (@ C A5) B6))) (@ (@ tptp.produc4927758841916487424_num_o C) P2))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat Bool))) (=> (forall ((A5 tptp.nat) (B6 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat A5) B6)) (@ (@ C A5) B6))) (@ (@ tptp.produc6081775807080527818_nat_o C) P2))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A5 tptp.int) (B6 tptp.int)) (=> (= P2 (@ (@ tptp.product_Pair_int_int A5) B6)) (@ (@ C A5) B6))) (@ (@ tptp.produc4947309494688390418_int_o C) P2))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex))) (=> (forall ((A5 tptp.code_integer) (B6 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B6)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real))) (=> (forall ((A5 tptp.code_integer) (B6 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B6)) (@ (@ tptp.member_real Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat))) (=> (forall ((A5 tptp.code_integer) (B6 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B6)) (@ (@ tptp.member_nat Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int))) (=> (forall ((A5 tptp.code_integer) (B6 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B6)) (@ (@ tptp.member_int Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex))) (=> (forall ((A5 tptp.num) (B6 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B6)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real))) (=> (forall ((A5 tptp.num) (B6 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B6)) (@ (@ tptp.member_real Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat))) (=> (forall ((A5 tptp.num) (B6 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B6)) (@ (@ tptp.member_nat Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int))) (=> (forall ((A5 tptp.num) (B6 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B6)) (@ (@ tptp.member_int Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_nat_num) (Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex))) (=> (forall ((A5 tptp.nat) (B6 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B6)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P2)))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_nat_num) (Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real))) (=> (forall ((A5 tptp.nat) (B6 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B6)) (@ (@ tptp.member_real Z) (@ (@ C A5) B6)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P2)))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((P2 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((A5 tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A5) B6) P2) (@ (@ (@ C A5) B6) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P2) X))))
% 6.37/6.65 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.37/6.65 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.37/6.65 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.37/6.65 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.37/6.65 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= M N2))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= M N2))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))))
% 6.37/6.65 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 6.37/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))))
% 6.37/6.65 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))))
% 6.37/6.65 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))))
% 6.37/6.65 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))))
% 6.37/6.65 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X)) Y) (@ (@ tptp.dvd_dvd_complex X) Y))))
% 6.37/6.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X)) Y) (@ (@ tptp.dvd_dvd_rat X) Y))))
% 6.37/6.65 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X)) Y) (@ (@ tptp.dvd_dvd_Code_integer X) Y))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.37/6.65 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.37/6.65 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.37/6.65 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.37/6.65 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.37/6.65 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.37/6.65 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.37/6.65 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.37/6.65 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.37/6.65 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.37/6.65 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.37/6.65 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.37/6.65 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.37/6.65 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.37/6.65 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.37/6.65 (assert (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M N2) (=> (not (= M tptp.zero_zero_nat)) (= X Y))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) N2)))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N2) X)) N2)))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X)) N2)))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (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)))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.65 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.37/6.65 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.37/6.65 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.37/6.65 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.37/6.65 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.37/6.65 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.37/6.65 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.37/6.65 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.37/6.65 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.37/6.65 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.37/6.65 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.37/6.65 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.37/6.65 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.37/6.65 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.37/6.65 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.37/6.65 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.37/6.65 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.37/6.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.37/6.65 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.37/6.65 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.37/6.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.37/6.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.37/6.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.37/6.65 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 6.37/6.65 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 6.37/6.65 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.37/6.65 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.37/6.65 (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)))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N2) _let_1) _let_1))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.37/6.65 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.37/6.65 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.37/6.65 (assert (forall ((X tptp.set_nat) (N2 tptp.nat) (Y tptp.set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.37/6.65 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.37/6.65 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.37/6.65 (assert (forall ((X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.37/6.65 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.37/6.65 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))))
% 6.37/6.65 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I) X))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I) X))))
% 6.37/6.65 (assert (forall ((I tptp.nat) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I) X))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (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))))))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.37/6.65 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.37/6.65 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= N2 tptp.one))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= N2 tptp.one))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N2 tptp.one))))
% 6.37/6.65 (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))))
% 6.37/6.65 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N2 tptp.one))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.65 (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))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P2))) P2)))
% 6.37/6.66 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P2))) P2)))
% 6.37/6.66 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P2))) P2)))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.37/6.66 (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)))
% 6.37/6.66 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.37/6.66 (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))
% 6.37/6.66 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.37/6.66 (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))
% 6.37/6.66 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))
% 6.37/6.66 (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)))
% 6.37/6.66 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.37/6.66 (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)))
% 6.37/6.66 (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)))
% 6.37/6.66 (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)))
% 6.37/6.66 (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)))
% 6.37/6.66 (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)))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) (@ tptp.zero_n2687167440665602831ol_nat Q3)) (= P2 Q3))))
% 6.37/6.66 (assert (forall ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) (@ tptp.zero_n2684676970156552555ol_int Q3)) (= P2 Q3))))
% 6.37/6.66 (assert (forall ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) (@ tptp.zero_n356916108424825756nteger Q3)) (= P2 Q3))))
% 6.37/6.66 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.37/6.66 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.37/6.66 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.37/6.66 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.37/6.66 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.37/6.66 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X)))))
% 6.37/6.66 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 6.37/6.66 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.37/6.66 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.37/6.66 (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 ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X3) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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 ((X3 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X3) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y3)))))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.37/6.66 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.37/6.66 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.37/6.66 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.37/6.66 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.37/6.66 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 6.37/6.66 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 6.37/6.66 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.37/6.66 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 6.37/6.66 (assert (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A4) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A4)) B)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A4) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A4)) B)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.37/6.66 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.37/6.66 (assert (forall ((C (-> tptp.code_integer Bool Bool)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.produc7828578312038201481er_o_o C) P2) (not (forall ((X3 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.37/6.66 (assert (forall ((C (-> tptp.num tptp.num Bool)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.produc5703948589228662326_num_o C) P2) (not (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.37/6.66 (assert (forall ((C (-> tptp.nat tptp.num Bool)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.produc4927758841916487424_num_o C) P2) (not (forall ((X3 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.37/6.66 (assert (forall ((C (-> tptp.nat tptp.nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o C) P2) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.37/6.66 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P2 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P2) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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 ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ (@ (@ C X3) Y3) Z))))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.37/6.66 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.37/6.66 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.37/6.66 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))
% 6.37/6.66 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.37/6.66 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.37/6.66 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))
% 6.37/6.66 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.37/6.66 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.37/6.66 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.37/6.66 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.37/6.66 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.37/6.66 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.37/6.66 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.37/6.66 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.37/6.66 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.37/6.66 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.66 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.37/6.66 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.37/6.66 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.37/6.66 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.37/6.66 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.37/6.66 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.66 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.37/6.66 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.37/6.66 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.37/6.66 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.37/6.66 (assert (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 6.37/6.66 (assert (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))))
% 6.37/6.66 (assert (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.37/6.66 (assert (forall ((W tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.37/6.66 (assert (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real N2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat N2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.37/6.66 (assert (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.37/6.66 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B3 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.37/6.66 (assert (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B3 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.37/6.66 (assert (forall ((B3 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B3 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.37/6.66 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B3 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 6.37/6.66 (assert (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B3 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.37/6.66 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.37/6.66 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.37/6.66 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.37/6.66 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.37/6.66 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.37/6.66 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.37/6.66 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.37/6.66 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.37/6.66 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.37/6.66 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_complex) (N2 tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N2) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_complex N2) X))))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_real) (N2 tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_real N2) X))))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_set_nat) (N2 tptp.nat) (X tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs2) N2) (=> (forall ((Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y3) (@ tptp.set_set_nat2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_set_nat N2) X))))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_nat) (N2 tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N2) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_nat N2) X))))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N2) X))))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_o) (N2 tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N2) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_o N2) X))))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_int) (N2 tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N2) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_int N2) X))))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X) Xs2))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_o) (X Bool)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X) Xs2))))
% 6.37/6.66 (assert (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X) Xs2))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (forall ((U tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X) X))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (= tptp.numeral_numeral_nat (lambda ((K2 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K2)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y2)))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.37/6.66 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.37/6.66 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.37/6.66 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.37/6.66 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.37/6.66 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.37/6.66 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.37/6.66 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.37/6.66 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ (@ tptp.power_power_int X) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ (@ tptp.power_power_complex X) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ (@ tptp.power_power_rat X) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (assert (= tptp.pred_numeral (lambda ((K2 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K2)) tptp.one_one_nat))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.37/6.66 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.37/6.66 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.37/6.66 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.37/6.66 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1482373934393186551omplex Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y)))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N2)) (@ (@ tptp.divide_divide_int A2) N2))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (forall ((U tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (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)))))))))))
% 6.37/6.66 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q3))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q3) 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))))))))))
% 6.37/6.66 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A5 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.nat) (B6 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B6)) (@ (@ tptp.times_times_nat _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.37/6.66 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A5 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A5) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.int) (B6 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B6)) (@ (@ tptp.times_times_int _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.37/6.66 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A5 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A5) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.code_integer) (B6 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B6)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (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)))))))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (= tptp.divmod_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M5) N3)) (@ (@ tptp.modulo_modulo_nat M5) N3)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.37/6.66 (assert (forall ((Q3 tptp.int) (R2 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q3) R2)) (@ (@ tptp.plus_plus_int Q3) (@ tptp.zero_n2684676970156552555ol_int (not (= R2 tptp.zero_zero_int)))))))
% 6.37/6.66 (assert (= tptp.ring_1_of_int_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K2) _let_1))))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K2) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 6.37/6.66 (assert (= tptp.ring_1_of_int_real (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 6.37/6.66 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 6.37/6.66 (assert (= tptp.ring_1_of_int_rat (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 6.37/6.66 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.37/6.66 (assert (forall ((P Bool) (Q (-> tptp.int tptp.int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (B2 tptp.int)) (and P (@ (@ Q A3) B2)))) (lambda ((Ab tptp.product_prod_int_int)) (and P (@ (@ tptp.produc4947309494688390418_int_o Q) Ab))))))
% 6.37/6.66 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.37/6.66 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.37/6.66 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.37/6.66 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.37/6.66 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.37/6.66 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.37/6.66 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.37/6.66 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.37/6.66 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.37/6.66 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.37/6.66 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.37/6.66 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.37/6.66 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.37/6.66 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.37/6.66 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.37/6.66 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.37/6.66 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.37/6.66 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X 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 X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X 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 X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N2) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2) Y))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((X 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 X))) 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 X))) N2)) A))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.37/6.66 (assert (forall ((X 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 X))) 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 X))) N2)) A))))
% 6.37/6.66 (assert (forall ((X 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 X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X 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 X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X 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 X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.37/6.66 (assert (forall ((X 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 X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.37/6.66 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X 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 X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X 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 X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.37/6.66 (assert (forall ((Prod tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((Uu3 tptp.int) (Uv3 tptp.int)) true)) Prod)))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.37/6.66 (assert (= tptp.ord_less_eq_int (lambda ((N3 tptp.int) (M5 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N3)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M5)) tptp.one_one_real)))))
% 6.37/6.66 (assert (= tptp.ord_less_int (lambda ((N3 tptp.int) (M5 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 M5)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D))) _let_1))))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X))))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X)))) tptp.one_one_real)))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.37/6.66 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.37/6.66 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.37/6.66 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X3)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y4)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X3)))))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X3)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y4)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X3)))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))
% 6.37/6.66 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 6.37/6.66 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z6) (@ (@ tptp.ord_less_int Z6) Z3))))))))
% 6.37/6.66 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z3) (@ (@ tptp.ord_less_int Z6) Z3))))))))
% 6.37/6.66 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ tptp.ln_ln_real X) (@ tptp.ln_ln_real Y)) (= X Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (= (@ _let_1 (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (= (@ tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X)) (=> (@ _let_1 X) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (= (@ tptp.ln_ln_real X) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y)) Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X))) (@ tptp.uminus_uminus_real X))))))
% 6.37/6.66 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N tptp.nat)) (and (not (@ P N)) (@ P (@ tptp.suc N))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z2)))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z2)))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)))))))
% 6.37/6.66 (assert (= tptp.artanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X) Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X)))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.37/6.66 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((M tptp.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.37/6.66 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.37/6.66 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_int N2))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.37/6.66 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.37/6.66 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.37/6.66 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.37/6.66 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X) (@ tptp.abs_abs_int Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X) (@ tptp.abs_abs_rat Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y))))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X) (@ tptp.abs_abs_Code_integer Y)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y))))))
% 6.37/6.66 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 6.37/6.66 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 6.37/6.66 (assert (forall ((L tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L) K))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.one_one_real)))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E2))) (= X tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) E2))) (= X tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X))))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.37/6.66 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))))
% 6.37/6.66 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.37/6.66 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.37/6.66 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.37/6.66 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.37/6.66 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.37/6.66 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.37/6.66 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.37/6.66 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.37/6.66 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.37/6.66 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X) (@ (@ tptp.ord_le3102999989581377725nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.37/6.66 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X) (@ (@ tptp.ord_le6747313008572928689nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.37/6.66 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 6.37/6.66 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.37/6.66 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y4))) D3) (and (@ (@ tptp.ord_less_real A) Y4) (@ (@ tptp.ord_less_real Y4) B))))))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) U)) Y))) V)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X)))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 6.37/6.66 (assert (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 6.37/6.66 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y4))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) X))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) X))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) (@ 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 X) N2))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) (@ 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 X) N2))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X) tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X) tptp.one_one_rat))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X) tptp.one_one_real))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2) (@ (@ tptp.power_power_rat A) N2)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) Y))))))
% 6.37/6.66 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))))
% 6.37/6.66 (assert (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) Y))))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))))
% 6.37/6.66 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X tptp.code_integer)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (@ (@ P X3) (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X)) (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ P X3) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (@ (@ P X3) (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X)) (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ (@ P X3) (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 6.37/6.66 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A2) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A2) tptp.zero_zero_complex)))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A2) tptp.zero_zero_nat)))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A2) tptp.zero_zero_real)))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A3 tptp.int)) (@ tptp.abs_abs_int (@ F A3)))) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A3 tptp.int)) (@ tptp.abs_abs_int (@ F A3)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((A3 tptp.nat)) (@ tptp.abs_abs_real (@ F A3)))) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((A3 tptp.nat)) (@ tptp.abs_abs_real (@ F A3)))) A2))))
% 6.37/6.66 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.37/6.66 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N2) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))))
% 6.37/6.66 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.37/6.66 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.int)) (A2 tptp.set_complex)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.ring_17405671764205052669omplex (@ F X2)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X2)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X2)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X2)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X2)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))))
% 6.37/6.66 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B3 tptp.set_int) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (@ G I3)) B3))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.66 (assert (forall ((G (-> tptp.complex tptp.complex tptp.complex)) (B3 tptp.set_complex) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (@ G I3)) B3))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.66 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B3 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G I3)) B3))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.66 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (B3 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ G I3)) B3))) A2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N3 tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N3)))) A2))))
% 6.37/6.66 (assert (forall ((R2 tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R2) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.times_times_complex R2) (@ F N3)))) A2))))
% 6.37/6.66 (assert (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N3)))) A2))))
% 6.37/6.66 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R2) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ F N3)))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N3 tptp.int)) (@ (@ tptp.times_times_int (@ F N3)) R2))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N3)) R2))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N3)) R2))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) R2))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B3 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I3)) (@ G J3)))) B3))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B3 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B3)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I3)) (@ G J3)))) B3))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I3)) (@ G J3)))) B3))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I3)) (@ G J3)))) B3))) A2))))
% 6.37/6.66 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))))
% 6.37/6.66 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))))
% 6.37/6.66 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))))
% 6.37/6.66 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) A2)))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) A2)))))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) R2))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) R2))) A2))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.uminus_uminus_int (@ F X2)))) A2) (@ tptp.uminus_uminus_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)))))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.uminus1482373934393186551omplex (@ F X2)))) A2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.uminus_uminus_real (@ F X2)))) A2) (@ tptp.uminus_uminus_real (@ (@ tptp.groups6591440286371151544t_real F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_int) (G (-> tptp.real tptp.int tptp.int)) (R (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((X2 tptp.real)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups1932886352136224148al_int (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_int) (G (-> tptp.nat tptp.int tptp.int)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ (@ G X2) Y2))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_int) (G (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X2 tptp.complex)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X2 tptp.complex)) (@ (@ G X2) Y2))) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_complex) (G (-> tptp.real tptp.complex tptp.complex)) (R (-> tptp.real tptp.complex Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((X2 tptp.real)) (@ (@ tptp.groups7754918857620584856omplex (@ G X2)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_complex) (G (-> tptp.nat tptp.complex tptp.complex)) (R (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (@ G X2)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ (@ G X2) Y2))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_complex) (G (-> tptp.int tptp.complex tptp.complex)) (R (-> tptp.int tptp.complex Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((X2 tptp.int)) (@ (@ tptp.groups7754918857620584856omplex (@ G X2)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X2 tptp.int)) (@ (@ G X2) Y2))) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ G X2) Y2))) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ G X2) Y2))) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (G (-> tptp.real tptp.nat tptp.real)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((X2 tptp.real)) (@ (@ tptp.groups6591440286371151544t_real (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) tptp.zero_zero_nat))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) tptp.zero_zero_nat))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))
% 6.37/6.66 (assert (forall ((F (-> tptp.real tptp.rat)) (I5 tptp.set_real) (G (-> tptp.real tptp.rat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I5) (@ (@ tptp.groups1300246762558778688al_rat G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I5) (@ (@ tptp.groups2906978787729119204at_rat G) I5)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I5) (@ (@ tptp.groups5058264527183730370ex_rat G) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G (-> tptp.int tptp.rat)) (I tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I5) (@ (@ tptp.groups3906332499630173760nt_rat G) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.real tptp.nat)) (I5 tptp.set_real) (G (-> tptp.real tptp.nat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I5) (@ (@ tptp.groups1935376822645274424al_nat G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I5) (@ (@ tptp.groups5693394587270226106ex_nat G) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I5) (@ (@ tptp.groups4541462559716669496nt_nat G) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.real tptp.int)) (I5 tptp.set_real) (G (-> tptp.real tptp.int)) (I tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I5) (@ (@ tptp.groups1932886352136224148al_int G) I5)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I5) (@ (@ tptp.groups3539618377306564664at_int G) I5)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.complex tptp.int)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.int)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) I5) (@ (@ tptp.groups5690904116761175830ex_int G) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups5754745047067104278omplex G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.zero_zero_complex))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.zero_zero_complex))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups3049146728041665814omplex G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.zero_zero_complex))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups8097168146408367636l_real G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.zero_zero_real))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5808333547571424918x_real G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.zero_zero_real))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups8778361861064173332t_real G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.zero_zero_real))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.rat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1300246762558778688al_rat G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.zero_zero_rat))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.zero_zero_rat))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5058264527183730370ex_rat G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.zero_zero_rat))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups3906332499630173760nt_rat G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.zero_zero_rat))) A2)))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X2 tptp.int)) (= (@ G X2) tptp.zero_zero_complex))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X2 tptp.int)) (= (@ G X2) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X2 tptp.int)) (= (@ G X2) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X2 tptp.int)) (= (@ G X2) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.zero_zero_int))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (= (@ G X2) tptp.zero_zero_complex))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (= (@ G X2) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_nat) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) S)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) S)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) S)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F) A2) tptp.zero_zero_rat) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A2) tptp.zero_zero_rat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F) A2) tptp.zero_zero_rat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A2) tptp.zero_zero_rat) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.zero_zero_nat) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_complex X16) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2073611262835488442omplex H2) S3)) (@ (@ tptp.groups2073611262835488442omplex G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_complex X16) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3049146728041665814omplex H2) S3)) (@ (@ tptp.groups3049146728041665814omplex G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_real X16) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5808333547571424918x_real H2) S3)) (@ (@ tptp.groups5808333547571424918x_real G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_real X16) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H2) S3)) (@ (@ tptp.groups8778361861064173332t_real G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2906978787729119204at_rat H2) S3)) (@ (@ tptp.groups2906978787729119204at_rat G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5058264527183730370ex_rat H2) S3)) (@ (@ tptp.groups5058264527183730370ex_rat G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3906332499630173760nt_rat H2) S3)) (@ (@ tptp.groups3906332499630173760nt_rat G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_nat X16) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5693394587270226106ex_nat H2) S3)) (@ (@ tptp.groups5693394587270226106ex_nat G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_nat X16) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups4541462559716669496nt_nat H2) S3)) (@ (@ tptp.groups4541462559716669496nt_nat G) S3))))))))
% 6.37/6.66 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X16 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_int X16) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3539618377306564664at_int H2) S3)) (@ (@ tptp.groups3539618377306564664at_int G) S3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) (@ (@ tptp.groups8097168146408367636l_real G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) (@ (@ tptp.groups1300246762558778688al_rat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2)))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.nat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (B3 tptp.real) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (B3 tptp.real) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (B3 tptp.real) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat)) (B3 tptp.rat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B3 tptp.rat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) B3) (=> (@ (@ tptp.member_nat I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B3 tptp.rat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (B3 tptp.rat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (B3 tptp.nat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B3 tptp.nat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.37/6.66 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.nat)) (B3 tptp.nat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B6 tptp.real)) (=> (@ (@ tptp.member_real B6) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B6)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B6 tptp.complex)) (=> (@ (@ tptp.member_complex B6) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B6)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((B6 tptp.int)) (=> (@ (@ tptp.member_int B6) (@ (@ tptp.minus_minus_set_int B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B6)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B6 tptp.real)) (=> (@ (@ tptp.member_real B6) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B6)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B6 tptp.complex)) (=> (@ (@ tptp.member_complex B6) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B6)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((B6 tptp.int)) (=> (@ (@ tptp.member_int B6) (@ (@ tptp.minus_minus_set_int B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B6)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B6 tptp.real)) (=> (@ (@ tptp.member_real B6) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B6)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B6 tptp.complex)) (=> (@ (@ tptp.member_complex B6) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B6)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((B6 tptp.int)) (=> (@ (@ tptp.member_int B6) (@ (@ tptp.minus_minus_set_int B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B6)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B6 tptp.real)) (=> (@ (@ tptp.member_real B6) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B6)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B3) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B3) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I2)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I3 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I2)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I3 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I2)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I2)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I3 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I5) tptp.one_one_real) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I5) tptp.one_one_real) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I3 tptp.real)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I5) tptp.one_one_real) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I3 tptp.int)) (@ (@ tptp.times_times_real (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((I3 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I3 tptp.real)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X) I5) tptp.one_one_rat) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X I3)))) I5)) B))) Delta))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (assert (forall ((D tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 6.37/6.66 (assert (forall ((D tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.37/6.66 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.37/6.66 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.37/6.66 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.37/6.66 (assert (forall ((W tptp.complex) (Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.times_times_complex W))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.37/6.66 (assert (forall ((W tptp.real) (Y tptp.real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.37/6.66 (assert (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.37/6.66 (assert (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.37/6.66 (assert (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.37/6.66 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_complex (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y)))))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N3 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N3 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))))
% 6.37/6.66 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A3 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 A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))))
% 6.37/6.66 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A3 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 A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))))
% 6.37/6.66 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.37/6.66 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K2 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.37/6.66 (assert (= tptp.arctan (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X2) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.37/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) A) A)))
% 6.37/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) A) A)))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y)) (= X Y))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.37/6.66 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.zero_zero_int) A)))
% 6.37/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.zero_zero_nat) A)))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.zero_zero_int) A) A)))
% 6.37/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.zero_zero_nat) A) A)))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.37/6.66 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.37/6.66 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.37/6.66 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.37/6.66 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.37/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)))
% 6.37/6.66 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) X)))
% 6.37/6.66 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 6.37/6.66 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger X) _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int X) _let_1) _let_1))))
% 6.37/6.66 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger _let_1) X) _let_1))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) X) _let_1))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.37/6.66 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 6.37/6.66 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.37/6.66 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 6.37/6.66 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.37/6.66 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N2))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ 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 X)) (@ tptp.numeral_numeral_int Y))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ 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 X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ 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 X)) (@ tptp.numeral_numeral_int Y))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ 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 X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))
% 6.37/6.66 (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)))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3)))) A2) tptp.zero_zero_complex))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I3)))) A2) tptp.zero_zero_rat))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3)))) A2) tptp.zero_zero_real))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ 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 X)) (@ tptp.numeral_numeral_int Y))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ 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 X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ 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 X)) (@ tptp.numeral_numeral_int Y))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ 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 X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X))))
% 6.37/6.66 (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)))
% 6.37/6.66 (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)))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3))) (@ D I3)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I3))) (@ D I3)))) A2) tptp.zero_zero_complex))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I3))) (@ D I3)))) A2) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I3))) (@ D I3)))) A2) tptp.zero_zero_rat))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3))) (@ D I3)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I3))) (@ D I3)))) A2) tptp.zero_zero_real))))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_se2000444600071755411sk_int N3)))))
% 6.37/6.66 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ tptp.bit_se2002935070580805687sk_nat N3)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) (@ (@ tptp.plus_plus_int X) Y))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Z)) X) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y) X)) (@ (@ tptp.bit_se1409905431419307370or_int Z) X)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y) Z)) X) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) X)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int X))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int Y) Z)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int Y) Z)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B2) A3))))
% 6.37/6.66 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B2) A3))))
% 6.37/6.66 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int B2) A3))))
% 6.37/6.66 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat B2) A3))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int X) tptp.zero_zero_int) X)))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q3)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q3)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((A2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A2))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))))
% 6.37/6.66 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.exp_real A2))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer) (X 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 X) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 Y) _let_1) (= X Y))))))))))
% 6.37/6.66 (assert (forall ((A tptp.int) (X 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 X) tptp.zero_zero_int) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y) tptp.zero_zero_int) (=> (= (@ _let_2 Y) _let_1) (= X Y))))))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int) (S 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) S)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L S)))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.37/6.66 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X3 tptp.real)) (= (@ tptp.exp_real X3) Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A2) (@ (@ tptp.groups6591440286371151544t_real G) A2))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y)))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Y))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) X))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ (@ tptp.times_times_complex Y) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y) (@ (@ tptp.times_times_real Y) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y))))))
% 6.37/6.66 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.37/6.66 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))))
% 6.37/6.66 (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)))))))))))
% 6.37/6.66 (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)))))))))))
% 6.37/6.66 (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)))))))))))
% 6.37/6.66 (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)))))))))))
% 6.37/6.66 (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)))))))))))
% 6.37/6.66 (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)))))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_set_nat) (G (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A2)) (@ (@ tptp.groups8294997508430121362at_nat G) A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.37/6.66 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real X) _let_1) _let_1)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y))))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))) tptp.one_one_real)))
% 6.37/6.66 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (forall ((X tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 6.37/6.66 (assert (forall ((X tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 6.37/6.66 (assert (forall ((X tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I3)))) _let_1)))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I3)))) _let_1)))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) C)))) tptp.zero_zero_complex))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X)))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.minus_minus_real Y) tptp.one_one_real)) (= (@ tptp.exp_real X3) Y))))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_complex (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_complex (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups2073611262835488442omplex G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ G M)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N3 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.66 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.66 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.66 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.complex)) (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.groups2073611262835488442omplex G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_complex (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))))))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.modulo_modulo_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.66 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ tptp.exp_real X2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.37/6.66 (assert (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))) (let ((_let_2 (@ tptp.exp_complex X2))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X) Y)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y)))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X tptp.zero_zero_real)))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X) (= Y tptp.zero_zero_real)))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.37/6.66 (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)))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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 ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.37/6.66 (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 ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.37/6.66 (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 ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.37/6.66 (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 ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F M))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y)))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X) Y))))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.37/6.66 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.sqrt X)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.37/6.66 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.37/6.66 (assert (forall ((G (-> tptp.nat tptp.complex)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N2) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K2)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.37/6.66 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N3)) (@ (@ tptp.plus_plus_int K2) _let_1))) _let_1)))))
% 6.37/6.66 (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))))))))
% 6.37/6.66 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (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))))))))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X))))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 6.37/6.66 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.arcosh_real X) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I3) 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)))))
% 6.37/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.37/6.66 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 6.37/6.66 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.37/6.66 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K2) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.37/6.66 (assert (= tptp.arsinh_real (lambda ((X2 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.37/6.66 (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))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.37/6.66 (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)))
% 6.37/6.66 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.37/6.66 (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))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.37/6.66 (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)))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))
% 6.37/6.66 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (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)))))))
% 6.37/6.66 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.37/6.66 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P X3) (@ P (@ tptp.inc X3)))) (@ P X)))))
% 6.37/6.66 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) tptp.one) tptp.one)))
% 6.37/6.66 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.37/6.66 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (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)))))
% 6.37/6.66 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (= (@ tptp.inc (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.37/6.66 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.inc N2)) (@ tptp.bit1 N2))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X3 tptp.vEBT_VEBT) (S4 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_VEBT_VEBT X3) S4)))))) (@ P S3))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X3) S4)))))) (@ P S3))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X3) S4)))))) (@ P S3))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X3) S4)))))) (@ P S3))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X3 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X3) S4)))))) (@ P S3))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.num))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X3 tptp.vEBT_VEBT) (S4 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_VEBT_VEBT X3) S4)))))) (@ P S3))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X3 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X3) S4)))))) (@ P S3))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X3) S4)))))) (@ P S3))))))
% 6.37/6.66 (assert (forall ((S3 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X3) S4)))))) (@ P S3))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X3 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X3)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X3) S4)))))) (@ P S3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B6 tptp.real) (A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A6) (@ (@ tptp.ord_less_real B6) X5))) (=> (@ P A6) (@ P (@ (@ tptp.insert_real B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B6 tptp.rat) (A6 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A6) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.member_rat X5) A6) (@ (@ tptp.ord_less_rat B6) X5))) (=> (@ P A6) (@ P (@ (@ tptp.insert_rat B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B6 tptp.num) (A6 tptp.set_num)) (=> (@ tptp.finite_finite_num A6) (=> (forall ((X5 tptp.num)) (=> (@ (@ tptp.member_num X5) A6) (@ (@ tptp.ord_less_num B6) X5))) (=> (@ P A6) (@ P (@ (@ tptp.insert_num B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B6 tptp.nat) (A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A6) (@ (@ tptp.ord_less_nat B6) X5))) (=> (@ P A6) (@ P (@ (@ tptp.insert_nat B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B6 tptp.int) (A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A6) (@ (@ tptp.ord_less_int B6) X5))) (=> (@ P A6) (@ P (@ (@ tptp.insert_int B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B6 tptp.real) (A6 tptp.set_real)) (=> (@ tptp.finite_finite_real A6) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A6) (@ (@ tptp.ord_less_real X5) B6))) (=> (@ P A6) (@ P (@ (@ tptp.insert_real B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B6 tptp.rat) (A6 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A6) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.member_rat X5) A6) (@ (@ tptp.ord_less_rat X5) B6))) (=> (@ P A6) (@ P (@ (@ tptp.insert_rat B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B6 tptp.num) (A6 tptp.set_num)) (=> (@ tptp.finite_finite_num A6) (=> (forall ((X5 tptp.num)) (=> (@ (@ tptp.member_num X5) A6) (@ (@ tptp.ord_less_num X5) B6))) (=> (@ P A6) (@ P (@ (@ tptp.insert_num B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B6 tptp.nat) (A6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A6) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A6) (@ (@ tptp.ord_less_nat X5) B6))) (=> (@ P A6) (@ P (@ (@ tptp.insert_nat B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B6 tptp.int) (A6 tptp.set_int)) (=> (@ tptp.finite_finite_int A6) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A6) (@ (@ tptp.ord_less_int X5) B6))) (=> (@ P A6) (@ P (@ (@ tptp.insert_int B6) A6)))))) (@ P A2))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 6.37/6.67 (assert (forall ((A tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.37/6.67 (assert (forall ((A tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.37/6.67 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat) (F (-> tptp.set_nat tptp.nat))) (let ((_let_1 (@ tptp.groups8294997508430121362at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))) (let ((_let_4 (@ (@ tptp.member_set_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.37/6.67 (assert (forall ((A tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.37/6.67 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.37/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 6.37/6.67 (assert (forall ((Xs2 tptp.list_real) (I tptp.nat) (X tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I) X))) (@ (@ tptp.insert_real X) (@ tptp.set_real2 Xs2)))))
% 6.37/6.67 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I) X))) (@ (@ tptp.insert_int X) (@ tptp.set_int2 Xs2)))))
% 6.37/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X))) (@ (@ tptp.insert_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.37/6.67 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I) X))) (@ (@ tptp.insert_nat X) (@ tptp.set_nat2 Xs2)))))
% 6.37/6.67 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.37/6.67 (assert (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))))
% 6.37/6.67 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X)) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N2)) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N2)) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N2)) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N2)) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X)))) (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 X) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X)))) (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 X) tptp.bot_bot_set_nat))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X)))) (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 X) tptp.bot_bot_set_int))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X)))) (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 X) tptp.bot_bot_set_real))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X))) (let ((_let_2 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X))) (let ((_let_2 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X))) (let ((_let_2 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int)) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X))) (let ((_let_2 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.complex)) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X))) (let ((_let_2 (@ tptp.groups1794756597179926696omplex G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.complex))) (let ((_let_1 (@ tptp.groups1794756597179926696omplex G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_complex (@ G X)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_real _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ tptp.groups769130701875090982BT_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.37/6.67 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((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)) (= X (@ tptp.bit0 N))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N tptp.num)) (=> (= X (@ 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)) (=> (= X (@ 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)) (= X (@ tptp.bit1 N))) _let_2) (=> (forall ((N tptp.num)) (=> (= X (@ 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)) (=> (= X (@ tptp.bit1 N)) (forall ((M3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M3)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M3)))))))))))))))))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.real)) (C (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.groups2240296850493347238T_real C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.rat)) (C (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ (@ tptp.groups136491112297645522BT_rat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5058264527183730370ex_rat C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.nat)) (C (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ (@ tptp.groups771621172384141258BT_nat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups5693394587270226106ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.int)) (C (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ (@ tptp.groups769130701875090982BT_int C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups769130701875090982BT_int (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups769130701875090982BT_int (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups5690904116761175830ex_int C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.complex)) (C (-> tptp.vEBT_VEBT tptp.complex))) (let ((_let_1 (@ (@ tptp.groups1794756597179926696omplex C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups1794756597179926696omplex (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_complex (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1794756597179926696omplex (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups8778361861064173332t_real C) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 6.37/6.67 (assert (forall ((I tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ (@ tptp.member_VEBT_VEBT I) A2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups2240296850493347238T_real F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ (@ tptp.member_VEBT_VEBT I) A2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups136491112297645522BT_rat F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I) A2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))))
% 6.37/6.67 (assert (forall ((I tptp.vEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ (@ tptp.member_VEBT_VEBT I) A2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups771621172384141258BT_nat F) A2)))))))
% 6.37/6.67 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M5 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 M5) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 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 M5)) (not (@ _let_2 N3))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.37/6.67 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 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 M5)) (not (@ _let_2 N3))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.37/6.67 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N3) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) M5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M5) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1))))))))))
% 6.37/6.67 (assert (forall ((A tptp.vEBT_VEBT)) (= (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (= X2 A))) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.37/6.67 (assert (forall ((A tptp.product_prod_int_int)) (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (= X2 A))) (@ (@ tptp.insert5033312907999012233nt_int A) tptp.bot_bo1796632182523588997nt_int))))
% 6.37/6.67 (assert (forall ((A tptp.complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= X2 A))) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))
% 6.37/6.67 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (= X2 A))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 6.37/6.67 (assert (forall ((A tptp.nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (= X2 A))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 6.37/6.67 (assert (forall ((A tptp.int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (= X2 A))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 6.37/6.67 (assert (forall ((A tptp.real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (= X2 A))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 6.37/6.67 (assert (forall ((A tptp.vEBT_VEBT)) (= (@ tptp.collect_VEBT_VEBT (@ (lambda ((Y5 tptp.vEBT_VEBT) (Z5 tptp.vEBT_VEBT)) (= Y5 Z5)) A)) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.37/6.67 (assert (forall ((A tptp.product_prod_int_int)) (= (@ tptp.collec213857154873943460nt_int (@ (lambda ((Y5 tptp.product_prod_int_int) (Z5 tptp.product_prod_int_int)) (= Y5 Z5)) A)) (@ (@ tptp.insert5033312907999012233nt_int A) tptp.bot_bo1796632182523588997nt_int))))
% 6.37/6.67 (assert (forall ((A tptp.complex)) (= (@ tptp.collect_complex (@ (lambda ((Y5 tptp.complex) (Z5 tptp.complex)) (= Y5 Z5)) A)) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))
% 6.37/6.67 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (@ (lambda ((Y5 tptp.set_nat) (Z5 tptp.set_nat)) (= Y5 Z5)) A)) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 6.37/6.67 (assert (forall ((A tptp.nat)) (= (@ tptp.collect_nat (@ (lambda ((Y5 tptp.nat) (Z5 tptp.nat)) (= Y5 Z5)) A)) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 6.37/6.67 (assert (forall ((A tptp.int)) (= (@ tptp.collect_int (@ (lambda ((Y5 tptp.int) (Z5 tptp.int)) (= Y5 Z5)) A)) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 6.37/6.67 (assert (forall ((A tptp.real)) (= (@ tptp.collect_real (@ (lambda ((Y5 tptp.real) (Z5 tptp.real)) (= Y5 Z5)) A)) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 6.37/6.67 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.37/6.67 (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))))))))))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N2)) (= M N2))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N2)) (= M N2))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))))
% 6.37/6.67 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.37/6.67 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.37/6.67 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.37/6.67 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.37/6.67 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_rat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_real N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6690914467698888265omplex N2))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))))
% 6.37/6.67 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.37/6.67 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.37/6.67 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.37/6.67 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N2))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.37/6.67 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 6.37/6.67 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.37/6.67 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.37/6.67 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.complex tptp.nat)) (A2 tptp.set_complex)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.semiri8010041392384452111omplex (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.37/6.67 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.37/6.67 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.37/6.67 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.37/6.67 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 6.37/6.67 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.37/6.67 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 6.37/6.67 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 6.37/6.67 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 6.37/6.67 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 6.37/6.67 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.37/6.67 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 6.37/6.67 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 6.37/6.67 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.37/6.67 (assert (forall ((I tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)) X))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (I tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N2) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N2) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.nat_set_encode A2)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)) tptp.zero_zero_rat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.37/6.67 (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))))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.37/6.67 (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))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X)) (@ tptp.semiri4216267220026989637d_enat Y)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.37/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) X))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) X)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y4 tptp.real)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)))))))
% 6.37/6.67 (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))))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))
% 6.37/6.67 (assert (= tptp.ord_less_int (lambda ((W2 tptp.int) (Z3 tptp.int)) (exists ((N3 tptp.nat)) (= Z3 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (assert (= tptp.ord_less_nat (lambda ((N3 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M5)))))
% 6.37/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((N3 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M5)) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)))
% 6.37/6.67 (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))))))))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D))) _let_1))))))
% 6.37/6.67 (assert (= tptp.bot_bo1796632182523588997nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) false))))
% 6.37/6.67 (assert (= tptp.bot_bot_set_complex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) false))))
% 6.37/6.67 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) false))))
% 6.37/6.67 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) false))))
% 6.37/6.67 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X2 tptp.int)) false))))
% 6.37/6.67 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real (lambda ((X2 tptp.real)) false))))
% 6.37/6.67 (assert (forall ((A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (@ (@ tptp.insert_VEBT_VEBT A) (@ tptp.collect_VEBT_VEBT P)) (@ tptp.collect_VEBT_VEBT (lambda ((U2 tptp.vEBT_VEBT)) (=> (not (= U2 A)) (@ P U2)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.insert_real A) (@ tptp.collect_real P)) (@ tptp.collect_real (lambda ((U2 tptp.real)) (=> (not (= U2 A)) (@ P U2)))))))
% 6.37/6.67 (assert (forall ((A tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.insert5033312907999012233nt_int A) (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int (lambda ((U2 tptp.product_prod_int_int)) (=> (not (= U2 A)) (@ P U2)))))))
% 6.37/6.67 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.insert_complex A) (@ tptp.collect_complex P)) (@ tptp.collect_complex (lambda ((U2 tptp.complex)) (=> (not (= U2 A)) (@ P U2)))))))
% 6.37/6.67 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.insert_set_nat A) (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat (lambda ((U2 tptp.set_nat)) (=> (not (= U2 A)) (@ P U2)))))))
% 6.37/6.67 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A) (@ tptp.collect_nat P)) (@ tptp.collect_nat (lambda ((U2 tptp.nat)) (=> (not (= U2 A)) (@ P U2)))))))
% 6.37/6.67 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.insert_int A) (@ tptp.collect_int P)) (@ tptp.collect_int (lambda ((U2 tptp.int)) (=> (not (= U2 A)) (@ P U2)))))))
% 6.37/6.67 (assert (= tptp.insert_VEBT_VEBT (lambda ((A3 tptp.vEBT_VEBT) (B5 tptp.set_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (or (= X2 A3) (@ (@ tptp.member_VEBT_VEBT X2) B5)))))))
% 6.37/6.67 (assert (= tptp.insert_real (lambda ((A3 tptp.real) (B5 tptp.set_real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (or (= X2 A3) (@ (@ tptp.member_real X2) B5)))))))
% 6.37/6.67 (assert (= tptp.insert5033312907999012233nt_int (lambda ((A3 tptp.product_prod_int_int) (B5 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (or (= X2 A3) (@ (@ tptp.member5262025264175285858nt_int X2) B5)))))))
% 6.37/6.67 (assert (= tptp.insert_complex (lambda ((A3 tptp.complex) (B5 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (or (= X2 A3) (@ (@ tptp.member_complex X2) B5)))))))
% 6.37/6.67 (assert (= tptp.insert_set_nat (lambda ((A3 tptp.set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (or (= X2 A3) (@ (@ tptp.member_set_nat X2) B5)))))))
% 6.37/6.67 (assert (= tptp.insert_nat (lambda ((A3 tptp.nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (or (= X2 A3) (@ (@ tptp.member_nat X2) B5)))))))
% 6.37/6.67 (assert (= tptp.insert_int (lambda ((A3 tptp.int) (B5 tptp.set_int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (or (= X2 A3) (@ (@ tptp.member_int X2) B5)))))))
% 6.37/6.67 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)))) E)))))))
% 6.37/6.67 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) E)))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N2)))) N2) (@ tptp.exp_real X)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N2)))) N2) (@ tptp.exp_complex X)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M3)) X)) C))) (= X tptp.zero_zero_real)))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X)))) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ln_ln_real X))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N2))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K3 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) L4)) (=> (=> (not (and (@ (@ tptp.member_int K3) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K3) L4)))))) (@ (@ P A0) A1)))))
% 6.37/6.67 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (A tptp.vEBT_VEBT)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (and (= X2 A) (@ P X2)))) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))) (=> (not _let_1) (= (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (and (= X2 A) (@ P X2)))) tptp.bot_bo8194388402131092736T_VEBT))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (A tptp.product_prod_int_int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (and (= X2 A) (@ P X2)))) (@ (@ tptp.insert5033312907999012233nt_int A) tptp.bot_bo1796632182523588997nt_int))) (=> (not _let_1) (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (and (= X2 A) (@ P X2)))) tptp.bot_bo1796632182523588997nt_int))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.complex Bool)) (A tptp.complex)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (= X2 A) (@ P X2)))) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))) (=> (not _let_1) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (= X2 A) (@ P X2)))) tptp.bot_bot_set_complex))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (and (= X2 A) (@ P X2)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (and (= X2 A) (@ P X2)))) tptp.bot_bot_set_set_nat))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (= X2 A) (@ P X2)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (= X2 A) (@ P X2)))) tptp.bot_bot_set_nat))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (= X2 A) (@ P X2)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (= X2 A) (@ P X2)))) tptp.bot_bot_set_int))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (= X2 A) (@ P X2)))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (= X2 A) (@ P X2)))) tptp.bot_bot_set_real))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (A tptp.vEBT_VEBT)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (and (= A X2) (@ P X2)))) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))) (=> (not _let_1) (= (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (and (= A X2) (@ P X2)))) tptp.bot_bo8194388402131092736T_VEBT))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (A tptp.product_prod_int_int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (and (= A X2) (@ P X2)))) (@ (@ tptp.insert5033312907999012233nt_int A) tptp.bot_bo1796632182523588997nt_int))) (=> (not _let_1) (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (and (= A X2) (@ P X2)))) tptp.bot_bo1796632182523588997nt_int))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.complex Bool)) (A tptp.complex)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (= A X2) (@ P X2)))) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))) (=> (not _let_1) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (= A X2) (@ P X2)))) tptp.bot_bot_set_complex))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (and (= A X2) (@ P X2)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (and (= A X2) (@ P X2)))) tptp.bot_bot_set_set_nat))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (= A X2) (@ P X2)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (= A X2) (@ P X2)))) tptp.bot_bot_set_nat))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (= A X2) (@ P X2)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (= A X2) (@ P X2)))) tptp.bot_bot_set_int))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (= A X2) (@ P X2)))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (= A X2) (@ P X2)))) tptp.bot_bot_set_real))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I3)) 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))))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I3)) 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))))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I3)) 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))))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I3)) 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))))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I3)) 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))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N2))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I3)) 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))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I3)) 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))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_rat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M5 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M5)))) (@ (@ (@ 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))))))))
% 6.37/6.67 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M5 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M5)))) (@ (@ (@ 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))))))))
% 6.37/6.67 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_real (= N3 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M5 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M5)))) (@ (@ (@ 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))))))))
% 6.37/6.67 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M5 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M5)))) (@ (@ (@ 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))))))))
% 6.37/6.67 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_complex (= N3 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M5 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M5)))) (@ (@ (@ 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))))))))
% 6.37/6.67 (assert (forall ((U tptp.real) (Deg tptp.nat) (T tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (=> (= U (@ (@ tptp.power_power_real _let_1) Deg)) (=> (@ (@ tptp.vEBT_invar_vebt T) Deg) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ _let_2 (@ _let_2 U))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) 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 X) _let_1))))))))
% 6.37/6.67 (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)))))))))))))
% 6.37/6.67 (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))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ tptp.suminf_real (lambda ((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 X) tptp.one_one_real)) (@ tptp.suc N3))))))))))
% 6.37/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X) (= (@ _let_2 (@ (@ tptp.log A) X)) (@ _let_1 X))))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_real A) X)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) A))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y)))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real A) X))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) A))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (= tptp.log (lambda ((A3 tptp.real) (X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real A3)))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 B))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N2)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_1 X)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.log A) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 X) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X)))))))
% 6.37/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (U tptp.real) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (let ((_let_3 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= U (@ (@ tptp.power_power_real _let_1) N2)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_3)) (@ _let_2 (@ _let_2 U))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.log _let_1) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.37/6.67 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.37/6.67 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.37/6.67 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) A)))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S3))) (@ (@ tptp.groups8097168146408367636l_real G) S3)))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_set_nat) (F (-> tptp.set_nat tptp.complex)) (G (-> tptp.set_nat tptp.real))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups8255218700646806128omplex F) S3))) (@ (@ tptp.groups5107569545109728110t_real G) S3)))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S3))) (@ (@ tptp.groups8778361861064173332t_real G) S3)))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S3))) (@ (@ tptp.groups5808333547571424918x_real G) S3)))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I3)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I3)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I3)))) A2))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (R2 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real R2) S))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real R2) S))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))))
% 6.37/6.67 (assert (forall ((X tptp.real) (R2 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.37/6.67 (assert (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))) E))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))) E))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.37/6.67 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.37/6.67 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X) tptp.one_one_real))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 6.37/6.67 (assert (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.37/6.67 (assert (= (@ tptp.suminf_nat (lambda ((N3 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.37/6.67 (assert (= (@ tptp.suminf_int (lambda ((N3 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.37/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height T)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.37/6.67 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N tptp.nat)) (=> (not (@ (@ tptp.member_nat N) N5)) (= (@ F N) tptp.zero_zero_complex))) (= (@ tptp.suminf_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N5))))))
% 6.37/6.67 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N tptp.nat)) (=> (not (@ (@ tptp.member_nat N) N5)) (= (@ F N) tptp.zero_zero_int))) (= (@ tptp.suminf_int F) (@ (@ tptp.groups3539618377306564664at_int F) N5))))))
% 6.37/6.67 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N tptp.nat)) (=> (not (@ (@ tptp.member_nat N) N5)) (= (@ F N) tptp.zero_zero_nat))) (= (@ tptp.suminf_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N5))))))
% 6.37/6.67 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N tptp.nat)) (=> (not (@ (@ tptp.member_nat N) N5)) (= (@ F N) tptp.zero_zero_real))) (= (@ tptp.suminf_real F) (@ (@ tptp.groups6591440286371151544t_real F) N5))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.archim7802044766580827645g_real (@ _let_1 X)) (@ tptp.archim7802044766580827645g_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))))))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)) X) (exists ((N3 tptp.int)) (= X (@ tptp.ring_1_of_int_rat N3))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)) X) (exists ((N3 tptp.int)) (= X (@ tptp.ring_1_of_int_real N3))))))
% 6.37/6.67 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.37/6.67 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.37/6.67 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 6.37/6.67 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) Z))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) Z))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) Z))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) Z))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X)))))
% 6.37/6.67 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y)) (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) Z) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) A))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) A))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)))))
% 6.37/6.67 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) (@ (@ tptp.plus_plus_real R2) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R2))) (@ (@ tptp.plus_plus_rat R2) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) tptp.one_one_real)) R2)))
% 6.37/6.67 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R2))) tptp.one_one_rat)) R2)))
% 6.37/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.37/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1)))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1)))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.archim7802044766580827645g_real X) Z))))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X) Z))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I3))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I3)))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I3))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T) (@ (@ tptp.ord_less_eq_rat T) _let_1)) (@ P I3)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.37/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) Z) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))))
% 6.37/6.67 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real P2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q3)))) Q3)))))
% 6.37/6.67 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat P2) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) Q3)))))
% 6.37/6.67 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q3)))) tptp.one_one_real)) Q3)) P2))))
% 6.37/6.67 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) tptp.one_one_rat)) Q3)) P2))))
% 6.37/6.67 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))))
% 6.37/6.67 (assert (forall ((N2 tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N2))) (=> (@ (@ tptp.ord_less_rat _let_1) X) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))))
% 6.37/6.67 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.37/6.67 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((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) A1)))))
% 6.37/6.67 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q4)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.37/6.67 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q4)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.37/6.67 (assert (forall ((H2 tptp.real) (Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q4)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.37/6.67 (assert (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or890127255671739683et_nat K)) (@ (@ tptp.ord_less_set_nat I) K))))
% 6.37/6.67 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I) K))))
% 6.37/6.67 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I) K))))
% 6.37/6.67 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 6.37/6.67 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))))
% 6.37/6.67 (assert (forall ((I Bool) (K Bool)) (= (@ (@ tptp.member_o I) (@ tptp.set_ord_lessThan_o K)) (@ (@ tptp.ord_less_o I) K))))
% 6.37/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (= R5 I)) (@ F R5)) tptp.zero_zero_complex)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I)) (@ F R5)) tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I)) (@ F R5)) tptp.zero_zero_nat)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I)) (@ F R5)) tptp.zero_zero_int)))))
% 6.37/6.67 (assert (@ tptp.summable_complex (lambda ((N3 tptp.nat)) tptp.zero_zero_complex)))
% 6.37/6.67 (assert (@ tptp.summable_real (lambda ((N3 tptp.nat)) tptp.zero_zero_real)))
% 6.37/6.67 (assert (@ tptp.summable_nat (lambda ((N3 tptp.nat)) tptp.zero_zero_nat)))
% 6.37/6.67 (assert (@ tptp.summable_int (lambda ((N3 tptp.nat)) tptp.zero_zero_int)))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))) (@ tptp.summable_complex F))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X)) (@ tptp.set_ord_lessThan_rat Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.37/6.67 (assert (forall ((X Bool) (Y Bool)) (= (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_ord_lessThan_o X)) (@ tptp.set_ord_lessThan_o Y)) (@ (@ tptp.ord_less_eq_o X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) A)) (not (= X tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R5)) (@ F R5)) tptp.zero_zero_complex))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R5)) (@ F R5)) tptp.zero_zero_real))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R5)) (@ F R5)) tptp.zero_zero_nat))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R5)) (@ F R5)) tptp.zero_zero_int))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_complex))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_real))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_nat))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_int))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X)) X)))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N2))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N3)))) (@ tptp.summable_real F))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N3)))) (@ tptp.summable_complex F))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N))) (@ G N))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N))) (@ G N))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N))) (@ G N)))) (@ tptp.summable_real F)))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N))) (@ G N)))) (@ tptp.summable_complex F)))))
% 6.37/6.67 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_complex))))
% 6.37/6.67 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N3)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) C))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N3)) (@ G N3))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N3)) (@ G N3))))))))
% 6.37/6.67 (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.minus_minus_real (@ F N3)) (@ G N3))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) (@ tptp.summable_real F))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) (@ tptp.summable_complex F))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_real (@ F N3)))) (@ tptp.summable_real F))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N3)))) (@ tptp.summable_complex F))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_real (@ F N3)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N3)))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.real))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ tptp.summable_real (@ F I2)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat tptp.real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ tptp.summable_real (@ F I2)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I3 tptp.real)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ tptp.summable_real (@ F I2)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat tptp.complex))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ tptp.summable_complex (@ F I2)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((I3 tptp.real)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.complex))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ tptp.summable_complex (@ F I2)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.complex))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ tptp.summable_complex (@ F I2)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.int))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ tptp.summable_int (@ F I2)))) (@ tptp.summable_int (lambda ((N3 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.complex))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ tptp.summable_complex (@ F I2)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ tptp.summable_nat (@ F I2)))) (@ tptp.summable_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ tptp.summable_real (@ F I2)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (X 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))) X)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (X 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))) X)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (X 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))) X)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.abs_abs_real (@ F N3)))) (@ tptp.summable_real F))))
% 6.37/6.67 (assert (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X2) U2))))))
% 6.37/6.67 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat X2) U2))))))
% 6.37/6.67 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U2))))))
% 6.37/6.67 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U2))))))
% 6.37/6.67 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U2))))))
% 6.37/6.67 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U2))))))
% 6.37/6.67 (assert (= tptp.set_ord_lessThan_o (lambda ((U2 Bool)) (@ tptp.collect_o (lambda ((X2 Bool)) (@ (@ tptp.ord_less_o X2) U2))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (X 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))) X)) (@ tptp.summable_int F)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (X 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))) X)) (@ tptp.summable_nat F)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (X 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))) X)) (@ tptp.summable_real F)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex X) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real A) B))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex F) (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K))))) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((M Bool) (N2 Bool)) (= (@ (@ tptp.ord_less_set_o (@ tptp.set_ord_lessThan_o M)) (@ tptp.set_ord_lessThan_o N2)) (@ (@ tptp.ord_less_o M) N2))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.37/6.67 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.37/6.67 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.37/6.67 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.37/6.67 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.37/6.67 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.37/6.67 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N3)))) (@ (@ tptp.times_times_complex C) (@ tptp.suminf_complex F))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex F)) C) (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) C)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (= (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex F)) (@ tptp.suminf_complex G)) (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N3)) (@ G N3)))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (= (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ tptp.suminf_complex G)) (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N3)) (@ G N3)))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N3)) (@ G N3)))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_real (@ F N3)))) (@ tptp.uminus_uminus_real (@ tptp.suminf_real F))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N3)))) (@ tptp.uminus1482373934393186551omplex (@ tptp.suminf_complex F))))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.real))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ tptp.summable_real (@ F I2)))) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ tptp.suminf_real (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat tptp.real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ tptp.summable_real (@ F I2)))) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I3 tptp.real)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I3 tptp.real)) (@ tptp.suminf_real (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ tptp.summable_real (@ F I2)))) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I3 tptp.int)) (@ tptp.suminf_real (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat tptp.complex))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ tptp.summable_complex (@ F I2)))) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((I3 tptp.real)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups5754745047067104278omplex (lambda ((I3 tptp.real)) (@ tptp.suminf_complex (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.complex))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ tptp.summable_complex (@ F I2)))) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ tptp.suminf_complex (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.complex))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ tptp.summable_complex (@ F I2)))) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups3049146728041665814omplex (lambda ((I3 tptp.int)) (@ tptp.suminf_complex (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.int))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ tptp.summable_int (@ F I2)))) (= (@ tptp.suminf_int (lambda ((N3 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.suminf_int (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.complex))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ tptp.summable_complex (@ F I2)))) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ tptp.suminf_complex (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ tptp.summable_nat (@ F I2)))) (= (@ tptp.suminf_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ tptp.suminf_nat (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ tptp.summable_real (@ F I2)))) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.suminf_real (@ F I3)))) I5)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I 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) I) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (I 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) I) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (I 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) I) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X) Y)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) B))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X) A)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) B)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.37/6.67 (assert (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (@ tptp.powr_real W))) (= (@ _let_1 (@ (@ tptp.minus_minus_real Z1) Z22)) (@ (@ tptp.divide_divide_real (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) 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))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) 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))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.abs_abs_real (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ tptp.abs_abs_real (@ F N3))))))))
% 6.37/6.67 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N2 tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N2))) (=> (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.37/6.67 (assert (forall ((Q (-> Bool tptp.nat)) (P (-> Bool tptp.nat)) (N2 Bool)) (let ((_let_1 (@ tptp.set_ord_lessThan_o N2))) (=> (forall ((X3 Bool)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8507830703676809646_o_nat P) _let_1)) (@ (@ tptp.groups8507830703676809646_o_nat Q) _let_1)) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X2 Bool)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.37/6.67 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3))))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3))))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) N2)))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X)))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex X) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ F tptp.zero_zero_nat))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.37/6.67 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.37/6.67 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_complex (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I3)) R2))) _let_1)))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I3)) R2))) _let_1)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (R2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex F) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) R2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F I3)) R2))) _let_1)))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I3)) R2))) _let_1)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N3))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N3))))))))
% 6.37/6.67 (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 ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.37/6.67 (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 ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.member_nat N) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I5)) (@ tptp.suminf_int F)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (I5 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.member_nat N) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I5)) (@ tptp.suminf_nat F)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (I5 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.member_nat N) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I5)) (@ tptp.suminf_real F)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.37/6.67 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.37/6.67 (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)))
% 6.37/6.67 (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)))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.37/6.67 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (not (= X tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) A))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y)))))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N8 tptp.nat)) (not (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M4) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M4) N9)))) E)))))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N8 tptp.nat)) (not (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M4) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M4) N9)))) E)))))))))))
% 6.37/6.67 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N9)))))) R2))))))))
% 6.37/6.67 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N9)))))) R2))))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I3)) (@ (@ tptp.power_power_real Z) I3))))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.37/6.67 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P5)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.37/6.67 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.37/6.67 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P5)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.37/6.67 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.power_power_rat Y) N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_rat X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_int X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P5)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) P5)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.37/6.67 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P5)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P5)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.37/6.67 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.37/6.67 (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))
% 6.37/6.67 (assert (= tptp.powr_real (lambda ((X2 tptp.real) (A3 tptp.real)) (@ (@ (@ tptp.if_real (= X2 tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A3) (@ tptp.ln_ln_real X2)))))))
% 6.37/6.67 (assert (forall ((C tptp.real) (N5 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 N5) 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)))))
% 6.37/6.67 (assert (forall ((C tptp.real) (N5 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 N5) 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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.times_times_rat (@ _let_1 X)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (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))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N2)))))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ F I3)) (@ G I3)))) (@ 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 ((I3 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) tptp.one_one_nat)))) _let_1))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))))))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M5)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (= tptp.arcosh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ F N3)))) (@ tptp.summable_real F))))
% 6.37/6.67 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.37/6.67 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.one_one_complex) (= X tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.sin_real X))))
% 6.37/6.67 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.37/6.67 (assert (forall ((F (-> tptp.complex tptp.real)) (S tptp.set_complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.real_V4546457046886955230omplex (@ F X2)))) S))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.set_nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.groups6591440286371151544t_real F) S)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ F X2)))) S))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.set_nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.groups6591440286371151544t_real F) S)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.real_V1803761363581548252l_real (@ F X2)))) S))))
% 6.37/6.67 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.37/6.67 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 6.37/6.67 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.37/6.67 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) tptp.zero_zero_real)))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.37/6.67 (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)))
% 6.37/6.67 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.37/6.67 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.37/6.67 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) _let_1))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real B))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.cos_real X))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) tptp.one_one_complex))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) tptp.one_one_complex))))
% 6.37/6.67 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.37/6.67 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 6.37/6.67 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 6.37/6.67 (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)))
% 6.37/6.67 (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)))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.37/6.67 (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)))
% 6.37/6.67 (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)))
% 6.37/6.67 (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))
% 6.37/6.67 (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)))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.sin_complex Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.37/6.67 (assert (= tptp.uminus612125837232591019t_real (lambda ((A7 tptp.set_real)) (@ tptp.collect_real (@ tptp.uminus_uminus_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus6221592323253981072nt_int (lambda ((A7 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ tptp.uminus7117520113953359693_int_o (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus8566677241136511917omplex (lambda ((A7 tptp.set_complex)) (@ tptp.collect_complex (@ tptp.uminus1680532995456772888plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A7 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ tptp.uminus6401447641752708672_nat_o (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A7 tptp.set_nat)) (@ tptp.collect_nat (@ tptp.uminus_uminus_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A7 tptp.set_int)) (@ tptp.collect_int (@ tptp.uminus_uminus_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A7)))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (not (@ P X2)))) (@ tptp.uminus6221592323253981072nt_int (@ tptp.collec213857154873943460nt_int P)))))
% 6.37/6.67 (assert (forall ((P (-> tptp.complex Bool))) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (not (@ P X2)))) (@ tptp.uminus8566677241136511917omplex (@ tptp.collect_complex P)))))
% 6.37/6.67 (assert (forall ((P (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (not (@ P X2)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P)))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (not (@ P X2)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P)))))
% 6.37/6.67 (assert (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (not (@ P X2)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P)))))
% 6.37/6.67 (assert (= tptp.uminus612125837232591019t_real (lambda ((A7 tptp.set_real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (not (@ (@ tptp.member_real X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus6221592323253981072nt_int (lambda ((A7 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (not (@ (@ tptp.member5262025264175285858nt_int X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus8566677241136511917omplex (lambda ((A7 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (not (@ (@ tptp.member_complex X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A7 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A7 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (not (@ (@ tptp.member_nat X2) A7)))))))
% 6.37/6.67 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A7 tptp.set_int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (not (@ (@ tptp.member_int X2) A7)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X (@ _let_1 (@ tptp.cos_real A5))) (= Y (@ _let_1 (@ tptp.sin_real A5))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X)))))))
% 6.37/6.67 (assert (forall ((M tptp.int) (X tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X))))))
% 6.37/6.67 (assert (forall ((M tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X)))))))
% 6.37/6.67 (assert (forall ((M tptp.int) (X tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.37/6.67 (assert (= tptp.sin_real (lambda ((X2 tptp.real)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)))))
% 6.37/6.67 (assert (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X2)))))
% 6.37/6.67 (assert (= tptp.cos_real (lambda ((X2 tptp.real)) (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)))))
% 6.37/6.67 (assert (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X2)))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X))) (@ tptp.cos_complex X))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X))) (@ tptp.cos_real X))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1803761363581548252l_real (@ X8 N3)))))))
% 6.37/6.67 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ X8 N3)))))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1))))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1))))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y))))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) (@ tptp.sin_real X)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y)) (= X Y)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ _let_1 X))))))))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_2)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_2)))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (= (@ tptp.real_V1803761363581548252l_real (@ tptp.suminf_real X8)) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1803761363581548252l_real (@ X8 N3))))))))
% 6.37/6.67 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.suminf_real X8)) (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ X8 N3))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 6.37/6.67 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X)))))))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.pi) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I3 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) tptp.pi))))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.pi) (= X (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.37/6.67 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.37/6.67 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.37/6.67 (assert (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X3))))))
% 6.37/6.67 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real B)) (@ tptp.real_V1803761363581548252l_real A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.37/6.67 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.37/6.67 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.cos_real X3) Y) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.cos_real Y4) Y)) (= Y4 X3)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T3)) (not (= Y (@ tptp.sin_real T3))))))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X))) tptp.one_one_real))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X)))))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y)) (= X Y))))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.cos_real X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X) Y))))))))))
% 6.37/6.67 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.sin_real X3) Y) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ tptp.sin_real Y4) Y)) (= Y4 X3)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X2 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X2 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I3) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I3)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) 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) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) 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) (= X (@ (@ 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) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) 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)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) 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)) (= X (@ (@ 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)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.37/6.67 (assert (= tptp.arsinh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat 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 X) N2))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat 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 X) N2))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat 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 X) N2))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.37/6.67 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.37/6.67 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.37/6.67 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.37/6.67 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.37/6.67 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.37/6.67 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.37/6.67 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.37/6.67 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))))
% 6.37/6.67 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.37/6.67 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.37/6.67 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.37/6.67 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.37/6.67 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N2))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.37/6.67 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.37/6.67 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.37/6.67 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.37/6.67 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X))))
% 6.37/6.67 (assert (forall ((Z tptp.complex)) (exists ((A5 tptp.complex) (R3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A5))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N2)) tptp.zero_zero_rat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N2) N2)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.37/6.67 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))
% 6.37/6.67 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_rat (= M5 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M5)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.37/6.67 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_int (= M5 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.37/6.67 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_complex (= M5 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M5)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.37/6.67 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_real (= M5 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M5)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.37/6.67 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M5)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri5044797733671781792omplex N2) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y) (@ tptp.tan_real X3)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.37/6.67 (assert (forall ((Y tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))))))
% 6.37/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))
% 6.37/6.67 (assert (forall ((Y tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ tptp.tan_real Y4) Y)) (= Y4 X3)))))))))
% 6.37/6.67 (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)))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.37/6.67 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X3) Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X))) tptp.one_one_real))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y) (= (@ tptp.arctan Y) X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X)) X))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.37/6.67 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M5)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H2) M5)))) (@ 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)))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.plus_plus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z2 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)) Z2) (@ (@ tptp.ord_less_real Z2) _let_1) (= (@ tptp.tan_real Z2) X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M5)) (@ tptp.semiri2265585572941072030t_real M5)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))
% 6.37/6.67 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.37/6.67 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (not (= X 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 X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M5)) (@ tptp.semiri2265585572941072030t_real M5)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat 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 X) N2))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat 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 X) N2)))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat 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 X) N2))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat 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 X) N2)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))))))))
% 6.37/6.67 (assert (forall ((X 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 X) _let_1))))) (@ tptp.sin_real X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (assert (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 6.37/6.67 (assert (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.37/6.67 (assert (@ (@ tptp.sums_nat (lambda ((N3 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.37/6.67 (assert (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.37/6.67 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.37/6.67 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.37/6.67 (assert (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ A N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.37/6.67 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 6.37/6.67 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.37/6.67 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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.times_times_complex C) (@ F N3)))) (@ (@ tptp.times_times_complex C) A)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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.times_times_complex (@ F N3)) C))) (@ (@ tptp.times_times_complex A) C)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (G (-> tptp.nat tptp.complex)) (B tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (=> (@ (@ tptp.sums_complex G) B) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N3)) (@ G N3)))) (@ (@ tptp.minus_minus_complex A) B))))))
% 6.37/6.67 (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.minus_minus_real (@ F N3)) (@ G N3)))) (@ (@ tptp.minus_minus_real A) B))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_real (@ F N3)))) (@ tptp.uminus_uminus_real A)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N3)))) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T tptp.real)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N)) (@ G N))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S) T))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ G N))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S) T))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T tptp.int)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ G N))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S) T))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (G (-> tptp.nat tptp.complex)) (B tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (=> (@ (@ tptp.sums_complex G) B) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N3)) (@ G N3)))) (@ (@ tptp.plus_plus_complex A) B))))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (= R5 I)) (@ F R5)) tptp.zero_zero_complex))) (@ F I))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I)) (@ F R5)) tptp.zero_zero_real))) (@ F I))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I)) (@ F R5)) tptp.zero_zero_nat))) (@ F I))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I)) (@ F R5)) tptp.zero_zero_int))) (@ F I))))
% 6.37/6.67 (assert (forall ((X8 (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real X8) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1803761363581548252l_real (@ X8 N3)))) (@ tptp.real_V1803761363581548252l_real A)))))
% 6.37/6.67 (assert (forall ((X8 (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real X8) A) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ X8 N3)))) (@ tptp.real_V4546457046886955230omplex A)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1803761363581548252l_real (@ F N3)))) (@ tptp.real_V1803761363581548252l_real C)) (@ (@ tptp.sums_real F) C))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ F N3)))) (@ tptp.real_V4546457046886955230omplex C)) (@ (@ tptp.sums_real F) C))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.real)) (X (-> tptp.complex tptp.real))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.sums_real (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I3 tptp.complex)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups5808333547571424918x_real X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat tptp.real)) (X (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.sums_real (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I3 tptp.real)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups8097168146408367636l_real X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.real)) (X (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.sums_real (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups8778361861064173332t_real X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat tptp.complex)) (X (-> tptp.real tptp.complex))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I5) (@ (@ tptp.sums_complex (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((I3 tptp.real)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups5754745047067104278omplex X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.complex)) (X (-> tptp.nat tptp.complex))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.sums_complex (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups2073611262835488442omplex X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.complex)) (X (-> tptp.int tptp.complex))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.sums_complex (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups3049146728041665814omplex X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat tptp.int)) (X (-> tptp.int tptp.int))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.sums_int (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups4538972089207619220nt_int X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.complex)) (X (-> tptp.complex tptp.complex))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.sums_complex (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I3 tptp.complex)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups7754918857620584856omplex X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.nat)) (X (-> tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.sums_nat (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups3542108847815614940at_nat X) I5)))))
% 6.37/6.67 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.real)) (X (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.sums_real (@ F I2)) (@ X I2)))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ F I3) N3))) I5))) (@ (@ tptp.groups6591440286371151544t_real X) I5)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.numera6690914467698888265omplex W)) (and (= A (@ tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S) (@ (@ tptp.sums_complex F) S)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (L tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) L) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex L) (@ F tptp.zero_zero_nat))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ F tptp.zero_zero_nat))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S) (@ F tptp.zero_zero_nat))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ F I2) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_complex F) S)))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ F I2) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) A2)))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R5)) (@ F R5)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) _let_1))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R5)) (@ F R5)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) _let_1))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R5)) (@ F R5)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) _let_1))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R5)) (@ F R5)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) _let_1))))))
% 6.37/6.67 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N tptp.nat)) (=> (not (@ (@ tptp.member_nat N) N5)) (= (@ F N) tptp.zero_zero_complex))) (@ (@ tptp.sums_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N5))))))
% 6.37/6.67 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N tptp.nat)) (=> (not (@ (@ tptp.member_nat N) N5)) (= (@ F N) tptp.zero_zero_int))) (@ (@ tptp.sums_int F) (@ (@ tptp.groups3539618377306564664at_int F) N5))))))
% 6.37/6.67 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N tptp.nat)) (=> (not (@ (@ tptp.member_nat N) N5)) (= (@ F N) tptp.zero_zero_nat))) (@ (@ tptp.sums_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N5))))))
% 6.37/6.67 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N tptp.nat)) (=> (not (@ (@ tptp.member_nat N) N5)) (= (@ F N) tptp.zero_zero_real))) (@ (@ tptp.sums_real F) (@ (@ tptp.groups6591440286371151544t_real F) N5))))))
% 6.37/6.67 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((R2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R2)) (@ (@ tptp.times_times_real Y) R2)))))
% 6.37/6.67 (assert (forall ((R2 tptp.real) (X tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X)) Y))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X) R2)) Y))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y)) (= X Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y)) (= X Y))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (S tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (S tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) (@ (@ tptp.minus_minus_complex S) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_complex F) S))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_real F) S))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.sums_complex F) S) (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) (@ (@ tptp.minus_minus_complex S) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.sums_real F) S) (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.complex)) (S3 tptp.complex) (A2 tptp.set_nat) (S5 tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.sums_complex G) S3) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_complex S3) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N3)) (@ G N3)))) A2))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat N3) A2)) (@ F N3)) (@ G N3)))) S5))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.real)) (S3 tptp.real) (A2 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S3) (=> (@ tptp.finite_finite_nat A2) (=> (= S5 (@ (@ tptp.plus_plus_real S3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N3)) (@ G N3)))) A2))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N3) A2)) (@ F N3)) (@ G N3)))) S5))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.set_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ (@ tptp.complex2 (@ F X2)) tptp.zero_zero_real))) S) (@ (@ tptp.complex2 (@ (@ tptp.groups6591440286371151544t_real F) S)) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((F (-> tptp.complex tptp.real)) (S tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.complex2 (@ F X2)) tptp.zero_zero_real))) S) (@ (@ tptp.complex2 (@ (@ tptp.groups5808333547571424918x_real F) S)) tptp.zero_zero_real))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X)) X)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X)) tptp.zero_zero_real))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X) (= (@ tptp.arccos (@ tptp.cos_real X)) (@ tptp.uminus_uminus_real X))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X)) tptp.zero_zero_real))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ 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)))))) X))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((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 X) Y))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X)) X))))))
% 6.37/6.67 (assert (forall ((X 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 X) _let_1))))) (@ tptp.cos_real X))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X))))))))))
% 6.37/6.67 (assert (forall ((Theta tptp.real)) (not (forall ((K3 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X) 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 X) (@ (@ 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 X) N3))))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X) 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 X) (@ (@ 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 X) N3))))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_real (@ X4 M5)) (@ X4 N3)))) (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_real (@ X4 N3)) (@ X4 M5))))))))
% 6.37/6.67 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X4 (-> tptp.nat tptp.set_nat))) (or (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X4 M5)) (@ X4 N3)))) (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X4 N3)) (@ X4 M5))))))))
% 6.37/6.67 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_rat (@ X4 M5)) (@ X4 N3)))) (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_rat (@ X4 N3)) (@ X4 M5))))))))
% 6.37/6.67 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_num (@ X4 M5)) (@ X4 N3)))) (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_num (@ X4 N3)) (@ X4 M5))))))))
% 6.37/6.67 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_nat (@ X4 M5)) (@ X4 N3)))) (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_nat (@ X4 N3)) (@ X4 M5))))))))
% 6.37/6.67 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_int (@ X4 M5)) (@ X4 N3)))) (forall ((M5 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.ord_less_eq_int (@ X4 N3)) (@ X4 M5))))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.diffs_complex (lambda ((N3 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ F N3)))) (lambda ((N3 tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.diffs_real F) N3))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.int))) (= (@ tptp.diffs_int (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_int (@ C N3)))) (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_int (@ (@ tptp.diffs_int C) N3))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.real))) (= (@ tptp.diffs_real (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_real (@ C N3)))) (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_real (@ (@ tptp.diffs_real C) N3))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.complex))) (= (@ tptp.diffs_complex (lambda ((N3 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ C N3)))) (lambda ((N3 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.diffs_complex C) N3))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.rat))) (= (@ tptp.diffs_rat (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ C N3)))) (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ (@ tptp.diffs_rat C) N3))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.code_integer))) (= (@ tptp.diffs_Code_integer (lambda ((N3 tptp.nat)) (@ tptp.uminus1351360451143612070nteger (@ C N3)))) (lambda ((N3 tptp.nat)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.diffs_Code_integer C) N3))))))
% 6.37/6.67 (assert (= tptp.diffs_rat (lambda ((C3 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C3 _let_1))))))
% 6.37/6.67 (assert (= tptp.diffs_int (lambda ((C3 (-> tptp.nat tptp.int)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C3 _let_1))))))
% 6.37/6.67 (assert (= tptp.diffs_real (lambda ((C3 (-> tptp.nat tptp.real)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C3 _let_1))))))
% 6.37/6.67 (assert (= tptp.diffs_complex (lambda ((C3 (-> tptp.nat tptp.complex)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C3 _let_1))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((X3 tptp.complex)) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N3)) (@ (@ tptp.power_power_complex X3) N3))))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X) N3)))))))
% 6.37/6.67 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((X3 tptp.real)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ C N3)) (@ (@ tptp.power_power_real X3) N3))))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X) N3)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) K5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) K5) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ C N3)) (@ (@ tptp.power_power_real X3) N3)))))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X) N3))))))))
% 6.37/6.67 (assert (forall ((X tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) K5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) K5) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N3)) (@ (@ tptp.power_power_complex X3) N3)))))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X) N3))))))))
% 6.37/6.67 (assert (forall ((A (-> tptp.nat tptp.int))) (=> (@ tptp.topolo4899668324122417113eq_int A) (@ tptp.topolo4899668324122417113eq_int (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_int (@ A N3)))))))
% 6.37/6.67 (assert (forall ((A (-> tptp.nat tptp.rat))) (=> (@ tptp.topolo4267028734544971653eq_rat A) (@ tptp.topolo4267028734544971653eq_rat (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_rat (@ A N3)))))))
% 6.37/6.67 (assert (forall ((A (-> tptp.nat tptp.code_integer))) (=> (@ tptp.topolo2919662092509805066nteger A) (@ tptp.topolo2919662092509805066nteger (lambda ((N3 tptp.nat)) (@ tptp.uminus1351360451143612070nteger (@ A N3)))))))
% 6.37/6.67 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.topolo6980174941875973593q_real (lambda ((N3 tptp.nat)) (@ tptp.uminus_uminus_real (@ A N3)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))
% 6.37/6.67 (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))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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))))))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X)) X) (exists ((N3 tptp.int)) (= X (@ tptp.ring_1_of_int_real N3))))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X)) X) (exists ((N3 tptp.int)) (= X (@ tptp.ring_1_of_int_rat N3))))))
% 6.37/6.67 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.37/6.67 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.37/6.67 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 6.37/6.67 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 6.37/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.37/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.37/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.37/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.37/6.67 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X)) (@ tptp.uminus1482373934393186551omplex X)))))
% 6.37/6.67 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) Z))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) Z))))
% 6.37/6.67 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real V)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))))
% 6.37/6.67 (assert (forall ((X tptp.num) (N2 tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.37/6.67 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.37/6.67 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.37/6.67 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))) X)))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X))) X)))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N2))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N2))))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N2))))))
% 6.37/6.67 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N2))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.37/6.67 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.37/6.67 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.37/6.67 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.37/6.67 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) Z) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X)))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.ring_1_of_int_rat Z))))))
% 6.37/6.67 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L))) (@ (@ tptp.divide_divide_int K) L))))
% 6.37/6.67 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K)) (@ tptp.ring_1_of_int_rat L))) (@ (@ tptp.divide_divide_int K) L))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (=> (= X (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (=> (= X (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N2)))))
% 6.37/6.67 (assert (forall ((X tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N2)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X) Y) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N2))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ _let_1 N2))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2)))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N2) tptp.zero_zero_rat) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K2))))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))))))))
% 6.37/6.67 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((Z tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) M))))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) Z))))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X) Z))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I3))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I3)))))))
% 6.37/6.67 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I3))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I3)))))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.37/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))))
% 6.37/6.67 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X))))
% 6.37/6.67 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.37/6.67 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) Z) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.37/6.67 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.37/6.67 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N2))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.37/6.67 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.37/6.67 (assert (= tptp.complex2 (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A3)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B2))))))
% 6.37/6.67 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q3)))) Q3)) P2))))
% 6.37/6.67 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) Q3)) P2))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real P2) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q3)))) tptp.one_one_real)) Q3)))))
% 6.37/6.67 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_rat P2) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) tptp.one_one_rat)) Q3)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A5 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A5))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A5)))))))))
% 6.37/6.67 (assert (= tptp.archim8280529875227126926d_real (lambda ((X2 tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.37/6.67 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X2 tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X) (@ (@ tptp.ord_less_real X) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.37/6.67 (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)))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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 ((K2 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K2)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.37/6.67 (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 ((K2 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.37/6.67 (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 ((K2 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K2)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.37/6.67 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 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 A3) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.37/6.67 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 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 A3) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.37/6.67 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 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 A3) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.37/6.67 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A3 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 A3) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.37/6.67 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 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 A3) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.37/6.67 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X2 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X2 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X2 tptp.nat)) (@ tptp.ring_1_of_int_rat (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ tptp.ring_1_of_int_int (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X2)))) A2))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 6.37/6.67 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 6.37/6.67 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 6.37/6.67 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups225925009352817453ex_rat G) A2) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups1072433553688619179nt_rat G) A2) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups861055069439313189ex_nat G) A2) tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 6.37/6.67 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A2))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.37/6.67 (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))))))))))))
% 6.37/6.67 (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))))))))))))
% 6.37/6.67 (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))))))))))))
% 6.37/6.67 (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))))))))))))
% 6.37/6.67 (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))))))))))))
% 6.37/6.67 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B3 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ G I3)) B3))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (B3 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ G I3)) B3))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.int tptp.int)) (B3 tptp.set_int) (A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.groups1705073143266064639nt_int (@ G I3)) B3))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.nat tptp.int)) (B3 tptp.set_nat) (A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.groups705719431365010083at_int (@ G I3)) B3))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I3 tptp.int)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B3 tptp.set_int) (A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.groups1705073143266064639nt_int (@ G I3)) B3))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I3 tptp.int)) (@ (@ G I3) J3))) A2))) B3))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A2) tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A2) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A2) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.complex tptp.rat)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups225925009352817453ex_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_rat)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.real tptp.rat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4061424788464935467al_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_rat)))))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A2)) (@ (@ tptp.groups708209901874060359at_nat H2) A2)))))
% 6.37/6.67 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A2)) (@ (@ tptp.groups705719431365010083at_int H2) A2)))))
% 6.37/6.67 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A2)) (@ (@ tptp.groups1705073143266064639nt_int H2) A2)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X2)) N2))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N2) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_int (@ F X2)) N2))) A2))))
% 6.37/6.67 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.power_power_int (@ F X2)) N2))) A2))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.groups708209901874060359at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups4696554848551431203al_nat (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X2 tptp.complex)) (@ (@ tptp.groups708209901874060359at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X2 tptp.complex)) (@ (@ G X2) Y2))) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X2 tptp.int)) (@ (@ G X2) Y2))) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (G (-> tptp.real tptp.nat tptp.int)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((X2 tptp.real)) (@ (@ tptp.groups705719431365010083at_int (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.int)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X2 tptp.complex)) (@ (@ tptp.groups705719431365010083at_int (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X2 tptp.complex)) (@ (@ G X2) Y2))) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_int) (G (-> tptp.real tptp.int tptp.int)) (R (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups4694064378042380927al_int (lambda ((X2 tptp.real)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups4694064378042380927al_int (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_int) (G (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X2 tptp.complex)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X2 tptp.complex)) (@ (@ G X2) Y2))) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_real) (G (-> tptp.nat tptp.real tptp.nat)) (R (-> tptp.nat tptp.real Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_real B3) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.groups4696554848551431203al_nat (@ G X2)) (@ tptp.collect_real (lambda ((Y2 tptp.real)) (and (@ (@ tptp.member_real Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups4696554848551431203al_nat (lambda ((Y2 tptp.real)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ G X2) Y2))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_complex) (G (-> tptp.nat tptp.complex tptp.nat)) (R (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.groups861055069439313189ex_nat (@ G X2)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups861055069439313189ex_nat (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ G X2) Y2))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_int) (G (-> tptp.nat tptp.int tptp.nat)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((Y2 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ G X2) Y2))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))))
% 6.37/6.67 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I3 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I3)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.37/6.67 (assert (forall ((A2 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) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))
% 6.37/6.67 (assert (forall ((A2 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) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))
% 6.37/6.67 (assert (forall ((A2 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) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups713298508707869441omplex G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups713298508707869441omplex (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups3708469109370488835omplex G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups7440179247065528705omplex G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups7440179247065528705omplex (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.one_one_complex))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1681761925125756287l_real G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups1681761925125756287l_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups129246275422532515t_real (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups766887009212190081x_real G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups766887009212190081x_real (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups2316167850115554303t_real G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.rat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups4061424788464935467al_rat G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups4061424788464935467al_rat (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.one_one_rat))) A2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.one_one_rat))) A2)))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.37/6.67 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_real C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((A3 tptp.nat)) (@ (@ tptp.power_power_real C) (@ F A3)))) A2))))
% 6.37/6.67 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_complex C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((A3 tptp.nat)) (@ (@ tptp.power_power_complex C) (@ F A3)))) A2))))
% 6.37/6.67 (assert (forall ((C tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_nat C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A3 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A3)))) A2))))
% 6.37/6.67 (assert (forall ((C tptp.int) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A3 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A3)))) A2))))
% 6.37/6.67 (assert (forall ((C tptp.int) (F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A3 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A3)))) A2))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.37/6.67 (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 ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) tptp.one_one_real))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) tptp.one_one_rat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) tptp.one_one_nat))))
% 6.37/6.67 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_real X16) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2316167850115554303t_real H2) S3)) (@ (@ tptp.groups2316167850115554303t_real G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X16) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups73079841787564623at_rat H2) S3)) (@ (@ tptp.groups73079841787564623at_rat G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X16) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups225925009352817453ex_rat H2) S3)) (@ (@ tptp.groups225925009352817453ex_rat G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X16) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1072433553688619179nt_rat H2) S3)) (@ (@ tptp.groups1072433553688619179nt_rat G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_nat X16) Y15)) (@ (@ tptp.times_times_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups861055069439313189ex_nat H2) S3)) (@ (@ tptp.groups861055069439313189ex_nat G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_nat X16) Y15)) (@ (@ tptp.times_times_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1707563613775114915nt_nat H2) S3)) (@ (@ tptp.groups1707563613775114915nt_nat G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X16 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_int X16) Y15)) (@ (@ tptp.times_times_int X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups858564598930262913ex_int H2) S3)) (@ (@ tptp.groups858564598930262913ex_int G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_nat X16) Y15)) (@ (@ tptp.times_times_nat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups708209901874060359at_nat H2) S3)) (@ (@ tptp.groups708209901874060359at_nat G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X16 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_int X16) Y15)) (@ (@ tptp.times_times_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups705719431365010083at_int H2) S3)) (@ (@ tptp.groups705719431365010083at_int G) S3))))))))
% 6.37/6.67 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ (@ R tptp.one_one_int) tptp.one_one_int) (=> (forall ((X16 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_int X16) Y15)) (@ (@ tptp.times_times_int X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1705073143266064639nt_int H2) S3)) (@ (@ tptp.groups1705073143266064639nt_int G) S3))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))))
% 6.37/6.67 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M))))))
% 6.37/6.67 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 6.37/6.67 (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)))
% 6.37/6.67 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.37/6.67 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.37/6.67 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.37/6.67 (assert (= tptp.cis (lambda ((B2 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B2))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K2 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri5074537144036343181t_real N2))))) (@ tptp.set_ord_lessThan_nat N2)) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) tptp.one_one_complex)))))))
% 6.37/6.67 (assert (= tptp.binomial (lambda ((N3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N3) K2))) (let ((_let_2 (@ tptp.ord_less_nat N3))) (@ (@ (@ tptp.if_nat (@ _let_2 K2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2))) (@ (@ tptp.binomial N3) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N3) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K2)))))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_1) N2) _let_1))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) N2) tptp.one_one_nat)))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) (@ tptp.suc tptp.zero_zero_nat)) N2)))
% 6.37/6.67 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.37/6.67 (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))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.one_one_nat) N2)))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial K2) M))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M)))))
% 6.37/6.67 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K2)) K2))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N2))) N2))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K2)) (@ (@ tptp.minus_minus_nat M) K2)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N2)) M)))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K2)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R2) K2))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N2)) R2))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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 ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K2))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N2) K2)) (@ 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))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (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))))))
% 6.37/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat I3) (@ (@ tptp.binomial N2) I3)))) (@ 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))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))
% 6.37/6.67 (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)))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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))))))))
% 6.37/6.67 (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)))))
% 6.37/6.67 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N2 tptp.nat) (B (-> tptp.nat tptp.nat)) (X 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 ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ (@ tptp.power_power_nat X) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K2)) (@ B (@ (@ tptp.minus_minus_nat R5) K2))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.37/6.67 (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)))))))
% 6.37/6.67 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N2)))))
% 6.37/6.67 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) N3)))
% 6.37/6.67 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.37/6.67 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))))
% 6.37/6.67 (assert (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y2)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((Y tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y) A))))))
% 6.37/6.68 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.37/6.68 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((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) E) (@ P E))))))
% 6.37/6.68 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3)))) (and (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real _let_1) X) (@ tptp.inverse_inverse_real _let_1))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.37/6.68 (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 ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) C))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X)) tptp.zero_zero_real)))))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.root N2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ _let_1 X))))))
% 6.37/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N2))) (= (@ _let_1 (@ _let_2 X)) (@ _let_2 (@ _let_1 X)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.37/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N2)) X) (@ (@ tptp.root M) (@ (@ tptp.root N2) X)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.37/6.68 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N2) X))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ _let_1 X)))))))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 6.37/6.68 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.times_times_complex X2) (@ tptp.invers8013647133539491842omplex Y2)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))))))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N2) X)))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N5) X)) (@ (@ tptp.root N2) X)))))))
% 6.37/6.68 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N2) X))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N5) X))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N5) X)) (@ (@ tptp.root N2) X)))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X) N2)) X)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N2) X) (= (@ (@ tptp.root N2) X) Y))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (= (@ (@ tptp.power_power_real Y) N2) X) (= (@ (@ tptp.root N2) X) Y)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X) N2)) X))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N5) X))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N2) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) X)))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.cot_real X))))
% 6.37/6.68 (assert (= tptp.arctan (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.tan_real X2) Y2))))))))
% 6.37/6.68 (assert (= tptp.arcsin (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.sin_real X2) Y2))))))))
% 6.37/6.68 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K2)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N3))))))))
% 6.37/6.68 (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)))))))))))))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= tptp.ln_ln_real (lambda ((X2 tptp.real)) (@ tptp.the_real (lambda ((U2 tptp.real)) (= (@ tptp.exp_real U2) X2))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X2 tptp.real)) false))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N3) K2) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N3)))))))
% 6.37/6.68 (assert (forall ((K tptp.int)) (not (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M4 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (= (@ _let_1 M4) (@ _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)))))))))))
% 6.37/6.68 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K2 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int _let_1) N3))))))))
% 6.37/6.68 (assert (= tptp.arccos (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.cos_real X2) Y2)))))))
% 6.37/6.68 (assert (forall ((R2 tptp.int) (L tptp.int) (K tptp.int) (Q3 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 Q3) L)) R2)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R2)))))))
% 6.37/6.68 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K2 tptp.int)) (and (= A12 K2) (= A23 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K2)))) (exists ((L2 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A12 K2) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K2 (@ (@ tptp.times_times_int Q4) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A12 K2) (= A23 L2) (= 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)) (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L2)) R5))))))))
% 6.37/6.68 (assert (forall ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A33) (=> (=> (= A22 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q2 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q2) A22)))))) (not (forall ((R3 tptp.int) (Q2 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q2) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A22)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A22)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) A22)) R3)))))))))))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.plus_plus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K2) N3)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))))))
% 6.37/6.68 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.minus_minus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N3))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))))))
% 6.37/6.68 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real))))))
% 6.37/6.68 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))))))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X)) (@ _let_1 X)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N2)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (= N2 tptp.zero_zero_nat))))
% 6.37/6.68 (assert (= tptp.sgn_sgn_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real X2) (@ tptp.abs_abs_real X2)))))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N2) X)) (@ tptp.sgn_sgn_real X)))))
% 6.37/6.68 (assert (= tptp.sgn_sgn_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (= A3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))
% 6.37/6.68 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M5 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 M5) (@ (@ tptp.power_power_nat _let_1) N3))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N2) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N2)) X)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((Z tptp.complex) (X tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arg Z) X))))))
% 6.37/6.68 (assert (forall ((P (-> tptp.real Bool)) (N2 tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N2) X)) (and (=> (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (forall ((Y2 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N2)) X) (@ P Y2))))))))
% 6.37/6.68 (assert (= tptp.archim6058952711729229775r_real (lambda ((X2 tptp.real)) (@ tptp.the_int (lambda ((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)))))))))
% 6.37/6.68 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis _let_1)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X))))))
% 6.37/6.68 (assert (= tptp.modulo_modulo_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K2))))) _let_2)))))))))))
% 6.37/6.68 (assert (= tptp.divide_divide_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K2))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 6.37/6.68 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.37/6.68 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.68 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 6.37/6.68 (assert (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.68 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.37/6.68 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.37/6.68 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.37/6.68 (assert (= tptp.numeral_numeral_nat (lambda ((I3 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I3)))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y)))))
% 6.37/6.68 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.37/6.68 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M5) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((X tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N2) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) M)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 6.37/6.68 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.37/6.68 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.37/6.68 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.37/6.68 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.37/6.68 (assert (= tptp.minus_minus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.37/6.68 (assert (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.37/6.68 (assert (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))))
% 6.37/6.68 (assert (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))))
% 6.37/6.68 (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)))))))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((X tptp.real) (N2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N2)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N2)))))))))))))
% 6.37/6.68 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((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)))))))))
% 6.37/6.68 (assert (= tptp.arg (lambda ((Z3 tptp.complex)) (@ (@ (@ tptp.if_real (= Z3 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z3) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((S tptp.vEBT_VEBT) (M tptp.nat) (Listy tptp.list_VEBT_VEBT) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M))))) (=> (@ (@ tptp.vEBT_invar_vebt S) M) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Listy)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (=> (= M (@ tptp.suc N2)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Listy)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height X3)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2)))))) (=> (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height S)) _let_1) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT S) (@ tptp.set_VEBT_VEBT2 Listy))))) _let_1)))))))))
% 6.37/6.68 (assert (forall ((T tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 TreeList))) (=> (@ (@ tptp.member_VEBT_VEBT T) _let_1) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_height T)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary) _let_1))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X14 tptp.vEBT_VEBT) (M tptp.nat) (X13 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_VEBT_height X14))) (let ((_let_2 (@ tptp.times_times_nat N2))) (@ (@ tptp.ord_less_eq_nat (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat M) (@ _let_2 (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat _let_1) (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13)))))))))))
% 6.37/6.68 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (Foo tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I))) (@ (@ tptp.ord_max_nat Foo) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))
% 6.37/6.68 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (N2 tptp.nat) (X14 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I)))) (@ tptp.suc (@ tptp.suc (@ _let_1 (@ (@ tptp.ord_max_nat (@ tptp.vEBT_VEBT_height X14)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) N2)))) N2))))
% 6.37/6.68 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S2) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R2 (@ (@ tptp.plus_plus_rat S2) T3)))))))))))
% 6.37/6.68 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Uu) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary) (@ tptp.set_VEBT_VEBT2 TreeList))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X) Y) (=> (=> (exists ((A5 Bool) (B6 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B6))) (not (= Y tptp.zero_zero_nat))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList3) Summary2)) (not (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary2) (@ tptp.set_VEBT_VEBT2 TreeList3))))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.37/6.68 (assert (= tptp.divide_divide_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N3)) M5))))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((M7 tptp.set_nat) (N5 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N5) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N5))))
% 6.37/6.68 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 6.37/6.68 (assert (forall ((N2 tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (@ (@ tptp.dvd_dvd_int D2) N2)))) (@ tptp.abs_abs_int N2)))))
% 6.37/6.68 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) B2)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P2)))))
% 6.37/6.68 (assert (forall ((Q3 tptp.int) (P2 tptp.int)) (=> (@ (@ tptp.ord_less_int Q3) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P2)) (@ tptp.uminus_uminus_int Q3)))))))
% 6.37/6.68 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 6.37/6.68 (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))))
% 6.37/6.68 (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)))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.37/6.68 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 6.37/6.68 (assert (forall ((P2 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P2) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) B2)) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P2)))))
% 6.37/6.68 (assert (forall ((P2 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P2) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C3) B2))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P2)))))
% 6.37/6.68 (assert (forall ((R2 tptp.rat) (N2 tptp.int) (D tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int N2) D)) (= R2 (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N2)) (@ tptp.ring_1_of_int_rat D))))))
% 6.37/6.68 (assert (forall ((P2 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P2) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int B2) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P2)))))
% 6.37/6.68 (assert (forall ((R2 tptp.rat) (P2 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 6.37/6.68 (assert (forall ((P2 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P2) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int B2) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P2)))))
% 6.37/6.68 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A3)) __flatten_var_0))) (@ tptp.quotient_of P2)))))
% 6.37/6.68 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A3)) __flatten_var_0))) (@ tptp.quotient_of P2)))))
% 6.37/6.68 (assert (forall ((R2 tptp.product_prod_int_int) (P2 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 6.37/6.68 (assert (forall ((Q3 tptp.int) (S tptp.int) (P2 tptp.int) (R2 tptp.int)) (=> (not (= Q3 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S))) (= (@ (@ tptp.times_times_int P2) S) (@ (@ tptp.times_times_int R2) Q3)))))))
% 6.37/6.68 (assert (= tptp.ord_less_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C3) B2)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 6.37/6.68 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P5 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P5)))))
% 6.37/6.68 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C3) B2)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 6.37/6.68 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.37/6.68 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 6.37/6.68 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N3) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) M5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M5) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1))))))))))
% 6.37/6.68 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 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 M5)) (not (@ _let_2 N3)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ _let_1 K)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N2) L))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N2) K)))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y)))))))
% 6.37/6.68 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M5) tptp.one_one_nat)))))
% 6.37/6.68 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M5) tptp.one_one_nat)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.37/6.68 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q3)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q3) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.37/6.68 (assert (= tptp.bit_concat_bit (lambda ((N3 tptp.nat) (K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N3) K2)) (@ (@ tptp.bit_se545348938243370406it_int N3) L2)))))
% 6.37/6.68 (assert (= tptp.bit_concat_bit (lambda ((N3 tptp.nat) (K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N3) K2)) (@ (@ tptp.bit_se545348938243370406it_int N3) L2)))))
% 6.37/6.68 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 6.37/6.68 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.68 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N3 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.times_times_nat M5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.68 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 6.37/6.68 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 6.37/6.68 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A))) (= (@ tptp.frct (@ _let_1 (@ tptp.uminus_uminus_int B))) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ _let_1 B)))))))
% 6.37/6.68 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A)) B)) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) B))))))
% 6.37/6.68 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y)) _let_1)))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) X) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_1) (=> (= Y tptp.zero_zero_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1)))))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary2) (@ tptp.set_VEBT_VEBT2 TreeList3)))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1))))))))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ tptp.bit_ri7919022796975470100ot_int L2))))))
% 6.37/6.68 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K2)) tptp.one_one_int))))
% 6.37/6.68 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.37/6.68 (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)))
% 6.37/6.68 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int))))))
% 6.37/6.68 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int L2))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) L2)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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)))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))
% 6.37/6.68 (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))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K2))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K2) _let_1))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_1) (=> (and (=> B6 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B6) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (=> (= X _let_1) (=> (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B6 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B6) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_T_m_i_n_t X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) X) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X _let_1) (=> (= Y (@ _let_2 (@ (@ (@ tptp.if_nat A5) tptp.zero_zero_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_i_n_t_rel) _let_1)))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_T_m_a_x_t X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) X) (=> (forall ((A5 Bool) (B6 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B6))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X _let_1) (=> (= Y (@ _let_2 (@ (@ (@ tptp.if_nat B6) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1)))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel))) (=> (= (@ tptp.vEBT_T_m_i_n_N_u_l_l X) Y) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (=> Y (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va2) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (@ _let_2 X) (=> (=> (= X _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.37/6.68 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X4 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M5) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N3) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X4 M5)) (@ X4 N3)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.37/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.37/6.68 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 6.37/6.68 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N2) (@ P M5))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N2) (@ P M5))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.37/6.68 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_nat I3) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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 ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ B I3)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.37/6.68 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.37/6.68 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.37/6.68 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.37/6.68 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.37/6.68 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.37/6.68 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.37/6.68 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.37/6.68 (assert (forall ((Z tptp.complex) (R2 tptp.real)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R2))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) R2))))
% 6.37/6.68 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.37/6.68 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.numeral_numeral_real W)))))
% 6.37/6.68 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.68 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)))
% 6.37/6.68 (assert (= tptp.unique3479559517661332726nteger (lambda ((M5 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M5))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex X8) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ tptp.re (@ X8 N3)))) (@ tptp.re A)))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.complex))) (=> (@ tptp.topolo6517432010174082258omplex X8) (@ tptp.topolo4055970368930404560y_real (lambda ((N3 tptp.nat)) (@ tptp.re (@ X8 N3)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X)) (@ tptp.real_V1022390504157884413omplex X))))
% 6.37/6.68 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y)))))
% 6.37/6.68 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.re X)))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.re X)) (@ tptp.re Y)))))
% 6.37/6.68 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (@ tptp.summable_real (lambda ((X2 tptp.nat)) (@ tptp.re (@ F X2)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.37/6.68 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.37/6.68 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= tptp.csqrt (lambda ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z3))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z3))) (let ((_let_4 (@ tptp.im Z3))) (@ (@ 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)))))))))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (assert (= tptp.code_integer_of_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.37/6.68 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 6.37/6.68 (assert (forall ((Z tptp.complex) (R2 tptp.real)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R2))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) R2))))
% 6.37/6.68 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_real (@ tptp.re X)) N2)))))
% 6.37/6.68 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 6.37/6.68 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.numeral_numeral_real W)))))
% 6.37/6.68 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.im X))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.37/6.68 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa2) X)))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex X8) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ tptp.im (@ X8 N3)))) (@ tptp.im A)))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.complex))) (=> (@ tptp.topolo6517432010174082258omplex X8) (@ tptp.topolo4055970368930404560y_real (lambda ((N3 tptp.nat)) (@ tptp.im (@ X8 N3)))))))
% 6.37/6.68 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.37/6.68 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa2) X)))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y)))))
% 6.37/6.68 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.im X)))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.im X)) (@ tptp.im Y)))))
% 6.37/6.68 (assert (= tptp.sums_complex (lambda ((F3 (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (and (@ (@ tptp.sums_real (lambda ((Y2 tptp.nat)) (@ tptp.re (@ F3 Y2)))) (@ tptp.re X2)) (@ (@ tptp.sums_real (lambda ((Y2 tptp.nat)) (@ tptp.im (@ F3 Y2)))) (@ tptp.im X2))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (@ tptp.summable_real (lambda ((X2 tptp.nat)) (@ tptp.im (@ F X2)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.37/6.68 (assert (= tptp.summable_complex (lambda ((F3 (-> tptp.nat tptp.complex))) (and (@ tptp.summable_real (lambda ((X2 tptp.nat)) (@ tptp.re (@ F3 X2)))) (@ tptp.summable_real (lambda ((X2 tptp.nat)) (@ tptp.im (@ F3 X2))))))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.im Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.re Y))))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.abs_abs_real (@ tptp.re Y)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.abs_abs_real (@ tptp.im Y)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.37/6.68 (assert (= tptp.plus_plus_complex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y2))) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y2))))))
% 6.37/6.68 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X2))) (@ _let_1 (@ tptp.im X2)))))))
% 6.37/6.68 (assert (= tptp.minus_minus_complex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ tptp.re X2)) (@ tptp.re Y2))) (@ (@ tptp.minus_minus_real (@ tptp.im X2)) (@ tptp.im Y2))))))
% 6.37/6.68 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.csqrt Z))) (let ((_let_2 (@ tptp.re _let_1))) (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (and (= _let_2 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im _let_1))))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (= tptp.times_times_complex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.re Y2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X2)))) (let ((_let_3 (@ tptp.im Y2))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X2)))) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_4 _let_1)) (@ _let_2 _let_3))) (@ (@ tptp.plus_plus_real (@ _let_4 _let_3)) (@ _let_2 _let_1))))))))))
% 6.37/6.68 (assert (= tptp.exp_complex (lambda ((Z3 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z3)))) (@ tptp.cis (@ tptp.im Z3))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X))) (@ tptp.im X))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z3 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 Z3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z3)) _let_1)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= tptp.invers8013647133539491842omplex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (let ((_let_3 (@ tptp.re X2))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 6.37/6.68 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X2)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X2)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) R2)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.re R2))))))
% 6.37/6.68 (assert (forall ((Y tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y) X) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.37/6.68 (assert (forall ((Y tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= X (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.37/6.68 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) R2)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.re R2))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.37/6.68 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 6.37/6.68 (assert (forall ((F (-> tptp.nat tptp.complex)) (L tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((X2 tptp.nat)) (@ tptp.cnj (@ F X2)))) (@ tptp.cnj L)) (@ (@ tptp.sums_complex F) L))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z3 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z3) (@ tptp.cnj Z3)))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B2))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K2) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K2)))))))
% 6.37/6.68 (assert (= tptp.code_num_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.37/6.68 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.37/6.68 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K2) L2)) (@ (@ tptp.modulo364778990260209775nteger K2) L2)))))
% 6.37/6.68 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K2)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.37/6.68 (assert (= tptp.code_nat_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.37/6.68 (assert (= tptp.code_int_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K2)))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.37/6.68 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.37/6.68 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X) Xa2)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.37/6.68 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X) Xa2)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.37/6.68 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.37/6.68 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs J) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer J)))))
% 6.37/6.68 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))))
% 6.37/6.68 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.37/6.68 (assert (= tptp.code_divmod_abs (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L2))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.37/6.68 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K2)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L2) S6)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L2)) S6)))))) _let_1))))))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat I3) N2)))) N2)))
% 6.37/6.68 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.37/6.68 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I3) N2)))) (@ tptp.suc N2))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.37/6.68 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.37/6.68 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 6.37/6.68 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 6.37/6.68 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 6.37/6.68 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A2))))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (= A2 _let_1)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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 ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M6)))) M)))))
% 6.37/6.68 (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 ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M6) N2)))) M)))))
% 6.37/6.68 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S3)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S3))))))
% 6.37/6.68 (assert (forall ((N5 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N5)) N2))))
% 6.37/6.68 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) S3))))
% 6.37/6.68 (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 ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) C)))) N2)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N2) tptp.one_one_complex)))) N2))))
% 6.37/6.68 (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 ((K2 tptp.nat)) K2)) (@ _let_1 N2))))))
% 6.37/6.68 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.37/6.68 (assert (= tptp.binomial (lambda ((N3 tptp.nat) (K2 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) K2))))))))
% 6.37/6.68 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) (@ _let_1 K)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N3 tptp.nat) (K2 tptp.int)) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.68 (assert (= tptp.nat_prod_decode_aux (lambda ((K2 tptp.nat) (M5 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M5) K2)) (@ (@ tptp.product_Pair_nat_nat M5) (@ (@ tptp.minus_minus_nat K2) M5))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M5) _let_1)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.divide_divide_nat M) N2))))
% 6.37/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.modulo_modulo_nat M) N2))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)))))
% 6.37/6.68 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N3 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.divide_divide_nat M5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 6.37/6.68 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y2) (@ (@ tptp.modulo_modulo_nat X2) Y2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y2 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y2)))))))))))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2))))))))))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))))
% 6.37/6.68 (assert (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.gcd_gcd_int X))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.37/6.68 (assert (forall ((N2 tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X) (@ (@ tptp.gcd_gcd_int _let_1) X)))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (exists ((U3 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X)) (@ (@ tptp.times_times_int V2) Y)) (@ (@ tptp.gcd_gcd_int X) Y)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ (@ tptp.gcd_gcd_int M) N2) (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (and (@ _let_1 M) (@ _let_1 N2))))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I4) (@ P I4))) (@ P K3)))) (@ P M)))))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.37/6.68 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M5 tptp.nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M5) N3) (@ (@ tptp.member_nat N3) S3)))))))
% 6.37/6.68 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.37/6.68 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.37/6.68 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X3))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X3))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.gcd_gcd_nat M) N2) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 M) (@ _let_1 N2))))))))))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 6.37/6.68 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M5 tptp.nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N3) (@ (@ tptp.member_nat N3) S3)))))))
% 6.37/6.68 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M3) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N9) (@ (@ tptp.member_nat N9) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))))
% 6.37/6.68 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S3))) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N9) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N9)) S3))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))))
% 6.37/6.68 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_nat Y2) X2))))
% 6.37/6.68 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M5 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M5) N3) (not (= M5 N3))))))
% 6.37/6.68 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ (@ (@ 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 K2) (@ tptp.sgn_sgn_Code_integer L2))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L2)) S6)))))) _let_1))))))))))
% 6.37/6.68 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y2))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X)))))
% 6.37/6.68 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.37/6.68 (assert (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y3))))))))
% 6.37/6.68 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X))))
% 6.37/6.68 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.37/6.68 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N3 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N3) tptp.zero_zero_nat)))))
% 6.37/6.68 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y2) X2))) X)))))
% 6.37/6.68 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.37/6.68 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0))) Xa2) X))))
% 6.37/6.68 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0))) Xa2) X))))
% 6.37/6.68 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y2) V4)))) __flatten_var_0))) Xa2) X)))))
% 6.37/6.68 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y2) U2)))) __flatten_var_0))) Xa2) X)))))
% 6.37/6.68 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (forall ((Q3 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q3)) Q3)))
% 6.37/6.68 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y2 tptp.nat) (Z3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y2) V4)) (@ (@ tptp.plus_plus_nat U2) Z3)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa3)))))
% 6.37/6.68 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa3 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y2 tptp.nat) (Z3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y2) V4)) (@ (@ tptp.plus_plus_nat U2) Z3)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa3)))))
% 6.37/6.68 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M5 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M5) N3))) M5)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= tptp.nat2 (lambda ((X2 tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X2)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y2) X2))))))
% 6.37/6.68 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y2))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.37/6.68 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y2) U2)))) __flatten_var_0))))))
% 6.37/6.68 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y2) V4)))) __flatten_var_0))))))
% 6.37/6.68 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X)))))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N2))))))
% 6.37/6.68 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.37/6.68 (assert (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))
% 6.37/6.68 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N2)) N2))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((A tptp.int) (B tptp.int) (P2 tptp.int) (Q3 tptp.int)) (let ((_let_1 (@ (@ tptp.fract A) B))) (=> (= (@ tptp.quotient_of _let_1) (@ (@ tptp.product_Pair_int_int P2) Q3)) (= (@ (@ tptp.fract P2) Q3) _let_1)))))
% 6.37/6.68 (assert (forall ((A tptp.int) (B tptp.int) (P2 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ tptp.product_Pair_int_int P2) Q3)) (= (@ (@ tptp.fract P2) Q3) (@ (@ tptp.fract A) B)))))
% 6.37/6.68 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.37/6.68 (assert (= tptp.numeral_numeral_rat (lambda ((K2 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K2)) tptp.one_one_int))))
% 6.37/6.68 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.quotient_of (@ (@ tptp.fract A) B)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.37/6.68 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.37/6.68 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M5) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I2))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I3)))) tptp.top_top_set_nat)))))))
% 6.37/6.68 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.37/6.68 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.37/6.68 (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)))))))
% 6.37/6.68 (assert (= tptp.root (lambda ((N3 tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= N3 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N3)))) X2)))))
% 6.37/6.68 (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)))))))))))
% 6.37/6.68 (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)))))))))))))
% 6.37/6.68 (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))))))))))))
% 6.37/6.68 (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))))))))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= tptp.char_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q0 tptp.code_integer) (B02 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q1 tptp.code_integer) (B12 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q22 tptp.code_integer) (B23 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q32 tptp.code_integer) (B33 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q42 tptp.code_integer) (B43 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q52 tptp.code_integer) (B53 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q62 tptp.code_integer) (B63 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Uu3 tptp.code_integer) (__flatten_var_0 Bool)) (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B02) B12) B23) B33) B43) B53) B63) __flatten_var_0))) (@ tptp.code_bit_cut_integer Q62)))) (@ tptp.code_bit_cut_integer Q52)))) (@ tptp.code_bit_cut_integer Q42)))) (@ tptp.code_bit_cut_integer Q32)))) (@ tptp.code_bit_cut_integer Q22)))) (@ tptp.code_bit_cut_integer Q1)))) (@ tptp.code_bit_cut_integer Q0)))) (@ tptp.code_bit_cut_integer K2)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= tptp.upto_aux (lambda ((I3 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I3)) Js) (@ (@ (@ tptp.upto_aux I3) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.37/6.68 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X3) Xs3)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.37/6.68 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 6.37/6.68 (assert (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))))
% 6.37/6.68 (assert (forall ((I tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J)) K) _let_1)))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I)) tptp.one_one_int)))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (assert (= tptp.upto_aux (lambda ((I3 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I3) J3)) __flatten_var_0))))
% 6.37/6.68 (assert (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I3) J3) tptp.nil_int))))
% 6.37/6.68 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J3)))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) 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))))))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) 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))))))))
% 6.37/6.68 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.37/6.68 (assert (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I3) J3)) (@ (@ tptp.cons_int I3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ (@ tptp.upto I) J) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) 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)))))))
% 6.37/6.68 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) 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)))))))))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs2)))))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.37/6.68 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (=> (not (= M7 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M5 tptp.nat)) (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M5))))) M7)))))))))
% 6.37/6.68 (assert (forall ((N5 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N5) (= (@ tptp.gcd_Gcd_nat N5) tptp.one_one_nat))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X 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 X)) (@ (@ 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 (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 6.37/6.68 (assert (forall ((N5 tptp.set_nat)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) N5)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat N5)))))
% 6.37/6.68 (assert (forall ((K5 tptp.set_int)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_int_int tptp.abs_abs_int) K5)) (@ tptp.gcd_Gcd_int K5))))
% 6.37/6.68 (assert (forall ((K5 tptp.set_int)) (= (@ tptp.gcd_Gcd_nat (@ (@ tptp.image_int_nat (lambda ((K2 tptp.int)) (@ tptp.nat2 (@ tptp.abs_abs_int K2)))) K5)) (@ tptp.nat2 (@ tptp.gcd_Gcd_int K5)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((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 X)) (@ F (@ (@ tptp.minus_minus_real X) H4))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X) H4))) (@ F X)))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((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 X)) (@ F (@ (@ tptp.plus_plus_real X) H4))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((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 X) H4))) (@ F X)))))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ (@ tptp.minus_minus_real B) A)) K)))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (Y tptp.real)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ F X) (@ F Y)))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (Y tptp.real) (X tptp.real)) (= (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real (@ tptp.uminus_uminus_real X)) tptp.top_top_set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ F (@ tptp.uminus_uminus_real X2)))) (@ tptp.uminus_uminus_real Y)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (= (@ F X) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F4 Z2)))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ G A)) (@ G B)))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X)))) (= L tptp.zero_zero_real))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real X2) N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S))))
% 6.37/6.68 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ G X2)) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ G X)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) M)) _let_1)))))
% 6.37/6.68 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z3 tptp.real)) (@ (@ tptp.powr_real Z3) 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)))))
% 6.37/6.68 (assert (forall ((X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.37/6.68 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) R2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.37/6.68 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (let ((_let_3 (@ F X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) (@ F X2)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R2) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))
% 6.37/6.68 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2))))
% 6.37/6.68 (assert (forall ((X 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 X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X) 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 X) tptp.top_top_set_real)))))))))
% 6.37/6.68 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.37/6.68 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.37/6.68 (assert (= tptp.gcd_Gcd_int (lambda ((K7 tptp.set_int)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) K7))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.37/6.68 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M3 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))
% 6.37/6.68 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.37/6.68 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H2) M5)))) (@ 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))))))))))))
% 6.37/6.68 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H2) M5)))) (@ 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)))))))))))
% 6.37/6.68 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H2) M5)))) (@ 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))))))))))))
% 6.37/6.68 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M3 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))))
% 6.37/6.68 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((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 X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((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 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T3) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T3) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M5)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N2))))))))))))))))))))
% 6.37/6.68 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M5)))) (@ tptp.set_ord_lessThan_nat 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)))))))))))))
% 6.37/6.68 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M5)))) (@ tptp.set_ord_lessThan_nat 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)))))))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B3 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 ((M4 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M4))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N2) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M4) 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) M4))) (@ (@ tptp.minus_minus_real (@ (@ Diff M4) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M4) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U2) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M4)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T4) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B3) (@ (@ 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))))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 6.37/6.68 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N3)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) (@ (@ tptp.power_power_real X3) 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 ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X2) (@ 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)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X) _let_1) (=> (@ (@ tptp.member_real Y) _let_1) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (= (@ F X) (@ F Y)))))))))
% 6.37/6.68 (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 ((X2 tptp.real)) (@ (@ F X2) N))) (@ (@ F4 X0) N)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X3)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N tptp.nat) (X3 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X3) N)) (@ (@ F Y3) N)))) (@ (@ tptp.times_times_real (@ L5 N)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (@ F X2)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.37/6.68 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num tptp.one))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N2)) tptp.none_num)))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.37/6.68 (assert (forall ((M tptp.num) (N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) (@ tptp.some_num Q3)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int Q3)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N2))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= tptp.bit_take_bit_num (lambda ((N3 tptp.nat) (M5 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N3) (@ tptp.numeral_numeral_nat M5)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.37/6.68 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.37/6.68 (assert (= tptp.bit_take_bit_num (lambda ((N3 tptp.nat) (M5 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 tptp.nat) (X2 tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P5 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num O) P5)))) (lambda ((P5 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P5))))) X2))) A3))) (@ (@ tptp.product_Pair_nat_num N3) M5)))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F))) (exists ((L6 tptp.real) (M9 tptp.real)) (and (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y4) (@ (@ tptp.ord_less_eq_real Y4) M9)) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B) (= (@ F X3) Y4)))))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.sqrt)))
% 6.37/6.68 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ tptp.root N2))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (not (@ (@ tptp.member_real X) tptp.ring_1_Ints_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.archim2898591450579166408c_real))))
% 6.37/6.68 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (= (@ G (@ F Z2)) Z2)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (not (@ (@ tptp.member_real X) tptp.ring_1_Ints_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ (@ tptp.comp_int_real_real tptp.ring_1_of_int_real) tptp.archim6058952711729229775r_real)))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y3) (=> (@ (@ tptp.ord_less_real Y3) B) (= (@ F (@ G Y3)) Y3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arccos)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.37/6.68 (assert (forall ((B tptp.real) (X tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real B) X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.37/6.68 (assert (forall ((D tptp.real) (X tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X))) D) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 6.37/6.68 (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 ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) G)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F4 C2))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X5))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (not (= (@ F X5) tptp.zero_zero_real))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (@ (@ tptp.ord_less_real (@ F X5)) tptp.zero_zero_real)))))))))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 6.37/6.68 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N9 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.37/6.68 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N9 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.37/6.68 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I2))) B3)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 6.37/6.68 (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))
% 6.37/6.68 (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 ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N9)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N9))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) 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))))
% 6.37/6.68 (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))
% 6.37/6.68 (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))))
% 6.37/6.68 (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))
% 6.37/6.68 (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)))
% 6.37/6.68 (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 ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N9)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.37/6.68 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X) N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X) N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.37/6.68 (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)))
% 6.37/6.68 (assert (forall ((X 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 X) (@ tptp.semiri5074537144036343181t_real N3)))) N3))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_nat)))
% 6.37/6.68 (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)))
% 6.37/6.68 (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))))))))
% 6.37/6.68 (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)))))))))
% 6.37/6.68 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K3 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.37/6.68 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K3 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.37/6.68 (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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ 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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat)))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) 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 X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.37/6.68 (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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ 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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat))))))
% 6.37/6.68 (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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))))))))
% 6.37/6.68 (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 ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ 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 ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ 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)))))))))
% 6.37/6.68 (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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ 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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat)))))
% 6.37/6.68 (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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ 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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))))) tptp.at_top_nat))))))
% 6.37/6.68 (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 ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I3)) (@ A I3)))) (@ 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)))))))))
% 6.37/6.68 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C3 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C3)))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y2 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y2)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.37/6.68 (assert (= tptp.real_V975177566351809787t_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y2)))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5984915006950818249n_real tptp.zero_zero_real))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N2))) tptp.at_bot_real) F5))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N2))) tptp.at_top_real) F5))))))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_top_real) tptp.at_top_real))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) tptp.at_top_real) tptp.at_top_real))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real) tptp.at_top_real) tptp.at_top_nat))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_bot_real) tptp.at_top_real))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_top_real) tptp.at_bot_real))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) tptp.at_top_real))
% 6.37/6.68 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 6.37/6.68 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) K)) (@ tptp.exp_real X2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.37/6.68 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y2 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y2))) Y2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 6.37/6.68 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X3) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.37/6.68 (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))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.37/6.68 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I3 tptp.nat)) (@ P (@ tptp.suc I3)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.37/6.68 (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))))
% 6.37/6.68 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I3 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I3) K)))) tptp.at_top_nat))))
% 6.37/6.68 (assert (not (@ (@ tptp.eventually_nat (lambda ((N3 tptp.nat)) false)) tptp.at_top_nat)))
% 6.37/6.68 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (@ P X3))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.37/6.68 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ P N3)))))))
% 6.37/6.68 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N6)) F5)))))
% 6.37/6.68 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ (@ tptp.plus_plus_real X2) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.37/6.68 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ tptp.uminus_uminus_real X2)))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 6.37/6.68 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 6.37/6.68 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ tptp.inverse_inverse_real X2)))) tptp.at_top_real))))
% 6.37/6.68 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) tptp.at_top_real) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ tptp.inverse_inverse_real X2)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F5) _let_1))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.37/6.68 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.37/6.68 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_1) tptp.at_top_real)))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F5) _let_1))))))))))))
% 6.37/6.68 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F0) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G0) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G0 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X2)) (@ G0 X2)))) F5) _let_1))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F5) _let_1))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.37/6.68 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.37/6.68 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.37/6.68 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X)) tptp.at_top_nat)))))
% 6.37/6.68 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.37/6.68 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 6.37/6.68 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N2))))))
% 6.37/6.68 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X8 I2))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.37/6.68 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3)))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X8 I2))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X8 I4)))))))))))
% 6.37/6.68 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (= Y (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))
% 6.37/6.68 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ 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) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima2)))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))))
% 6.37/6.68 (assert (= tptp.complete_Sup_Sup_int (lambda ((X4 tptp.set_int)) (@ tptp.the_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X4) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) X4) (@ (@ tptp.ord_less_eq_int Y2) X2)))))))))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) G))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C2) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (S tptp.set_real)) (= (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X) S)) (exists ((D6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D6) (@ (@ tptp.topolo2177554685111907308n_real X) S))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (S tptp.set_real)) (=> (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X) S)) (not (forall ((Df tptp.real)) (not (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Df) (@ (@ tptp.topolo2177554685111907308n_real X) S))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.37/6.68 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arcosh_real))))
% 6.37/6.68 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.arsinh_real (@ F X2))))))))
% 6.37/6.68 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.arcosh_real (@ F X2)))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (exists ((C2 tptp.real) (D3 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) D3)) (@ (@ tptp.ord_less_eq_real C2) D3)))))))
% 6.37/6.68 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.37/6.68 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.37/6.68 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.artanh_real))))
% 6.37/6.68 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_real (@ F X3)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.artanh_real (@ F X2)))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (= (@ F4 Z2) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F4 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B)))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X) (=> (@ (@ tptp.ord_less_eq_real X) B) (= (@ F X) (@ F A)))))))))
% 6.37/6.68 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))))))))
% 6.37/6.68 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X2) Y2)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.37/6.68 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X2) Y2)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.37/6.68 (assert (= tptp.topolo4860482606490270245n_real (lambda ((U4 tptp.set_real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) U4) (@ (@ tptp.eventu3244425730907250241l_real (@ tptp.produc5414030515140494994real_o (lambda ((X9 tptp.real) (Y2 tptp.real)) (=> (= X9 X2) (@ (@ tptp.member_real Y2) U4))))) tptp.topolo1511823702728130853y_real))))))
% 6.37/6.68 (assert (= tptp.topolo4110288021797289639omplex (lambda ((U4 tptp.set_complex)) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) U4) (@ (@ tptp.eventu5826381225784669381omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X9 tptp.complex) (Y2 tptp.complex)) (=> (= X9 X2) (@ (@ tptp.member_complex Y2) U4))))) tptp.topolo896644834953643431omplex))))))
% 6.37/6.68 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N6 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) M5) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N3) (@ P (@ (@ tptp.product_Pair_nat_nat N3) M5))))))))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I2)) B3)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.37/6.68 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 6.37/6.68 (assert (forall ((D tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) D))) (= (@ (@ tptp.filtermap_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real X2) D))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1))))))
% 6.37/6.68 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I2)) B3)) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) L6))))))))))
% 6.37/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) A))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.37/6.68 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real tptp.uminus_uminus_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))))
% 6.37/6.68 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)) (@ (@ tptp.filtermap_real_real tptp.uminus_uminus_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))))
% 6.37/6.68 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M5 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M5)) M5))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ tptp.order_mono_real_real F) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.semiri5074537144036343181t_real N3)))) _let_1) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_real_real F) _let_1) tptp.at_top_real))))))
% 6.37/6.68 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X) 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))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ 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)) (=> (= X (@ 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)) (=> (= X (@ tptp.bit1 M3)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ 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)) (=> (= X (@ 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))))))))))))))))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((X 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 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) 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)) (= X (@ tptp.bit0 M3))) (=> _let_2 _let_4)) (=> (forall ((M3 tptp.num)) (=> (= X (@ 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)) (=> (= X (@ 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)) (= X (@ tptp.bit1 M3))) _let_3) (=> (forall ((M3 tptp.num)) (=> (= X (@ 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)) (=> (= X (@ 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)))))))))))))))))))))))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.37/6.68 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num tptp.one))))
% 6.37/6.68 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N2)) tptp.none_num)))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) 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)) (=> (= X (@ tptp.bit0 M3)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ 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)) (=> (= X (@ 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)) (=> (= X (@ tptp.bit1 M3)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ 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)) (=> (= X (@ 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)))))))))))))))))))))
% 6.37/6.68 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num (@ tptp.bit1 N2)))))
% 6.37/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num (@ tptp.bit0 N2)))))
% 6.37/6.68 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.37/6.68 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (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))))))
% 6.37/6.68 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.37/6.68 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G) (= (@ (@ tptp.bfun_nat_real (lambda ((X2 tptp.nat)) (@ F (@ G X2)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2)))))
% 6.37/6.68 (assert (forall ((R2 (-> tptp.nat tptp.nat)) (P (-> tptp.nat Bool))) (=> (@ tptp.order_5726023648592871131at_nat R2) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((N3 tptp.nat)) (@ P (@ R2 N3)))) tptp.at_top_nat)))))
% 6.37/6.68 (assert (forall ((F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F4 X3))) (@ tptp.order_7092887310737990675l_real F)))))
% 6.37/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.inj_on_real_real (lambda ((Y2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N2)))) tptp.top_top_set_real))))
% 6.37/6.68 (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)))))
% 6.37/6.68 (assert (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.member_nat N) N5) (@ (@ tptp.ord_less_eq_nat K) N))) (@ (@ tptp.inj_on_nat_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat N3) K))) N5))))
% 6.37/6.68 (assert (forall ((N5 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N5)))
% 6.37/6.68 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G)))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G))) (@ tptp.suminf_real F)))))))
% 6.37/6.68 (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))))))))))))
% 6.37/6.68 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (=> (forall ((X3 tptp.nat)) (=> (not (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat))) (= (@ F X3) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G)) (@ tptp.suminf_real F))))))))
% 6.37/6.68 (assert (= tptp.topolo9180104560040979295open_o (@ tptp.topolo4667128019001906403logy_o (@ (@ tptp.sup_sup_set_set_o (@ (@ tptp.image_o_set_o tptp.set_ord_lessThan_o) tptp.top_top_set_o)) (@ (@ tptp.image_o_set_o tptp.set_or6416164934427428222Than_o) tptp.top_top_set_o)))))
% 6.37/6.68 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.37/6.68 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.37/6.68 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.37/6.68 (assert (= tptp.topolo4328251076210115529en_nat (@ tptp.topolo1613498594424996677gy_nat (@ (@ tptp.sup_sup_set_set_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)))))
% 6.37/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 6.37/6.68 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X4 tptp.real)) (@ P X4)))))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 6.37/6.68 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y) Y)))
% 6.37/6.68 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y) X)))
% 6.37/6.68 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 6.37/6.68 (assert (forall ((X tpt/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 17868 Alarm clock ( read result; case "$result" in
% 299.97/300.29 unsat)
% 299.97/300.29 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.97/300.29 ;;
% 299.97/300.29 sat)
% 299.97/300.29 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.97/300.29 ;;
% 299.97/300.29 esac; exit 1 )
% 299.97/300.30 Alarm clock
% 299.97/300.30 % cvc5---1.0.5 exiting
% 299.97/300.30 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------